Key Laboratory of Microscale Magnetic Resonance

Temporal non-analyticities in the rate function of the Loschmidt echo manifests a class of dynamical quantum phase transitions (DQPTs) that has emerged as a powerful framework for understanding far-from-equilibrium many-body dynamics. While such DQPT has been extensively studied theoretically in spin-boson systems such as the Dicke model, their experimental observation remains elusive. In particular, the dynamics of DQPT in asymmetric spin subspaces and under the influence of spin dissipation are largely unexplored. Here, we report an experimental study of temporal DQPT in a generalized Dicke model using a trapped-ion quantum simulator. By coupling a linear chain of $\rm{^{40}Ca^{+}}$ ions to a collective center-of-mass motional mode, we probe the quench dynamics starting from both symmetric and asymmetric initial states. We extract the rate function and identify temporal turn-around points that are in quantitative agreement with theoretical predictions. Additionally, we investigate the impact of spin dissipation on these dynamics. Our results establish an experimental platform for probing complex many-body out-of-equilibrium phenomena and advance the development of hybrid oscillator-spin quantum simulators.

Electron transfer through chiral structures can exhibit spin asymmetry, known as the chiral-induced spin selectivity effect, whose microscopic origin remains an open question. While path-interference within the chiral moiety has been proposed as a key mechanism, its experimental validation requires precise and versatile tunability of system parameters. Here we implement a programmable quantum simulation of spin-dependent electron transfer in a donor--chiral-bridge--acceptor model using a trapped ion. The bridge is encoded in internal states of the ion with tunable nearest- and next-nearest-neighbor couplings, while donor and acceptor states are coupled via a spectator bosonic motional mode. We observe spin-dependent interference within the bridge, and further reveal spin-dependence in donor-to-acceptor transfer dynamics, controlled by amplitude and phase of the coupling parameter. Our results identify interference among spin-dependent pathways as a microscopic origin of spin-dependent transfer, and open a route toward quantum simulations of complex chiral lattices with multi-level and bosonic degrees of freedom.

As trapped-ion quantum computing scales to larger qubit registers and more complex control protocols, classical control systems face a fundamental tradeoff: sub-microsecond board-level feedback requires tight hardware coupling, whereas maintainability and extensibility require clean, modular software abstractions. This paper presents QuCtrl-BELL (Bell), a compiler-driven software stack for trapped-ion quantum control. The design resolves this tradeoff by decoupling control flow -- including loops, branches, and synchronization -- from hardware state data. A Python-embedded domain-specific language (DSL) is lowered through a six-stage transpilation pipeline covering control flow graph (CFG) construction, static single-assignment (SSA) conversion, liveness analysis, and graph-coloring register allocation. The compiler generates deterministic distributed board-level programs and compact step-table data. A cross-board synchronization protocol supports feedback loops with latency below 700~ns without host intervention. Bell is deployed and evaluated on the QuCtrl-BELL platform (RISC-V + PXIe), demonstrating that a compiler-based infrastructure can provide programmability, deterministic timing, and modularity for scalable trapped-ion quantum control.

High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when coordinating multiple independent light sources for multi-step quantum protocols. Here, we develop an integrated phase-stabilization framework that incorporates a Bayesian phase estimator to optimally extract information from sparse single-photon detection events. This approach outperforms conventional maximum-likelihood estimation and achieves the shot-noise limit under minimal photon flux. The framework enables real-time correction of combined phase noise from both nodal lasers and transmission fibers, facilitating a two-step excitation protocol for heralded entanglement generation between separate trapped-ion nodes via single-photon interference. Operating with a detected photon rate of approximately 1 MHz and a duty cycle less than or equal to 6.5%, the system maintains interferometric visibility greater than 97% over fiber links of 10 km and 100 km. This phase control yields deterministic ion-ion entanglement with parity contrast exceeding 85% at both distances, enabling device-independent quantum key distribution. Moreover, the resulting memory-memory entanglement at 10 km survives beyond the average time required to establish it -- a fundamental requirement for quantum repeaters. This work establishes a robust and scalable foundation for practical long-distance quantum networks.

The rapid development of artificial intelligence (AI), Internet of Things (IoT), and edge computing applications has posed severe challenges to conventional memory technologies in terms of density, speed, and energy consumption. Herein, a single-ion transport mechanism is proposed to achieve picosecond (ps) switching capability. For monolayer hexagonal boron nitride (h-BN) with single-atom vacancy defects, first-principles calculations reveal that single-ion penetration across the BN plane dominates the resistive switching. The trapping and release of a single ion correspond to different states of the memory device for one bit of information. Experimentally fabricated single-ion memory exhibits nonvolatile resistive switching with ultra-fast switching speed of 20 ps and ultra-low energy consumption of 310 aJ/bit. This high performance is attributed to the extremely short distance for the single ion to travel through. Such devices pave the way for the realization of high-performance nonvolatile memory with ultra-fast speed, ultra-low energy consumption, and high storage density, that is called the "Unified Memory" long desired by the whole industry.

Ferroelectric materials are an ideal platform for high-speed reconfigurable photonic integrated circuits (PICs) for classical and quantum photonic computations, communications, and sensing. Most reconfigurable PIC devices achieve their functionalities via interference and are therefore highly sensitive to phase errors. Under static bias, carrier drift in ferroelectric waveguides induces continuous phase drift, creating a severe bottleneck for both PIC functionality and scalability. Here we propose achieving bias-stable and scalable ferroelectric PICs by exploiting the intrinsically low carrier drift of lithium tantalate (LT). Taking one of the PIC devices that is most sensitive to phase drift, the optical phased array (OPA), as an example, we designed and fabricated an integrated LT OPA that can keep the far-field main lobe 8 dB higher than side lobes for over 4 hours, representing at least a two-order-of-magnitude improvement over the state of the art. We demonstrated our device's capability in generating arbitrary spatiotemporal waveforms with a modulation frequency as low as 0.1 Hz, leading to practical applications in optical tweezers, trapped-ion quantum computers, adaptive optics for astronomy, AR, 3D printers, LiDAR, and free-space optical communications. Beyond OPA, our work establishes LT as a bias-stable, scalable, and high-speed PIC platform for large-scale classical and quantum photonic systems.

Hybrid quantum networks offer a promising architecture for scalable quantum information processing and a future quantum internet, as they can combine the complementary strengths of disparate physical platforms. While single-atom systems provide deterministic quantum logic gates, atomic ensembles enable large-capacity quantum storage. However, generating entanglement between such heterogeneous systems has remained an open challenge, primarily due to fundamental spectral mismatches and system complexity. Here, we demonstrate a hybrid quantum network that entangles a single trapped $\mathrm{^{171}Yb^{+}}$ ion and a quantum memory based on $\rm ^{153}Eu^{3+}\colon\!Y_2SiO_5$ crystal over a 75-m separation. Using polarization-maintaining quantum frequency conversion, we map spin-photon entanglement onto a hybrid entanglement between a single spin qubit and a collective excitation of the quantum memory. The resulting entangled state achieves a fidelity of $(89.21 \pm 2.23)\%$ and violates the CHSH-Bell inequality by 6 standard deviations ($S = 2.328 \pm 0.055$), confirming nonlocality between two heterogeneous nodes. This work establishes entanglement between a quantum processing module with a multiplexed quantum memory node, representing a key step toward a scalable, multifunctional quantum internet.

Quantum deep learning (QDL) explores the use of both quantum and quantum-inspired resources to determine when deep learning's core capabilities, such as expressivity, generalization, and scalability, can be enhanced based on specific resource constraints. Distinct from broader quantum machine learning, QDL emphasizes compositional depth at the pipeline level and the integration of quantum or quantum-inspired components within end-to-end workflows. This review provides an operational definition of QDL and introduces a taxonomy comprising four primary paradigms: hybrid quantum-classical models, quantum deep neural networks, quantum algorithms for deep learning primitives, and quantum-inspired classical algorithms. Theoretical principles are connected to advanced architectures, software toolchains, and experimental demonstrations across superconducting, trapped-ion, photonic, semiconductor spin, and neutral-atom systems, as well as quantum annealers. Claims of quantum advantage are critically assessed by distinguishing provable complexity-theoretic separations from empirical observations. The analysis characterizes trade-offs between model expressivity, trainability, and classical simulability, while systematically detailing the bottlenecks imposed by optimization landscapes, input-output access models, and hardware constraints. Applications are surveyed in domains encompassing image classification, natural language processing, scientific discovery, quantum data processing, and quantum optimal control, underscoring fair benchmarking against optimized classical counterparts and a comprehensive assessment of resource requirements. This review serves as a tutorial entry point for graduate students while guiding readers to specialized literature. It concludes with a verification-aware roadmap to transition QDL from near-term demonstrations to scalable and fault-tolerant implementations.

Aharonov-Bohm (AB) caging is a complete localization phenomenon in two-dimensional lattices due to destructive interference induced by the background gauge fields. However, current investigations of AB caging are mostly restricted to the Abelian gauge field case, and the observation of AB caging under non-Abelian gauge fields in a quantum system still remains elusive. Here, we report experimental realization of tunable synthetic non-Abelian SU(2) gauge fields in a rhombic lattice, engineered within the synthetic dimensions of a vibrating trapped ion with multiple levels. We realize AB caging under both Abelian and non-Abelian gauge fields and systematically investigate the distinctive transport properties of the non-Abelian case. In particular, we observe typical emergent quantum dynamics unique to non-Abelian AB caging, including initial-state-dependent dynamics, second-order effects, and asymmetric caging behavior. These observations demonstrate the trapped ion system as a powerful platform for simulating emergent phenomena in high-dimensional quantum systems with exotic synthetic gauge fields.

