Hybrid atom-ion Quantum Systems

We propose a sub-Doppler cooling scheme for trapped-ion crystals in Paul traps. The combination of a hollow tweezer and microwave drive creates an effective two-level system which is cooled through attractive Sisyphus cooling. For ${}^{171}\rm{Yb}^+$ ions, we numerically identify optimal parameters for one- and two-ion crystals, and investigate the cooling rate in ion crystals with up to three ions. Our cooling scheme utilizes a single ion addressed with a tweezer to achieve sub-Doppler cooling of the $N$ axial motional modes perpendicular to the tweezer propagation direction, does not rely on the Lamb-Dicke regime and uses off-resonant light. We reach $1/e$ cooling times for the center of mass mode of $τ_{\rm com}<2$ ms, and a steady-state excitation number of $\bar{n}_{\rm{com}}\approx 0.7$. Our scheme is well-suited as an intermediate stage between Doppler cooling and ground-state sideband cooling, and can be readily realized in trapped-ion platforms.

We demonstrate precision laser spectroscopy of a trapped $^{173}$Yb$^+$ ion that is not directly laser cooled by coupling it to ultracold atoms. The atomic bath continuously cools the internal degrees of freedom of the ion to its hyperfine ground state via spin-exchange collisions. Successful laser excitation is detected via state-selective charge transfer and subsequent ion loss. We probe the $6^2S_{1/2}\rightarrow 6^2P_{3/2}$ transition at 329 nm and measure the magnetic and electric hyperfine interaction constants for the $6^2P_{3/2}$ state to be $A=-241(1)$ MHz and $B=1460(8)$ MHz, respectively. Our results are in agreement with a previous measurement obtained in a hollow-cathode discharge experiment but are a factor of 6-9 more precise. The techniques demonstrated in this work may be extended to perform precision spectroscopy on other ions with complex level structures.

We study the occurrence of long-lived metastable states in the 4f$^{13}$5d6s electron configuration of Yb$^+$. By optical pumping of a single trapped ion on the $^2F^\text{o}_{7/2}\rightarrow (7/2,0)_{7/2}$ transition at 377.5 nm, we prepare a wide range of metastable electronic states. We use a co-trapped control ion to sympathetically cool the spectroscopy ion, allowing us to accurately time its subsequent decay. We record a strong decay signal corresponding to a lifetime of 0.92(8) s, a weaker decay signal with lifetime 9.8(+2.9, -2.0) s, and find evidence for a much longer lifetime, $>$ 30 s. We identify the metastable states with these lifetimes qualitatively, and corroborate our results with atomic structure calculations that support the observed lifetimes and decay paths. These long-lived states provide new opportunities in qubit and qudit state detection and optical clocks.

Quantum many-body systems driven far from equilibrium can exhibit chaos, entanglement, and non-classical correlations, yet directly observing these phenomena in large, closed quantum systems remains challenging. Here we realize the Dicke model -- a fundamental description of light-matter interactions -- in a two-dimensional crystal of approximately 100 trapped ions. The ions' internal state is optically coupled to the center of mass vibrational mode via an optical spin-dependent force, enabling unitary many-body dynamics beyond the mean-field and few-body limits. In the integrable regime, where the phonons can be adiabatically eliminated, we observe a dynamical phase transition between ferromagnetic to paramagnetic spin phases. In contrast, when the spins and phonons are strongly coupled, we observe clear signatures of non-integrable chaotic dynamics, including erratic phase-space trajectories and the exponential growth of excitations and entanglement quantified by the one-body Rényi entropy. By quenching from an unstable fixed point in the near-integrable regime, quantum noise can generate correlated spin-phonon excitations. Our numerical calculations, in clear agreement with experiment, reveal the generation of two-mode spin-phonon squeezing, 2.6 dB below the standard quantum limit (4.6 dB relative to the initial thermal state), followed by generalized vacuum Rabi collapses and revivals. Our results establish large ion crystals as scalable analog quantum simulators of non-equilibrium light-matter dynamics and provide a controlled platform for experimental studies of information scrambling and entanglement in closed many-body systems.