Quantum networks, integrating quantum communication, quantum metrology, and distributed quantum computing, could provide secure and efficient information transfer, high-resolution sensing, and an exponential speed-up in information processing. Deterministic entanglement distribution over long distances is a prerequisite for scalable quantum networks, enabling the utilization of device-independent quantum key distribution (DI-QKD) and quantum teleportation to achieve secure and efficient information transfer. However, the exponential photon loss in optical fibres prohibits efficient and deterministic entanglement distribution. Quantum repeaters, incorporating entanglement swapping and entanglement purification with quantum memories, offer the most promising means to overcome this limitation in fibre-based quantum networks. Despite numerous pioneering efforts toward realizing quantum repeaters, a critical bottleneck remains, as remote memory-memory entanglement suffers from decoherence more rapidly than it can be established and purified over long distances. We overcome this by developing long-lived trapped-ion memories, an efficient telecom interface, and a high-visibility single-photon entanglement protocol. This allows us to establish and maintain memory-memory entanglement over a 10 km fibre within the average entanglement establishment time for the same distance. As a direct application, we demonstrate metropolitan-scale DI-QKD, distilling 1,917 secret keys out of 4.05*10^5 Bell pairs over 10 km. We further report a positive key rate over 101 km in the asymptotic limit, extending the achievable distance by more than two orders of magnitude. Our work provides a critical building block for quantum repeaters and marks an important step toward scalable quantum networks.

It is found by using the gyrokinetic theory that significant radial electric fields, or zonal flows, can be generated by the radial redistribution of energetic ion pressure in a tokamak fusion device. Trapped energetic ions are more effective to generate the radial electric field than the isotropic energetic ions. This suggests that the energetic $α$ particles produced by DT fusion may induce significant radial electric field and thus help to improve the core plasma confinement in a fusion reactor.

Quantum information processing platforms based on array of matter qubits, such as neutral atoms, trapped ions, and quantum dots, face significant challenges in scalable addressing and readout as system sizes increase. Here, we propose the "Volcano" architecture that establishes a new quantum processing unit implementation method based on optical channel mapping on a arbitrarily arranged static qubit array. To support the feasibility of Volcano architecture, we show a proof-of-principle demonstration by employing a photonic chip that leverages custom-designed three-dimensional waveguide structures to transform one-dimensional beam arrays into arbitrary two-dimensional output patterns matching qubit array geometries. We demonstrate parallel and independent control of 49-channel with negligible crosstalk and high uniformity. This architecture addresses the challenges in scaling up quantum processors, including both the classical link for parallel qubit control and the quantum link for efficient photon collection, and holds the potential for interfacing with neutral atom arrays and trapped ion crystals, as well as networking of heterogeneous quantum systems.

Quantum coherence remains a fundamental challenge for advancing quantum technologies. Although dynamical decoupling can suppress decoherence noise, it frequently misestimates decoherence times due to control errors -- a previously underappreciated issue. Here, we present Hadamard phase cycling, a scalable non-Markovian quantum error mitigation method using group-structured phase configurations to filter spurious dynamics. Validated across molecular electron spins, nitrogen-vacancy centers in diamond, nuclear spins, trapped ions, and superconducting qubits, this technique enables accurate decoherence time characterization and enhanced state fidelity with linear complexity. Our results indicate that many reported ultralong decoherence times stem from artifacts like coherence-population mixing rather than genuine noise suppression. By ensuring dynamical authenticity, Hadamard phase cycling establishes a robust framework for reliable quantum control, paving the way for reassessment and advancement of coherence benchmarks in the NISQ era.

Scaling of quantum gates remains a central challenge in quantum information science. Ultrafast gates based on spin-dependent kicks provide a promising approach for trapped-ion systems. However, these gates require laser pulses with both high temporal tunability and stability, which are difficult to achieve with existing pulsed sources. Here, we propose a programmable pulsed source that allows flexible control of pulse intensity, waveform, and phase profiles. This enables precise manipulation of pulse sequences, thereby improving the fidelity of entangling gates. Furthermore, since the pulse parameters can be conveniently tuned, various coherent population-transfer schemes can be implemented adiabatic SDKs, thereby improving both the fidelity and robustness of fast quantum gate. Simulation results show that our programmable pulse system can achieve gate fidelities above 99.99% with strong robustness against variations in pulse intensity and single-photon detuning using stimulated Raman adiabatic rapid passage (STIRARP) protocols.

Trapped ions in micro-cavities constitute a key platform for advancing quantum information processing and quantum networking. By providing an efficient light-matter interface within a compact architecture, they serve as highly efficient quantum nodes with strong potential for scalable quantum network. However, in such systems, ion trapping stability is often compromised by surface charging effects, and nearby dielectric materials are known to cause a dramatic increase in the ion heating rate by several orders of magnitude. These challenges significantly hinder the practical implementation of ion trap systems integrated with micro-cavities. To overcome these limitations, we present the design and fabrication of metal-shielded micro-cavity mirrors, enabling the stable realization of ion trap systems integrated with micro cavities. Using this method, we constructed a needle ion trap integrated with fiber Fabry-Perot cavity and successfully achieved stable trapping of a single ion within the cavity. The measured ion heating rate was reduced by more than an order of magnitude compared with unshielded configurations. This work establishes a key technique toward fully integrated ion-photon interfaces for scalable quantum network.

The Unruh effect predicts that an accelerated observer perceives the Minkowski vacuum as a thermal bath, but its direct observation requires extreme accelerations beyond current experimental reach. Foundational theory [Olson & Ralph, Phys. Rev. Lett. 106, 110404 (2011)] shows that an equivalent thermal response, known as the timelike Unruh effect, can occur for detectors following specific timelike trajectories without acceleration, enabling laboratory tests with stationary yet time-dependent detectors. Here, we report a proof-of-principle demonstration of the timelike Unruh effect in a quantum system of trapped ion, where a two-level spin serves as the detector and is temporally coupled to the ambient field encoded in the ion's vibrational motion. Specifically, we study both excitation and emission dynamics of the detector moving along a spacetime trajectory in the future/past light cone, and demonstrate the thermal response of the detector to the Minkowski vacuum that resembles the Unruh effect. This work establishes a controllable tabletop platform for exploring relativistic quantum physics under accessible laboratory conditions.

The Unruh effect predicts an astonishing phenomenon that an accelerated detector would detect counts despite being in a quantum field vacuum in the rest frame. Since the required detector acceleration for its direct observation is prohibitively large, recent analog studies on quantum simulation platforms help to reveal various properties of the Unruh effect and explore the not-yet-understood physics of quantum gravity. To further reveal the quantum aspect of the Unruh effect, analogous experimental exploration of the correlation between the detector and the field, and the consequences for coherent quantum trajectories of the detector without classical counterparts, are essential steps but are currently missing. Here, we utilize a laser-controlled trapped ion to experimentally simulate an oscillating detector coupled with a cavity field. We observe joint excitation of both the detector and the field in the detector's frame, coincide with the coordinated dynamics predicted by the Unruh effect. Particularly, we simulate the detector moving in single and superposed quantum trajectories, where the latter case shows coherent interference of excitation. Our demonstration reveals properties of quantum coherent superposition of accelerating trajectories associated with quantum gravity theories that have no classical counterparts, and may offer a new avenue to investigate phenomena in quantum field theory and quantum gravity. We also show how a generalization of the method and results in this work may be beneficial for direct observation of the Unruh effect.

Quantum magnetometry represents a fundamental component of quantum metrology, where trapped-ion systems have achieved $\rm{pT}/\sqrt{\rm{Hz}}$ sensitivity in single-ion radio-frequency magnetic field measurements via dressed states based dynamical decoupling. Here we propose a scalable trapped-ion magnetometer utilizing the mixed dynamical decoupling method, combining dressed states with periodic sequences to suppress decoherence and spatial magnetic field inhomogeneity. With numerical simulations for a $10^4$ ion system with realistic experimental parameters, we demonstrate that a sensitivity of 13 $\rm{fT}/\sqrt{\rm{Hz}}$ for the radio-frequency field could be reached. Such a sensitivity could be obtained via robust resilience to magnetic field drift noise and inhomogeneity, where coherence time could be extended to the order of several minutes on average. This method enables scalable trapped-ion magnetometry, demonstrating its potential as a robust and practical solution for advancing quantum sensing applications.

Hydrogen isotope (HI) retention poses a key issue for tungsten (W)-based plasma-facing materials (PFMs) in fusion devices, where microstructures such as dislocations (DLs) and grain boundaries (GBs) play a dominant role. Existing theoretical sink strength models for microstructures like DLs and GBs fail to account for the observed saturation of HI retention. In this study, we propose a novel universal trapping-site model that dynamically represents sink strengths as time-dependent site concentrations, which is incorporated into an improved cluster dynamics model for high-fluence HI irradiation. Our simulations quantitatively reproduce the saturated low-energy deuterium (D) retention and depth profiles in W, in good agreement with experiments. A critical saturation fluence of approximately 1023 m-2 is identified, below which unsaturated D retention is governed by both GBs and ion-induced defects, whereas above this threshold GBs dominate D retention by trapping free D and approaching their theoretical saturation limit. The trapping-site sink strength model enables quantification of H trapping by diverse microstructures via unified effective site concentrations, providing mechanistic insights into microstructural effects and facilitating direct evaluation of HI retention in PFMs under different irradiation conditions.

Trapped-ion systems are one of the leading platforms for quantum information processing, where a key challenge is to scale up system size while maintaining high-fidelity two-qubit operations. A promising approach is to build high-performance modules interconnected via strong coupling. In particular, axial motional modes provide a feasible means of coupling short ion chains. However, previous implementations of fully connected 5-ion modules based on axial modes have been limited to fidelities of $96.6-98.0\%$. Here, we demonstrate two-qubit quantum logic gates in a 5-ion $^{40}$Ca$^{+}$ chain using axial modes, achieving fidelities exceeding $99\%$ for adjacent pairs and over $98\%$ for arbitrary pairs by carefully tackling dominant error sources. Our results are beneficial to the development of scalable ion-trap quantum processors, quantum simulation and quantum-enhanced metrology.

We investigate quantum quenches starting from a critical point and experimentally probe the associated defect statistics using a trapped-ion quantum simulator of the transverse-field Ising model. The cumulants of the defect number distribution exhibit universal scaling with quench depth, featuring Gaussian behavior at leading order and systematic subleading corrections. Our results are in excellent agreement with both exact and approximate theoretical predictions, establishing quench-depth scaling as a powerful and precise experimental benchmark for nonequilibrium quantum critical dynamics.

The construction of entangling gates with individual addressing capability represents a crucial approach for implementing quantum computation in trapped ion crystals. Conventional entangling gate schemes typically rely on laser beam wave vectors to couple the ions' spin and motional degrees of freedom. Here, we experimentally demonstrate an alternative method that employs a polarization gradient field generated by a tightly focused laser beam, previously proposed as a Magnus-type quantum logic gate. Using this technique, we perform Raman operations on nuclear spin qubits encoded in 171Yb+ ions, generating spin-dependent forces along axial motional modes in a linear trap. By utilizing an acousto-optic deflector to create arbitrary spot pairs for individual ion addressing in two-ion (four-ion) chains, we achieve MS gates with fidelities exceeding 98.5% (97.2%). Further improvements in numerical aperture and laser power could reduce gate durations while enhancing fidelity. This method is compatible with, and can significantly simplify, optical tweezer gate proposals, where motional mode engineering enables scalable trapped-ion quantum computation. The technique can be extended to two-dimensional ion crystals, representing a key step toward large-scale trapped-ion quantum processors.

We report a single-ion optical clock based on the 4S_1/2-3D_5/2 transition of the 40Ca+ ion, operated in a liquid nitrogen cryogenic environment,achieving a total systematic uncertainty of 4.4E-19. We employ a refined temperature evaluation scheme to reduce the frequency uncertainty due to blackbody radiation (BBR), and the 3D sideband cooling has been implemented to minimize the second-order Doppler shift. We have precisely determined the average Zeeman coefficient of the 40Ca+ clock transition to be 14.345(40) Hz/mT^2, thereby significantly reducing the quadratic Zeeman shift uncertainty. Moreover, the cryogenic environment enables the lowest reported heating rate due to ambient electric field noise in trapped-ion optical clocks.

In the lattice system, when the synthetic flux reaches a $π$ phase along a closed loop under the synthetic gauge field, destructive interference occurs and gives rise to the localization phenomenon. This is known as the Aharonov-Bohm (AB) caging effect. It provides a powerful tool for the study of quantum transportation and dynamical effects. In the system where lattice sites possess internal structure and the underlying gauge field is non-Abelian, localization can also occur, forming the non-Abelian AB caging. Here, we propose an experimental scheme to synthesize non-Abelian gauge fields with a single trapped ion by coupling multiple internal levels and Fock states in its motion via laser fields. In contrast to the Abelian AB caging, we numerically observe that the non-Abelian AB caging occurs either when the interference matrix is nilpotent, or when the initial state is specifically set. Our experimental scheme broadens the study of localization phenomena and provides a novel tool for the study of non-Abelian physics.

Estimating partition functions of Ising spin glasses is a cornerstone of statistical physics and computational science, yet it remains classically challenging due to its $\#$P-hard complexity. While Jarzynski's equality offers a theoretical pathway, its practical application is crippled at low temperatures by rare, divergent statistical fluctuations. Here, we introduce a quantum protocol that overcomes this fundamental limitation by synergizing reverse quantum annealing with optimized nonequilibrium initial distributions. Our method dramatically suppresses the estimator variance, achieving saturation in the low-temperature regime where existing methods fail. Numerical benchmarks on the Sherrington-Kirkpatrick spin glass and the 3-SAT problem demonstrate that our protocol reduces computational scaling exponents by over an order of magnitude (e.g., from $\sim 8.5$ to $\sim 0.5$), despite retaining exponential system-size dependence. Crucially, our protocol circumvents stringent adiabatic constraints, making it feasible for near-term quantum devices like superconducting qubits, trapped ions, and Rydberg atom arrays. This work provides a methodological framework for quantum-enhanced estimation in spin glass thermodynamics and beyond by harnessing non-adiabatic quantum dynamics to address a classically difficult problem.

Quantum error correction (QEC) is essential for practical quantum computing, as it protects fragile quantum information from errors by encoding it in high-dimensional Hilbert spaces. Conventional QEC protocols typically require repeated syndrome measurements, real-time feedback, and the use of multiple physical qubits for encoding. Such implementations pose significant technical complexities, particularly for trapped-ion systems, with high demands on precision and scalability. Here, we realize autonomous QEC with a logical qubit encoded in multiple internal spin states of a single trapped ion, surpassing the break-even point for qubit lifetime. Our approach leverages engineered spin-motion couplings to transfer error-induced entropy into motional modes, which are subsequently dissipated through sympathetic cooling with an ancilla ion, fully eliminating the need for measurement and feedback. By repetitively applying this autonomous QEC protocol under injected low-frequency noise, we extend the logical qubit lifetime to approximately 11.6 ms, substantially outperforming lifetime for both the physical qubit ($\simeq$0.9 ms) and the uncorrected logical qubit ($\simeq$0.8 ms), thereby beating the break-even point with autonomous protection of quantum information without measurement or post-selection. This work presents an efficient approach to fault-tolerant quantum computing that harnesses the intrinsic multi-level structure of trapped ions, providing a distinctive path toward scalable architectures and robust quantum memories with reduced overhead.

We present a symplectic electromagnetic fully-kinetic particle-in-cell simulation of microinstabilities in plasma, using parameters from the Cyclone Base Case [Dimits, et al., Physics of Plasmas 7, 969 (2000)]. The results show that the growth rates of unstable modes, including ion temperature gradient (ITG), trapped electron mode (TEM), and kinetic ballooning mode (KBM), are consistent with those obtained from previous gyrokinetic models. Additionally, the \b{eta}-stabilization of the ITG is reproduced. The analysis also reveals that the impact of the ion-electron mass ratio and the numerical speed of light on the growth rate of the most unstable modes is minimal. This suggests that the fully kinetic method offers a potential for reduced computational cost when investigating the physics of drift wave instabilities at relevant space-time scales.

Preparing high-fidelity logical magic states is crucial for fault-tolerant quantum computation. Among prior attempts to reduce the substantial cost of magic state preparation, magic state cultivation (MSC), a recently proposed protocol for preparing $\mathrm{T}$ states without magic state distillation, achieves state-of-the-art efficiency. Inspired by this work, we propose a new MSC procedure that would produce a logical $\mathrm{T}$ state on a rotated surface code at a further reduced cost. For our MSC protocol, we define a new code family, the $\mathbb {RP}^2$ code, by putting the rotated surface code on $\mathbb{RP}^2$ (a two-dimensional manifold), as well as two self-dual CSS codes named SRP-3 and SRP-5 respectively. Small $\mathbb{RP}^2$ codes are used to hold logical information and checked by syndrome extraction (SE) circuits. We design fast morphing circuits that enable switching between a distance 3 (5) $\mathbb{RP}^2$ code and an SRP-3 (SRP-5) code on which we can efficiently check the correctness of the logical state. To preserve the high accuracy of the cultivated logical $\mathrm{T}$ state, we design an efficient and easy-to-decode expansion stage that grows a small $\mathbb{RP}^2$ code to a large rotated surface code in one round. Our MSC protocol utilizes non-local connectivity, available on both neutral atom array and ion trap platforms. According to our Monte Carlo sampling results, our MSC protocol requires about an order of magnitude smaller space-time volume to reach a target logical error rate around $10^{-9}$ compared to the original MSC protocol.

Symmetry is crucial for gaining insights into the fundamental properties of physical systems, bringing possibilities in studying exotic phenomena such as quantum phase transitions and ground state entanglement. Here, we experimentally simulate a highly controllable extended quantum Rabi model, capable of tuning into the ultra-strong or deep coupling regime, in a spin-motion-coupled trapped ion. We observe that the phonon driven by such a model with parity symmetry preserved (broken) would experience double (single) excitation in the ultra-strong coupling regime. Quantum phenomena such as strong ground state entanglement and quantum superposition in systems occur with parity symmetry, and these phenomena disappear following the symmetry breaking. We also find sensitive responses for the two-level system entropy and phonon Wigner function in the deep coupling regime, depending on the parameter across the symmetry transition point. This work offers the prospect of exploring symmetry-controlled quantum phenomena and their applications in high-precision quantum technologies.

The nontrivial degeneracies in non-Hermitian systems, exceptional points (EPs), have attracted extensive attention due to intriguing phenomena. Compared with commonly observed second-order EPs, high-order EPs show rich physics due to their extended dimension and parameter space, ranging from the coalescence of EPs into higher order to potential applications in topological properties. However, these features also pose challenges in controlling multiple coherent and dissipative elements in a scaled system. Here we experimentally demonstrate a native programmable control to simulate a high-order non-Hermitian Hamiltonian in a multi-dimensional trapped ion system. We simulate a series of non-Hermitian systems with varied parameters and observe the coalescence of second-order EPs into a fourth-order EP. Our results pave the way for scalable quantum simulation of high-dimensional dissipative systems and can be beneficial for the application of high-order EPs in quantum sensing and quantum control.

Large-scale quantum computation requires to be performed in the fault-tolerant manner. One crucial challenge of fault-tolerant quantum computing (FTQC) is reducing the overhead of implementing logical gates. Recently work proposed correlated decoding and ``algorithmic fault tolerance" to achieve constant-time logical gates that enables universal quantum computation. However, for circuits involving mid-circuit measurements and feedback, the previous scheme for constant-time logical gates is incompatible with window-based decoding, which is a scalable approach for handling large-scale circuits. In this work, we propose an architecture that employs delayed fixup circuits and window-based correlated decoding, realizing scalable constant-time logical gates. This design significantly reduces both the frequency and duration of decoding, while maintaining support for constant-time and universal logical gates across a broad class of quantum codes. More importantly, by spatial parallelism of windows, this architecture well adapts to time-optimal FTQC, making it particularly useful for large-scale quantum computation. Using Shor's algorithm as an example, we explore the application of our architecture and reveals the promising potential of using constant-time logical gates to perform large-scale quantum computation with acceptable overhead on physical systems like ion traps.