We directly observe and spatially map an optical analog of the Magnus effect, where intrinsic spin-orbit-like coupling of light generates a spin-dependent transverse displacement of the atom-light interaction profile for a $^{40}$Ca$^+$ ion. Probed on a quadrupole transition using a tightly focused beam, we observe displacements of the maximum in the profile of the effective interaction by several 100 nm originating from intrinsic longitudinal electric field components beyond the paraxial approximation. The tight focus of the beam induces additional transverse polarization gradients, which we characterize through a phase-sensitive measurement and spatial maps for different beam configurations. The results establish the physical basis of polarization-gradient interactions relevant to optical tweezer-based quantum control.

Testing the predictions of quantum mechanics has been one of the main experimental endeavors for decades. Recent advancements in technology led to a number of demonstrations which test non-classicality via specific computational tasks. Limitations of these experiments include dependence on complexity theory assumptions, susceptibility to hardware noise and inefficient verification, raising questions about their scalability. We propose to test non-classicality using a game based on complement sampling, an efficiently verifiable problem that achieves the largest possible separation between quantum and classical computation when both input and output represent samples from probability distributions. When restricting the input to instances inspired by the Bernstein-Vazirani problem, our game admits an exponentially large violation of classicality without relying on computational hardness assumptions. We execute the game on Quantinuum System Model H2 trapped-ion quantum computers, with experiments consisting of thousands of different circuits on up to 55 qubits. The observed scores can be explained by a systematic adoption of a quantum strategy, further corroborating the quantum nature of the hardware in an efficient and scalable way.

Displacement sensing is a fundamental task in metrology. However, the development of quantum-enhanced sensors that fully utilize the available degrees of freedom in many-body quantum systems remains an outstanding challenge. We propose novel many-body displacement sensing schemes that use spin-dependent squeezed (SDS) states -- hybrid spin-boson states whose bosonic squeezed quadrature is conditioned on an auxiliary spin. We prove that SDS states are \emph{optimal}, i.e. their quantum Cramér-Rao bound saturates the Heisenberg limit. We propose explicit measurement sequences that can be readily implemented in systems such as trapped ions. We also introduce a scalable state-preparation protocol and numerically demonstrate the preparation of $8.7$~dB of spin-dependent squeezing $15$ times faster than the standard approach using second-order sidebands in trapped ions. The potential applications of our sensing protocols range from measuring single-photon scattering to searches for dark matter.

We present a fully quantum mechanical description of a free $^6$Li atom scattering from a trapped $^{171}$Yb$^+$ ion in one dimension. By reformulating the system in polar coordinates and employing the adiabatic representation, we extract a set of coupled adiabatic potentials representing the atom interacting with the ion in different trap states. In an approach similar to quantum defect theory (QDT), we leverage the vast difference in energy scale between the interaction, the trap, and the scattering energy to encapsulate the short-range atom-ion scattering behavior in a single phase parameter. The presence of trapped $({}^{171}\text{Yb}^6\text{Li})^+$ molecular-ion states leads to a series of roughly evenly spaced resonances in the scattering cross section. The predicted distribution of resonances at low collision energies is at odds with the expectation of quantum chaos and the Bohigas-Giannoni-Schmit (BGS) conjecture.

Electromagnetically Induced Transparency (EIT) cooling is a well-established method for preparing trapped ion systems in their motional ground state. However, isolating a three-level system, as required for EIT cooling, is often challenging or impractical. Nonetheless, multilevel systems can inherently host dark states. In this work, we extend the EIT cooling framework to such multilevel systems. We develop a formalism to accurately determine the cooling rate in the weak sideband coupling regime and provide an approximate estimate for cooling rates beyond this regime, without the need for explicit simulation of the motional degree of freedom. We clarify the connection between the cooling rate and the absorption spectrum, offering a pathway for efficient near-ground-state cooling of ions with complex electronic structures.