The origin and evolution of organic molecules represent a pivotal issue in the fields of astrobiology and astrochemistry, potentially shedding light on the origins of life. The James Webb Space Telescope (JWST), with its exceptional sensitivity and spectral resolution, is well suitable to observe molecules such as methane ($\rm CH_4$). Our analysis focused on the distribution of $\rm CH_4$, $\rm CO_2$, $\rm H_2O$, $\rm{CH_3OH+NH_4^+}$ ice and silicate absorption dips at approximately 7.7, 15.0, 6.0, 6.7 and 10.0 micrometres in two protostars: IRAS 16253-2429 and IRAS 23385+6053. We extract the $\rm CH_4$, $\rm CO_2$, $\rm H_2O$, $\rm{CH_3OH+NH_4^+}$ ice equivalent width (EW) maps and silicate extinction maps of the two sources. Our results reveal that the spatial distribution of $\rm CH_4$ in the protostellar system IRAS 16253-2429 closely mirrors that of its $\rm CO_2$ ice, forming a surrounded distribution that encircles the central protostar. This alignment suggests a common formation mechanism and subsequent trapping within the protostellar envelope, which is consistent with the "Classical" dark-cloud chemistry with ion-molecule reaction. In contrast, the spatial distributions of various molecules in the system IRAS 23385+6053 exhibit low similarities, which may be attributed to the dynamic influences of outflows or accretion processes. These discrepancies highlight the complex interplay between physical processes and chemical evolution in protostellar environments.

The Liouvillian skin effect describes the boundary affinity of Liouvillian eignemodes that originates from the intrinsic non-Hermiticity of the Liouvillian superoperators. Dynamically, it manifests as directional flow in the transient dynamics, and the accumulation of population near open boundaries at long times. Intriguingly, similar dynamic phenomena exist in the well-known process of optical pumping, where the system is driven into a desired state (or a dark-state subspace) through the interplay of dissipation and optical drive. In this work, we show that typical optical pumping processes can indeed be understood in terms of the Liouvillian skin effect. By studying the Liouvillian spectra under different boundary conditions, we reveal that the Liouvillian spectra of the driven-dissipative pumping process sensitively depend on the boundary conditions in the state space, a signature that lies at the origin of the Liouvillian skin effect. Such a connection provides insights and practical means for designing efficient optical-pumping schemes through engineering Liouvillian gaps under the open-boundary condition. Based on these understandings, we show that the efficiency of a typical side-band cooling scheme for trapped ions can be dramatically enhanced by introducing counterintuitive dissipative channels. Our results provide a useful perspective for optical pumping, with interesting implications for state preparation and cooling.

Recently, large-scale trapped ion systems have been realized in experiments for quantum simulation and quantum computation. They are the simplest systems for dynamical stability and parametric resonance. In this model, the Mathieu equation plays the most fundamental role for us to understand the stability and instability of a single ion. In this work, we investigate the dynamics of trapped ions with the Coulomb interaction based on the Hamiltonian equation. We show that the many-body interaction will not influence the phase diagram for instability. Then, the dynamics of this model in the large damping limit will also be analytically calculated using few trapped ions. Furthermore, we find that in the presence of modulation, synchronization dynamics can be observed, showing an exchange of velocities between distant ions on the left side and on the right side of the trap. These dynamics resemble to that of the exchange of velocities in Newton's cradle for the collision of balls at the same time. These dynamics are independent of their initial conditions and the number of ions. As a unique feature of the interacting Mathieu equation, we hope this behavior, which leads to a quasi-periodic solution, can be measured in current experimental systems. Finally, we have also discussed the effect of anharmonic trapping potential, showing the desynchronization during the collision process. It is hopped that the dynamics in this many-body Mathieu equation with damping may find applications in quantum simulations. This model may also find interesting applications in dynamics systems as a pure mathematical problem, which may be beyond the results in the Floquet theorem.

Quantum friction, a quantum analog of classical friction, reduces the performance of quantum machines, such as heat engines, and makes them less energy efficient. We here report the experimental realization of an energy efficient quantum engine coupled to a quantum battery that stores the produced work, using a single ion in a linear Paul trap. We first establish the quantum nature of the device by observing nonclassical work oscillations with the number of cycles as verified by energy measurements of the battery. We moreover successfully apply shortcut-to-adiabaticity techniques to suppress quantum friction and improve work production. While the average energy cost of the shortcut protocol is only about $3\%$, the work output is enhanced by up to approximately 33$\%$, making the machine significantly more energy efficient. In addition, we show that the quantum engine consistently outperforms its classical counterpart in this regime. Our results pave the way for energy efficient machines with quantum-enhanced performance.

Squeezing a quantum state along a specific direction has long been recognized as a crucial technique for enhancing the precision of quantum metrology by reducing parameter uncertainty. However, practical quantum metrology often involves the simultaneous estimation of multiple parameters, necessitating the use of high-quality squeezed states along multiple orthogonal axes to surpass the standard quantum limit for all relevant parameters. In addition, a temporally stabilized squeezed state can provide an event-ready probe for parameters, regardless of the initial state, and robust to the timing of the state preparation process once stabilized. In this work, we generate and stabilize a two-mode squeezed state along two secular motional modes in a vibrating trapped ion with reservoir engineering, despite starting from a thermal state of the motion. Leveraging this resource, we demonstrate an estimation of two simultaneous collective displacements along the squeezed axes, achieving improvements surpassing the classical limit by up to 6.9(3) and 7.0(3) decibels (dB), respectively. Our demonstration can be readily scaled to squeezed states with even more modes. The practical implications of our findings span a wide range of applications, including quantum sensing, quantum imaging, and various fields that demand precise measurements of multiple parameters.

Zeros of partition functions, in particular Lee-Yang zeros, in a complex plane provide important information for understanding phase transitions. A recent discovery on the equivalence between the coherence of a central quantum system and the partition function of the environment in the complex plane enabled the experimental study of Lee-Yang zeros, with several pioneering experiments on spin systems. Lee-Yang zeros have not been observed in Bosonic systems. Here we propose an experimental scheme to demonstrate Lee-Yang zeros in Bosonic systems associated with a single trapped ion by introducing strong coupling between the spin and motion degrees of freedom, i.e. beyond the weak coupling Lamb-Dicke regime. Our scheme provides new possibilities for quantum simulation of the thermodynamics of Bosonic systems in the complex plane.

The quantum to classical transition (QCT) is one of the central mysteries in quantum physics. This process is generally interpreted as state collapse from measurement or decoherence from interacting with the environment. Here we define the quantumness of a Hamiltonian by the free energy difference between its quantum and classical descriptions, which vanishes during QCT. We apply this criterion to the many-body Rabi model and study its scaling law across the phase transition, finding that not only the temperature and Planck constant, but also all the model parameters are important for this transition. We show that the Jaynes-Cummings and anti Jaynes-Cummings models exhibit greater quantumness than the Rabi model. Moreover, we show that the rotating wave and anti-rotating wave terms in this model have opposite quantumness in QCT. We demonstrate that the quantumness may be enhanced or suppressed at the critical point. Finally, we estimate the quantumness of the Rabi model in current trapped ion experiments. The quantumness provides an important tool to characterize the QCT in a vast number of many-body models.

Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space-time in general relativity to modern theories of quantum gravity. In quantum many-body systems, the entanglement structure can change if the constituents are connected differently, leading to altered bounds for correlation growth and difficulties for classical computers to simulate large systems. While a universal quantum computer can perform digital simulations, an analog-digital hybrid quantum processor offers advantages such as parallelism. Here, we engineer a class of high-dimensional Ising interactions using a linear one-dimensional (1D) ion chain with up to 8 qubits through stroboscopic sequences of commuting Hamiltonians. %with a thorough understanding of the error sources and deviation from the target Hamiltonian. In addition, we extend this method to non-commuting circuits and demonstrate the quantum XY and Heisenberg models using Floquet periodic drives with tunable symmetries. The realization of higher dimensional spin models offers new opportunities ranging from studying topological phases of matter or quantum spin glasses to future fault-tolerant quantum computation.

Advances in research such as quantum information and quantum chemistry require subtle methods for trapping particles (including ions, neutral atoms, molecules, etc.). Here we propose a hybrid ion trapping method by combining a Paul trap with optical tweezers. The trap combines the advances of the deep-potential feature for the Paul trap and the micromotion-free feature for the optical dipole trap. By modulating the optical-dipole trap synchronously with the radio frequency voltage of the Paul trap, the alternating electrical force in the trap center is fully counteracted, and the micromotion temperature of a cold trapped ion can reach the order of nK while the trap depth is beyond 300K. These features will enable cold collisions between an ion and an atom in the $s$-wave regime and stably trap the produced molecular ion in the cold hybrid system. This will provide a unique platform for probing the interactions between the ions and the surrounding neutral particles and enable the investigation of new reaction pathways and reaction products in the cold regime.

Large-scale programmable trapped ion hardware, featuring high gate fidelity and long coherence times, is promising for realizing a practical fault-tolerant quantum computer (FTQC). However, individual addressing (IA) methods, which are important for implementing programmable gates in near-term quantum devices, can lead to undesired errors between the target ions and neighboring ions. In this work, we present a low-crosstalk optical addressing system based on multiple optical objectives and acousto-optic deflectors (AODs) with a symmetrical configuration. Two counter-propagating Raman operation beams are both tightly focused, generating an overlapping spot with a waist radius of approximately $1~\upmu\mathrm{m}$, to address the target ion. As a result, IA crosstalk, characterized by Rabi rate crosstalk on the spectator ion, is measured to be $1.19(5)\times10^{-3}$, with the two ions separated by approximately 5.5~$\upmu\mathrm{m}$. This low-crosstalk optical addressing system holds promise for high-fidelity entangling operations, and the symmetrically-configured AODs in our method can be readily extended to two dimensions to address a two-dimensional ion crystal.

We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors. The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and, unlike the state of the art, requires neither weak-coupling Lamb-Dicke approximation nor perturbation treatment. With the application of gradient-based optimal control, it enables finding amplitude- and phase-modulated laser control protocols that work beyond the Lamb-Dicke regime, promising gate speed at the order of microseconds comparable to the characteristic trap frequencies. Also, robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections. Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation, and thus can find applications in near-future experiments.

Non-Hermitian skin effect (NHSE) describes the exponential localization of all eigenstates toward boundaries in non-Hermitian systems, and has attracted intense research interest of late. Here we theoretically propose a scheme in which the NHSE significantly impacts the external motion of a single trapped ion through complex spin-motion dynamics. On the one hand, we show the competition between the NHSE and the coherent Bloch dynamics. On the other hand, since the NHSE manifests as a non-reciprocal flow in occupied phonon modes, we demonstrate that such dynamics can have potential applications in cooling and sensing. Our proposal can be readily implemented using existing experimental techniques, and offers a scalable (in terms of the available ions and phonon modes) simulation platform for relevant non-Hermitian physics.

We report continuous Raman sideband cooling (CRSC) of a long ion chain to the motional ground state beyond the Lamb-Dicke (LD) regime. By driving multiple sideband transitions simultaneously, we show that nearly all axial modes of a 24-ion chain are cooled to the ground state, with an LD parameter as large as $η= 1.3$, spanning a frequency bandwidth of 4 MHz. Compared to traditional ground-state cooling methods such as pulsed sideband cooling or electromagnetic-induced-transparency (EIT) cooling, our method offers two key advantages: robustness to timing errors; and an ultra-wide bandwidth unlimited by the number of ions. This technique contributes as a crucial step for large-scale quantum information processing with linear ion chains and higher dimensions alike, and can be readily generalized to other atomic and molecular systems.

Quantum information processing with multi-level systems (qudits) provides additional features and applications than the two-level systems. However, qudits are more prone to dephasing and dynamical decoupling for qudits has never been experimentally demonstrated. Here, as a proof-of-principle demonstration, we experimentally apply dynamical decoupling to protect superpositions with three levels of a trapped $^9\rm{Be}^+$ ion from ambient noisy magnetic field, prolonging coherence by up to approximately an order of magnitude. Our demonstration, straightforwardly scalable to more levels, may open up a path toward long coherence quantum memory, metrology and information processing with qudits.

Triply degenerate points (TDPs), which correspond to new types of topological semimetals, can support novel quasiparticles possessing effective integer spins while preserving Fermi statistics. Here by mapping the momentum space to the parameter space of a three-level system in a trapped ion, we experimentally explore the transitions between different types of TDPs driven by spin-tensor--momentum couplings. We observe the phase transitions between TDPs with different topological charges by measuring the Berry flux on a loop surrounding the gap-closing lines, and the jump of the Berry flux gives the jump of the topological charge (up to a $2π$ factor) across the transitions. For the Berry flux measurement, we employ a new method by examining the geometric rotations of both spin vectors and tensors, which lead to a generalized solid angle equal to the Berry flux. The controllability of multi-level ion offers a versatile platform to study high-spin physics and our work paves the way to explore novel topological phenomena therein.

Along with the scaling of dimensions in quantum systems, transitions between the system's energy levels would become close in frequency, which are conventionally resolved by weak and lengthy pulses. Here, we extend and experimentally demonstrate analytically based swift quantum control techniques on a four-level trapped ion system, where we perform individual or simultaneous control over two pairs of spectrally nearby transitions with tailored time-varied drive, achieving operational fidelities ranging from 99.2(3)\% to 99.6(3)\%. Remarkably, we achieve approximately an order of magnitude speed up comparing with the case of weak square pulse for a general control. Therefore, our demonstration may be beneficial to a broad range of quantum systems with crowded spectrum, for spectroscopy, quantum information processing and quantum simulation.

In cold atomic systems, fast and high-resolution microscopy of individual atoms is crucial, since it can provide direct information on the dynamics and correlations of the system. Here, we demonstrate nanosecond-scale two-dimensional stroboscopic pictures of a single trapped ion beyond the optical diffraction limit, by combining the main idea of ground-state depletion microscopy with quantum state transition control in cold atoms. We achieve a spatial resolution up to 175~nm using an NA = 0.1 objective in the experiment, which represents a more than tenfold improvement compared with direct fluorescence imaging. To show the potential of this method, we apply it to observe the secular motion of the trapped ion, we demonstrate a temporal resolution up to 50~ns with a displacement detection sensitivity of 10~nm. Our method provides a powerful tool for probing particle positions, momenta, and correlations, as well as their dynamics in cold atomic systems.

The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of physicists working in Random Matrix Theory and Quantum Chaos for decades. Here we present an experimental observation of the lowest non-trivial Riemann zeros by using a trapped ion qubit in a Paul trap, periodically driven with microwave fields. The waveform of the driving is engineered such that the dynamics of the ion is frozen when the driving parameters coincide with a zero of the real component of the zeta function. Scanning over the driving amplitude thus enables the locations of the Riemann zeros to be measured experimentally to a high degree of accuracy, providing a physical embodiment of these fascinating mathematical objects in the quantum realm.

Robust and high-precision quantum control is crucial but challenging for scalable quantum computation and quantum information processing. Traditional adiabatic control suffers severe limitations on gate performance imposed by environmentally induced noise because of a quantum system's limited coherence time. In this work, we experimentally demonstrate an alternative approach {to quantum control} based on deep reinforcement learning (DRL) on a trapped $^{171}\mathrm{Yb}^{+}$ ion. In particular, we find that DRL leads to fast and robust {digital quantum operations with running time bounded by shortcuts to adiabaticity} (STA). Besides, we demonstrate that DRL's robustness against both Rabi and detuning errors can be achieved simultaneously without any input from STA. Our experiments reveal a general framework of digital quantum control, leading to a promising enhancement in quantum information processing.

Entanglement detection is one of the most conventional tasks in quantum information processing. While most experimental demonstrations of high-dimensional entanglement rely on fidelity-based witnesses, these are powerless to detect entanglement within a large class of entangled quantum states, the so-called unfaithful states. In this paper, we introduce a highly flexible automated method to construct optimal tests for entanglement detection given a bipartite target state of arbitrary dimension, faithful or unfaithful, and a set of local measurement operators. By restricting the number or complexity of the considered measurement settings, our method outputs the most convenient protocol which can be implemented using a wide range of experimental techniques such as photons, superconducting qudits, cold atoms or trapped ions. With an experimental quantum optics setup that can prepare and measure arbitrary high-dimensional mixed states, we implement some $3$-setting protocols generated by our method. These protocols allow us to experimentally certify 2- and 3-unfaithful entanglement in 4-dimensional photonic states, some of which contain well above 50% of noise.

The quantum walk (QW), as the quantum analog of classical random walk, provides a feasible platform to study the topological phenomenon and non-equilibrium dynamics. Here, we propose a novel scheme to realize the quantum walk with a single trapped ion where the Fock states provides the walk space and zero phonon state $\left|n=0\right\rangle $ serves as its natural boundary. Thus, our scheme offers the unique opportunity to investigate the dynamics of the bound states of the corresponding topological systems. Particularly, the quench dynamics of the bound states can be extensively studied by tuning the bulk parameters and the local boundary operator, which are experimentally accessible. Our proposal not only offers a new approach to exploring the character of the bound states of the topological systems, but also offers a way to determine different phases through the dynamical processes.

Nonadiabatic geometric quantum computation (NGQC) and nonadiabatic holonomic quantum computation (NHQC) have been proposed to reduce the run time of geometric quantum gates. However, in terms of robustness against experimental control errors, the existing NGQC and NHQC scenarios have no advantage over standard dynamical gates in most cases. Here, we give the reasons why nonadiabatic geometric gates are sensitive to the control errors and, further, we propose a scheme of super-robust nonadiabatic geometric quantum control, in which the super-robust condition can guarantee both high speed and robustness of the geometric gate. To illustrate the working mechanism of super-robust geometric quantum gates, we give two simple examples of SR-NGQC and SR-NHQC for two- and three-level quantum systems, respectively. Theoretical and numerical results with the experimental parameters indicate that our scheme can significantly improve the gate performance compared to the previous NGQC, NHQC, and standard dynamical schemes. Super-robust geometric quantum computation can be applied to various physical platforms such as superconducting qubits, quantum dots, and trapped ions. All of these sufficiently show that our scheme provides a promising way towards robust geometric quantum computation.

We present an all-optical mass spectrometry technique to identify trapped ions. The new method uses laser-cooled ions to determine the mass of a cotrapped dark ion with a sub-dalton resolution within a few seconds. We apply the method to identify the first controlled synthesis of cold, trapped $\mathrm{RaOH}^+$ and ${\mathrm{RaOCH}_3}^+$. These molecules are promising for their sensitivity to time and parity violations that could constrain sources of new physics beyond the standard model. The nondestructive nature of the mass spectrometry technique may help identify molecular ions or highly charged ions prior to optical spectroscopy. Unlike previous mass spectrometry techniques for small ion crystals that rely on scanning, the method uses a Fourier transform which is inherently broadband and comparatively fast. The technique's speed provides new opportunities for studying state-resolved chemical reactions in ion traps.

A general bound on the Lyapunov exponent of a quantum system is given by $λ_L\leq2π\,T/\hbar$, where $T$ is the system temperature, as established by Maldacena, Shenker, and Stanford (MSS). This upper bound is saturated when the system under consideration is the exact holographic dual of a black hole. It has also been shown that an inverted harmonic oscillator (IHO) may exhibit the behavior of thermal energy emission, in close analogy to the Hawking radiation emitted by black holes. We demonstrate that the Lyapunov exponent of the IHO indeed saturates the MSS bound, with an effective temperature equal to the analogue black hole radiation temperature, and propose using a trapped ion as a physical implementation of the IHO. We derive the corresponding out-of-time-ordered correlation function (OTOC) diagnosing quantum chaos, and theoretically show, for an experimentally realizable setup, that the effective temperature of the trapped-ion-IHO matches the upper MSS bound for the speed of scrambling.

The formation and evolution mechanism of fullerenes in the planetary nebula or in the interstellar medium are still not understood. Here we present the study on the cluster formation and the relative reactivity of fullerene cations (from smaller to larger, C$_{44}$ to C$_{70}$) with anthracene molecule (C$_{14}$H$_{10}$). The experiment is performed in the apparatus that combines a quadrupole ion trap with a time-of-flight mass spectrometer. By using a 355 nm laser beam to irradiate the trapped fullerenes cations (C$_{60}$$^+$ or C$_{70}$$^+$), smaller fullerene cations C$_{(60-2n)}$$^+$, n=1-8 or C$_{(70-2m)}$$^+$, m=1-11 are generated, respectively. Then reacting with anthracene molecules, series of fullerene/anthracene cluster cations are newly formed (e.g., (C$_{14}$H$_{10}$)C$_{(60-2n)}$$^+$, n=1-8 and (C$_{14}$H$_{10}$)C$_{(70-2m)}$$^+$, m=1-11), and slight difference of the reactivity within the smaller fullerene cations are observed. Nevertheless, smaller fullerenes show obviously higher reactivity when comparing to fullerene C$_{60}$$^+$ and C$_{70}$$^+$. A successive loss of C$_2$ fragments mechanism is suggested to account for the formation of smaller fullerene cations, which then undergo addition reaction with anthracene molecules to form the fullerene-anthracene cluster cations. It is found that the higher laser energy and longer irradiation time are key factors that affect the formation of smaller fullerene cations. This may indicate that in the strong radiation field environment (such as photon-dominated regions) in space, fullerenes are expected to follow the top-down evolution route, and then form small grain dust (e.g., clusters) through collision reaction with co-existing molecules, here, smaller PAHs.

Quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault tolerant quantum computation, due to its robustness against operational noises. However, because of the parametric restriction of previous schemes, the main robust advantage of holonomic quantum gates is smeared. Here, we experimentally demonstrate a solution scheme, demonstrating nonadiabatic holonomic single qubit quantum gates with optimal control in a trapped Yb ion based on three level systems with resonant drives, which also hold the advantages of fast evolution and convenient implementation. Compared with corresponding previous geometric gates and conventional dynamic gates, the superiority of our scheme is that it is more robust against control amplitude errors, which is confirmed by the measured gate infidelity through both quantum process tomography and random benchmarking methods. In addition, we also outline that nontrivial two qubit holonomic gates can also be realized within current experimental technologies. Therefore, our experiment validates the feasibility for this robust and fast holonomic quantum computation strategy.

Quantum machine learning aspires to overcome intractability that currently limits its applicability to practical problems. However, quantum machine learning itself is limited by low effective dimensions achievable in state-of-the-art experiments. Here we demonstrate highly successful classifications of real-life images using photonic qubits, combining a quantum tensor-network representation of hand-written digits and entanglement-based optimization. Specifically, we focus on binary classification for hand-written zeroes and ones, whose features are cast into the tensor-network representation, further reduced by optimization based on entanglement entropy and encoded into two-qubit photonic states. We then demonstrate image classification with a high success rate exceeding 98%, through successive gate operations and projective measurements. Although we work with photons, our approach is amenable to other physical realizations such as nitrogen-vacancy centers, nuclear spins and trapped ions, and our scheme can be scaled to efficient multi-qubit encodings of features in the tensor-product representation, thereby setting the stage for quantum-enhanced multi-class classification.

Employing recent developed magneto-optical trap recoil ion momentum spectroscopy (MOTRIMS) combining cold atom, strong laser pulse, and ultrafast technologies, we study momentum distributions of the multiply ionized cold rubidium (Rb) induced by the elliptically polarized laser pulses (35 fs, $1.3 \times 10^{15}$ W/cm$^2$). The complete vector momenta of Rbn+ ions up to charge state n = 4 are recorded with extremely high resolution (0.12 a.u. for Rb$^+$). Variations of characteristic multi-bands displayed in momentum distributions, as the ellipticity varies from the linear to circular polarization, are interpreted qualitatively with the classical over-barrier ionization model. Present momentum spectroscopy of cold heavy alkali atoms presents novel strong-field phenomena beyond the noble gases.

A reproducible stationary improved confinement mode (I-mode) has been achieved recently in the Experimental Advanced Superconducting Tokamak, featuring good confinement without particle transport barrier, which could be beneficial to solving the heat flux problem caused by edge localized modes (ELM) and the helium ash problem for future fusion reactors. The microscopic mechanism of sustaining stationary I-mode, based on the coupling between turbulence transition and the edge temperature oscillation, has been discovered for the first time. A radially localized edge temperature ring oscillation (ETRO) with azimuthally symmetric structure ($n=0$,$m=0$) has been identified and it is caused by alternative turbulence transitions between ion temperature gradient modes (ITG) and trapped electron modes (TEM). The ITG-TEM transition is controlled by local electron temperature gradient and consistent with the gyrokinetic simulations. The self-organizing system consisting with ETRO, turbulence and transport transitions plays the key role in sustaining the I-mode confinement. These results provide a novel physics basis for accessing, maintaining and controlling stationary I-mode in the future.

Spectroscopy is a powerful tool for studying molecules and is commonly performed on large thermal molecular ensembles that are perturbed by motional shifts and interactions with the environment and one another, resulting in convoluted spectra and limited resolution. Here, we use generally applicable quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the final state non-destructively, leaving the molecule ready for further manipulation. We resolve rotational transitions to 11 significant digits and derive the rotational constant of CaH+ to be B_R = 142501777.9(1.7) kHz. Our approach suits a wide range of molecular ions, including polyatomics and species relevant for tests of fundamental physics, chemistry, and astrophysics.

Besides buckminsterfullerene (C60), other fullerenes and their derivatives may also reside in space. In this work, we study the formation and photo-dissociation processes of astronomically relevant fullerene/anthracene (C14H10) cluster cations in the gas phase. Experiments are carried out using a quadrupole ion trap (QIT) in combination with time-of-flight (TOF) mass spectrometry. The results show that fullerene (C60, and C70)/anthracene (i.e., [(C14H10)nC60]+ and [(C14H10)nC70]+), fullerene (C56 and C58)/anthracene (i.e., [(C14H10)nC56]+ and [(C14H10)nC58]+) and fullerene (C66 and C68)/anthracene (i.e., [(C14H10)nC66]+ and [(C14H10)nC68]+) cluster cations, are formed in the gas phase through an ion-molecule reaction pathway. With irradiation, all the fullerene/anthracene cluster cations dissociate into mono$-$anthracene and fullerene species without dehydrogenation. The structure of newly formed fullerene/anthracene cluster cations and the bonding energy for these reaction pathways are investigated with quantum chemistry calculations. Our results provide a growth route towards large fullerene derivatives in a bottom-up process and insight in their photo-evolution behavior in the ISM, and clearly, when conditions are favorable, fullerene/PAH clusters can form efficiently. In addition, these clusters (from 80 to 154 atoms or ~ 2 nm in size) offer a good model for understanding the physical-chemical processes involved in the formation and evolution of carbon dust grains in space, and provide candidates of interest for the DIBs that could motivate spectroscopic studies.

Suppressing undesired nonunitary effects is a major challenge in quantum computation and quantum control. In this work, by considering the adiabatic dynamics in presence of a surrounding environment, we theoretically and experimentally analyze the robustness of adiabaticity in open quantum systems. More specifically, by considering a decohering scenario, we exploit the validity conditions of the adiabatic approximation as well as its sensitiveness to the resonance situation, which typically harm adiabaticity in closed systems. As an illustration, we implement an oscillating Landau-Zener Hamiltonian, which shows that decoherence may drive the resonant system with high fidelities to the adiabatic behavior of open systems. Moreover we also implement the adiabatic quantum algorithm for the Deutsch problem, where a distinction is established between the open system adiabatic density operator and the target pure state expected in the computation process. Preferred time windows for obtaining the desired outcomes are then analyzed. We experimentally realize these systems through a single trapped Ytterbium ion $^{171}$Yb$^+$, where the ion hyperfine energy levels are used as degrees of freedom of a two-level system, with both driven field and decohering strength efficiently controllable.

We experimentally probe the distribution of kink pairs resulting from driving a one-dimensional quantum Ising chain through the paramagnet-ferromagnet quantum phase transition, using a single trapped ion as a quantum simulator in momentum space. The number of kink pairs after the transition follows a Poisson binomial distribution, in which all cumulants scale with a universal power-law as a function of the quench time in which the transition is crossed. We experimentally verified this scaling for the first cumulants and report deviations due to noise-induced dephasing of the trapped ion. Our results establish that the universal character of the critical dynamics can be extended beyond the paradigmatic Kibble-Zurek mechanism, which accounts for the mean kink number, to characterize the full probability distribution of topological defects.

An experiment based on a trapped Ytterbium ion validates the inertial theorem for the SU(2) algebra. The qubit is encoded within the hyperfine states of the atom and controlled by RF fields. The inertial theorem generates analytical solutions for non-adiabatically driven systems that are `accelerated' slowly, bridging the gap between the sudden and adiabatic limits. These solutions are shown to be stable to small deviations, both experimentally and theoretically. As a result, the inertial solutions pave the way to rapid quantum control of closed, as well as open quantum systems. For large deviations from the inertial condition, the amplitude diverges while the phase remains accurate.

Quantum thermodynamics aims at investigating both the emergence and the limits of the laws of thermodynamics from a quantum mechanical microscopic approach. In this scenario, thermodynamic processes with no heat exchange, namely, adiabatic transformations, can be implemented through quantum evolutions in closed systems, even though the notion of a closed system is always an idealization and approximation. Here, we begin by theoretically discussing thermodynamic adiabatic processes in open quantum systems, which evolve non-unitarily under decoherence due to its interaction with its surrounding environment. From a general approach for adiabatic non-unitary evolution, we establish heat and work in terms of the underlying Liouville superoperator governing the quantum dynamics. As a consequence, we derive the conditions that an adiabatic open-system quantum dynamics implies in the absence of heat exchange, providing a connection between quantum and thermal adiabaticity. Moreover, we determine families of decohering systems exhibiting the same maximal heat exchange, which imply in classes of thermodynamic adiabaticity in open systems. We then approach the problem experimentally using a hyperfine energy-level quantum bit of an Ytterbium $^{171}$Yb$^+$ trapped ion, which provides a work substance for thermodynamic processes, allowing for the analysis of heat and internal energy throughout a controllable engineered dynamics.

Ballooning instabilities are widely believed to be a possible triggering mechanism for the onset of substorm and current disruption initiation in the near-Earth magnetotail. Yet the stability of the kinetic ballooning mode (KBM) in a global and realistic magnetotail configuration has not been well examined. In this paper, the growth rate of the KBM is calculated from analytical theory for the two-dimensional Voigt equilibrium within the framework of kinetic magnetohydrodynamic (MHD) model. The growth rate of the KBM is found to be strongly dependent on the field line stiffening factor $S$, which depends on the trapped electron dynamics, the finite ion gyroradius, and the magnetic drift motion of charged particles. Furthermore, calculations show that the KBM is unstable in a finite intermediate range of equatorial $β_{eq}$ values and the growth rate dependence on $β_{eq}$ is enhanced for larger $ρ_i$. The KBM stability is further analyzed in a broad range of $k_y$ for different values of ion Larmor radius $ρ_i$ and gradient ratio $η_j \equiv d\ln(T_j)/d\ln(n_j)$, where $T_j$ is the particle temperature and $n_j$ is the particle density. The KBM is found to be unstable for sufficiently high values of $k_y$, where the growth rate first increases to a maximum value and then decreases due to kinetic effects. The $k_y$ at the maximum growth rate decreases exponentially with $ρ_i$. The current sheet thinning is found to enhance the KBM growth rate and the unstable $β_{eq}$ regime in the near-Earth magnetotail.

In this work, we introduce machine learning methods to implement readout of a single qubit on $^{171}\mathrm{Yb^{+}}$ trapped-ion system. Different machine learning methods including convolutional neural networks and fully-connected neural networks are compared with traditional methods in the tests. The results show that machine learning methods have higher fidelity, more robust readout results in relatively short time. To obtain a 99% readout fidelity, neural networks only take half of the detection time needed by traditional threshold or maximum likelihood methods. Furthermore, we implement the machine learning algorithms on hardware-based field-programmable gate arrays and an ARM processor. An average readout fidelity of 99.5% (with $10^5$ magnitude trials) within 171 $μ$s is demonstrated on the embedded hardware system for $^{171}\mathrm{Yb^{+}}$ ion trap.

Validity conditions for the adiabatic approximation are useful tools to understand and predict the quantum dynamics. Remarkably, the resonance phenomenon in oscillating quantum systems has challenged the adiabatic theorem. In this scenario, inconsistencies in the application of quantitative adiabatic conditions have led to a sequence of new approaches for adiabaticity. Here, by adopting a different strategy, we introduce a validation mechanism for the adiabatic approximation by driving the quantum system to a non-inertial reference frame. More specifically, we begin by considering several relevant adiabatic approximation conditions previously derived and show that all of them fail by introducing a suitable oscillating Hamiltonian for a single quantum bit (qubit). Then, by evaluating the adiabatic condition in a rotated non-inertial frame, we show that all of these conditions, including the standard adiabatic condition, can correctly describe the adiabatic dynamics in the original frame, either far from resonance or at a resonant point. Moreover, we prove that this validation mechanism can be extended for general multi-particle quantum systems, establishing the conditions for the equivalence of the adiabatic behavior as described in inertial or non-inertial frames. In order to experimentally investigate our method, we consider a hyperfine qubit through a single trapped Ytterbium ion $^{171}$Yb$^{+}$, where the ion hyperfine energy levels are used as degrees of freedom of a two-level system. By monitoring the quantum evolution, we explicitly show the consistency of the adiabatic conditions in the non-inertial frame.

In this work, we study the photodissociation processes of small PAH clusters (e.g., pyrene clusters). The experiments are carried out using a quadrupole ion trap in combination with time-of-flight (QIT-TOF) mass spectrometry. The results show that pyrene clusters are converted into larger PAHs under the influence of a strong radiation field. Specifically, pyrene dimer cations (e.g., [C$_{16}$H$_{10}$$-$C$_{16}$H$_{9}$]$^+$ or C$_{32}$H$_{19}$$^+$), will photo-dehydrogenate and photo-isomerize to fully aromatic cations (PAHs) (e.g., C$_{32}$H$_{16}$$^+$) with laser irradiation. The structure of new formed PAHs and the dissociation energy for these reaction pathways are investigated with quantum chemical calculations. These studies provide a novel efficient evolution routes for the formation of large PAHs in the interstellar medium (ISM) in a bottom-up process that will counteract the top-down conversion of large PAHs into rings and chains, and provide a reservoir of large PAHs that can be converted into C$_{60}$ and other fullerenes and large carbon cages.

The first gas-phase infrared spectra of two isolated astronomically relevant and large PAH cations - diindenoperylene (DIP) and dicoronylene (DC) - in the 530$-$1800 cm$^{-1}$ (18.9$-$5.6 $μ$m) range - are presented. Vibrational band positions are determined for comparison to the aromatic infrared bands (AIBs). The spectra are obtained via infrared multiphoton dissociation (IRMPD) spectroscopy of ions stored in a quadrupole ion trap (QIT) using the intense and tunable radiation of the free electron laser for infrared experiments (FELIX). DIP$^{+}$ shows its main absorption peaks at 737 (13.57), 800 (12.50), 1001 (9.99), 1070 (9.35), 1115 (8.97), 1152 (8.68), 1278 (7.83), 1420 (7.04) and 1550 (6.45) cm$^{-1}$($μ$m), in good agreement with DFT calculations that are uniformly scaled to take anharmonicities into account. DC$^+$ has its main absorption peaks at 853 (11.72), 876 (11.42), 1032 (9.69), 1168 (8.56), 1300 (7.69), 1427 (7.01) and 1566 (6.39) cm$^{-1}$($μ$m), that also agree well with the scaled DFT results presented here. The DIP$^+$ and DC$^+$ spectra are compared with the prominent infrared features observed towards NGC 7023. This results both in matches and clear deviations. Moreover, in the 11.0$-$14.0 $μ$m region, specific bands can be linked to CH out-of-plane (oop) bending modes of different CH edge structures in large PAHs. The molecular origin of these findings and their astronomical relevance are discussed.

Entanglement generation can be robust against noise in approaches that deliberately incorporate dissipation into the system dynamics. The presence of additional dissipation channels may, however, limit fidelity and speed of the process. Here we show how quantum optimal control techniques can be used to both speed up the entanglement generation and increase the fidelity in a realistic setup, whilst respecting typical experimental limitations. For the example of entangling two trapped ion qubits [Lin et al., Nature 504, 415 (2013)], we find an improved fidelity by simply optimizing the polarization of the laser beams utilized in the experiment. More significantly, an alternate combination of transitions between internal states of the ions, when combined with optimized polarization, enables faster entanglement and decreases the error by an order of magnitude.

We study photoionization of cold rubidium atoms in a strong infrared laser field using a magneto-optical trap (MOT) recoil ion momentum spectrometer. Three types of cold rubidium target are provided, operating in two-dimension (2D) MOT, 2D molasses, and 3D MOT with densities in the orders of $10^7$ atoms/cm$^3$, $10^8$ atoms/cm$^3$, and $10^9$ atoms/cm$^3$, respectively. The density profile and the temperature of 3D MOT are characterized using the absorption imaging and photoionization. The momentum distributions of Rb$^+$ created by absorption of two- or three-photon illuminate a dipole-like double-peak structure, in good agreement with the results in the strong field approximation. The yielding momentum resolution of $0.12 \pm 0.03$ a.u. is achieved in comparison with theoretical calculations, exhibiting the great prospects for the study of electron correlations in alkali metal atoms through interaction with strong laser pulses.

It is known that high intensity fields are usually required to implement shortcuts to adiabaticity via Transitionless Quantum Driving (TQD). Here, we show that this requirement can be relaxed by exploiting the gauge freedom of generalized TQD, which is expressed in terms of an arbitrary phase when mimicking the adiabatic evolution. We experimentally investigate the performance of generalized TQD in comparison with both traditional TQD and adiabatic dynamics. By using a $^{171}$Yb$^+$ trapped ion hyperfine qubit, we implement a Landau-Zener adiabatic Hamiltonian and its (traditional and generalized) TQD counterparts. We show that the generalized theory provides optimally implementable Hamiltonians for TQD, with no additional fields required. In addition, the energetically optimal TQD Hamiltonian for the Landau-Zener model is investigated under dephasing. Remarkably, even using less intense fields, optimal TQD exhibits fidelities that are more robust against a decohering environment, with performance superior than that provided by the adiabatic dynamics.

Due to the exponential complexity of the resources required by quantum state tomography (QST), people are interested in approaches towards identifying quantum states which require less effort and time. In this paper, we provide a tailored and efficient method for reconstructing mixed quantum states up to $12$ (or even more) qubits from an incomplete set of observables subject to noises. Our method is applicable to any pure or nearly pure state $ρ$, and can be extended to many states of interest in quantum information processing, such as multi-particle entangled $W$ state, GHZ state and cluster states that are matrix product operators of low dimensions. The method applies the quantum density matrix constraints to a quantum compressive sensing optimization problem, and exploits a modified Quantum Alternating Direction Multiplier Method (Quantum-ADMM) to accelerate the convergence. Our algorithm takes $8,35$ and $226$ seconds respectively to reconstruct superposition state density matrices of $10,11,12$ qubits with acceptable fidelity, using less than $1 \%$ of measurements of expectation. To our knowledge it is the fastest realization that people can achieve using a normal desktop. We further discuss applications of this method using experimental data of mixed states obtained in an ion trap experiment of up to $8$ qubits.

We provide a comprehensive theoretical framework for describing the dynamics of a single trapped ion interacting with a neutral buffer gas, thus extending our previous studies on buffer-gas cooling of ions beyond the critical mass ratio [B. Höltkemeier et al., Phys. Rev. Lett. 116, 233003 (2016)]. By transforming the collisional processes into a frame, where the ion's micromotion is assigned to the buffer gas atoms, our model allows one to investigate the influence of non-homogeneous buffer gas configurations as well as higher multipole orders of the radio-frequency trap in great detail. Depending on the neutral-to-ion mass ratio, three regimes of sympathetic cooling are identified which are characterized by the form of the ion's energy distribution in equilibrium. We provide analytic expressions and numerical simulations of the ion's energy distribution, spatial profile and cooling rates for these different regimes. Based on these findings, a method for actively decreasing the ion's energy by reducing the spatial expansion of the buffer gas arises (Forced Sympathetic Cooling).

Quantum entanglement among multiple spatially separated particles is of fundamental interest, and can serve as central resources for studies in quantum nonlocality, quantum-to-classical transition, quantum error correction, and quantum simulation. The ability of generating an increasing number of entangled particles is an important benchmark for quantum information processing. The largest entangled states were previously created with fourteen trapped ions, eight photons, and five superconducting qubits. Here, based on spontaneous parametric down-converted two-photon entanglement source with simultaneously a high brightness of ~12 MHz/W, a collection efficiency of ~70% and an indistinguishability of ~91% between independent photons, we demonstrate, for the first time, genuine and distillable entanglement of ten single photons under different pump power. Our work creates a state-of-the-art platform for multi-photon experiments, and provide enabling technologies for challenging optical quantum information tasks such as high-efficiency scattershot boson sampling with many photons.

It is found that the Lorentz force generated by the magnetic drift drives a generic plasma pinch fluxes of particle, energy and momentum through the Stokes-Einstein relation. The proposed theoretical model applies for both electrons and ions, trapped particles and passing particles.

In this paper, two-dimensional (2-D) hybrid simulations are performed to investigate ion dynamics at a rippled quasi-parallel shock. The results show that the ripples around the shock front are inherent structures of a quasi-parallel shock, and the reformation of the shock is not synchronous along the surface of the shock front. By following the trajectories of the upstream ions, we find that these ions behave differently when they interact with the shock front at different positions along the shock surface. The upstream particles are easier to transmit through the upper part of a ripple, and the bulk velocity in the corresponding downstream is larger, where a high-speed jet is formed. In the lower part of the ripple, the upstream particles tend to be reflected by the shock. For the reflected ions by the shock, they may suffer multiple stage acceleration when moving along the shock surface, or trapped between the upstream waves and the shock front. At last, these ions may escape to the further upstream or enter the downstream, therefore, the superthermal ions can be found in both the upstream and downstream.

Full quantum state tomography (FQST) plays a unique role in the estimation of the state of a quantum system without \emph{a priori} knowledge or assumptions. Unfortunately, since FQST requires informationally (over)complete measurements, both the number of measurement bases and the computational complexity of data processing suffer an exponential growth with the size of the quantum system. A 14-qubit entangled state has already been experimentally prepared in an ion trap, and the data processing capability for FQST of a 14-qubit state seems to be far away from practical applications. In this paper, the computational capability of FQST is pushed forward to reconstruct a 14-qubit state with a run time of only 3.35 hours using the linear regression estimation (LRE) algorithm, even when informationally overcomplete Pauli measurements are employed. The computational complexity of the LRE algorithm is first reduced from $O(10^{19})$ to $O(10^{15})$ for a 14-qubit state, by dropping all the zero elements, and its computational efficiency is further sped up by fully exploiting the parallelism of the LRE algorithm with parallel Graphic Processing Unit (GPU) programming. Our result can play an important role in quantum information technologies with large quantum systems.

We propose a new dark-state cooling method of trapped ion systems in the Lamb-Dicke limit. With application of microwave dressing the ion, we can obtain two electromagnetically induced transparency structures. The heating effects caused by the carrier and the blue sideband transition vanish due to the EIT effects and the final mean phonon numbers can be much less than the recoil limit. Our scheme is robust to fluctuations of microwave power and laser intensities which provides a broad cooling bandwidth to cool motional modes of a linear ion chain. Moreover, it is more suitable to cool four-level ions on a large-scale ion chip.

We theoretically investigate the dynamics of a trapped ion immersed in a spatially localized buffer gas. For a homogeneous buffer gas, the ion reaches a stable equilibrium only if the mass ratio of the buffer gas atom to the ion is below a critical value. We show how this limitation can be overcome by using multipole traps and a spatially confined buffer gas. Using a generalized model for elastic collisions of the ion with the buffer gas atoms, the ion's energy distribution is derived for arbitrary buffer gas distributions and trap parameters. Three regimes characterized by the analytical form of the ion's energy distribution are found. Final ion temperatures down to the millikelvin regime can be achieved even for heavy buffer gases by actively controlling the size of the buffer gas or the trap voltage (forced sympathetic cooling).

The Kibble-Zurek mechanism is the paradigm to account for the nonadiabatic dynamics of a system across a continuous phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. We test the Kibble-Zurek mechanism in the quantum regime in the momentum space and find the measured scaling of excitations is in accordance with the theoretical prediction.

Flux-surface-averaged momentum loss and parallel rotation of the bulk ions at the edge of a tokamak plasma due to the ion orbit loss are calculated by computing the minimum loss energy of both the trapped and the passing thermal ions. The flux-surface-averaged parallel rotation of the bulk ions is in the co-current direction. The peak of the co-current rotation speed locates inside the last closed flux surface due to the orbit loss of the co-current thermal ions at the very edge of a tokamak plasma. The peaking position moves inward when the ion temperature increases.

A scenario is proposed to explain the preferential heating of minor ions and differential streaming velocity between minor ions and protons observed in the solar corona and in the solar wind. It is demonstrated by test particle simulations that minor ions can be nearly fully picked up by intrinsic Alfvén-cyclotron waves observed in the solar wind based on the observed wave energy density. Both high frequency ion-cyclotron waves and low frequency Alfvén waves play crucial roles in the pickup process. A minor ion can first gain a high magnetic moment through the resonant wave-particle interaction with ion-cyclotron waves, and then this ion with a large magnetic moment can be trapped by magnetic mirror-like field structures in the presence of the lower-frequency Alfvén waves. As a result, the ion is picked up by these Alfvén-cyclotron waves. However, minor ions can only be partially picked up in the corona due to low wave energy density and low plasma beta. During the pickup process, minor ions are stochastically heated and accelerated by Alfvén-cyclotron waves so that they are hotter and flow faster than protons. The compound effect of Alfvén waves and ion-cyclotron waves is important on the heating and acceleration of minor ions. The kinetic properties of minor ions from simulation results are generally consistent with in situ and remote features observed in the solar wind and solar corona.

Single photon sources based on semiconductor quantum dots offer distinct advantages for quantum information, including a scalable solid-state platform, ultrabrightness, and interconnectivity with matter qubits. A key prerequisite for their use in optical quantum computing and solid-state networks is a high level of efficiency and indistinguishability. Pulsed resonance fluorescence (RF) has been anticipated as the optimum condition for the deterministic generation of high-quality photons with vanishing effects of dephasing. Here, we generate pulsed RF single photons on demand from a single, microcavity-embedded quantum dot under s-shell excitation with 3-ps laser pulses. The pi-pulse excited RF photons have less than 0.3% background contributions and a vanishing two-photon emission probability. Non-postselective Hong-Ou-Mandel interference between two successively emitted photons is observed with a visibility of 0.97(2), comparable to trapped atoms and ions. Two single photons are further used to implement a high-fidelity quantum controlled-NOT gate.

This is a reply to the comment from Patrick Bruno (arXiv:1211.4792) on our paper (Phys. Rev. Lett. 109, 163001 (2012)).

Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.

Zitterbewegung (ZB), the trembling of free relativistic electrons in a vacuum could be simulated by a single trapped ion. We focus on the variations of ZB under different parity conditions and find no ZB in the case of odd or even parity. ZB occurs only for admixture of the odd and even parity states. We also show the similar role played by the parity operator for the trapped ion in Fock-state representation and the space inversion operator for a realistic relativistic electron. Although the ZB effect is invisible in a relativistic electron, preparation of the trapped ion in different parity states is a sophisticated job, which makes it possible to observe the parity relevant ZB effects with currently available techniques.

We derive schemes to measure the so-called weak values of quantum system observables by coupling of the system to a qubit meter system. We highlight, in particular, the meaning of the imaginary part of the weak values, and show how it can be measured directly on equal footing with the real part of the weak value. We present compact expressions for the weak value of single qubit observables and of product observables on qubit pairs. Experimental studies of the results are suggested with cold trapped ions.

We consider a single ion confined in a trap under radiation of two traveling waves of lasers. In the strong-excitation regime and without the restriction of Lamb-Dicke limit, the Hamiltonian of the system is similar to a driving Jaynes-Cummings model without rotating wave approximation (RWA). The approach we developed enables us to present a complete eigensolutions, which makes it available to compare with the solutions under the RWA. We find that, the ground state in our non-RWA solution is energically lower than the counterpart under the RWA. If we have the ion in the ground state, it is equivalent to a spin dependent force on the trapped ion. Discussion is made for the difference between the solutions with and without the RWA, and for the relevant experimental test, as well as for the possible application in quantum information processing.

We propose a feasible scheme to achieve holonomic quantum computation in a decoherence-free subspace (DFS) with trapped ions. By the application of appropriate bichromatic laser fields on the designated ions, we are able to construct two noncommutable single-qubit gates and one controlled-phase gate using the holonomic scenario in the encoded DFS.

The quantum behavior of a precooled cantilever can be probed highly efficiently by coupling to a trapped ultracold ion, in which a fast cooling of the cantilever down to the ground vibrational state is possible. We solve the dynamics of the coupling system by a squeezed-state expansion technique, and can in principle obtain the exact solution of the time-evolution of the coupling system. Compared to the treatment under rotating-wave approximation, we can present a more accurate description of the quantum behavior of the cantilever.

The hybrid entangled states generated, e.g., in a trapped-ion or atom-cavity system, have exactly one ebit of entanglement, but are not maximally entangled. We demonstrate this by showing that they violate, but in general do not maximally violate, Bell's inequality due to Clauser, Horne, Shimony and Holt. These states are interesting in that they exhibit the entanglement between two distinct degrees of freedom (one is discrete and another is continuous). We then demonstrate these entangled states as a valuable resource in quantum information processing including quantum teleportation, entanglement swapping and quantum computation with "parity qubits". Our work establishes an interesting link between quantum information protocols of discrete and continuous variables.