We demonstrate an optimal quantum control strategy for the deterministic preparation of entangled harmonic oscillator states in trapped ions. The protocol employs dynamical phase modulation of laser-driven Jaynes-Cummings and anti-Jaynes-Cummings interactions. We prepare Two-Mode Squeezed Vacuum (TMSV) states in the mechanical motions of a trapped ion and characterize the states with phase-space tomography. First, we verify continuous-variable entanglement by measuring an Einstein-Podolsky-Rosen entanglement parameter of 0.0132(7), which is below the threshold of 0.25 for Reid's EPR criterion. Second, we perform a continuous-variable Bell test and find a violation of the Clauser-Horne-Shimony-Holt inequality, measuring 2.26(3), which is above the entanglement threshold of 2. We also demonstrate the flexibility of our method by preparing a non-Gaussian entangled oscillator state--a superposition of TMSV states.

Tightly-focused laser beams, or optical tweezers, are essential for analogue and digital quantum simulation with neutral atoms and trapped ions. Despite this, most of the current intuition and theoretical treatment utilizes the paraxial approximation, which breaks down at the focus of optical tweezers. We develop an analytic model, which we use in tandem with numerical simulations, to quantify how non-paraxial effects will manifest in the next-generation of scalable quantum hardware, where tightly focused beams are used for individual qubit control. In particular, we calculate the light potentials of Gaussian and Laguerre-Gaussian beams driving the quadrupole $^2$S$_{1/2}\rightarrow$ $^2$D$_{5/2}$ transition in $^{40}$Ca$^+$. Longitudinal field components in the beam center cause spatially-dependent Rabi frequencies and AC Stark shifts, leading to unexpected qubit-motion coupling. We characterize single- and two-qubit gate infidelities due to this effect with an analytic model and numerical simulation. We identify regimes where non-paraxial effects should be taken into account for high-precision quantum control. Finally, we highlight that non-paraxial effects are potentially more severe in the case of neutral atom and molecule addressing.

We consider the quantum simulation of quadratic spin-phonon coupling in a crystal of trapped ions. The coupling is implemented using tightly focused optical tweezers on each ion that change the local trapping potential in a state-dependent way. By encoding spins in the internal states of the ions and adding a tunneling term via Mølmer-Sørensen-type interactions, we calculate the emergence of mobile bipolarons driven by the zero-point energy of the ion crystal phonons. We show that thermal occupation may pin the bipolarons for ion crystals at finite temperature. Our scheme can be used to study and illustrate the emergence of mobile bipolarons as a function of temperature.

We study the occurrence of Rydberg atom-ion molecules (RAIMs) in a hybrid atom-ion system with an ion crystal trapped in a Paul trap coupled to Rydberg atoms on its either ends. To assess the feasibility of such a system, we perform a detailed Floquet analysis of the effect of the Paul trap's rf potential on the RAIMs and provide a qualitative analysis of the survival probability based on scaling laws. We conclude that the RAIM survives for sufficiently weak and low frequency traps. We then use this hybrid system and propose a scheme to utilise the common motional modes of the ion crystal to suppress (blockade) or enhance (anti-blockade) the probability of forming two RAIMs at the ends of the chain, replacing the typical blockade radius by the length of the ion crystal.

We study the dynamics of phonon-mediated qubit-qubit interactions between trapped ions in the presence of an ultracold atomic gas. By deriving and solving a master equation to describe the combined system, we show that the presence of the atoms causes the quantum gate quality to reduce because of motional decoherence. On the other hand, we calculate that the gas may be used to keep the ion crystal cold in the presence of external heating due to electric field noise. We show that tuning the atom-ion scattering length allows one to tune the cooling rate of the ions and would make it possible to temporarily reduce the effects of the gas during a quantum gate while keeping the ions cold over long timescales. In this way, the trapped ion quantum computer may be buffer gas cooled. The system may also be used for quantum-enhanced measurements of the atom-ion interactions or properties of the atomic bath.

This paper presents a routine to align an optical tweezer on a single trapped ion and use the ion as a probe to characterize the tweezer. We find a smallest tweezer waist of $2.3(2)\,μ$m, which is in agreement with the theoretical minimal attainable waist of $2.5(2)\,μ$m in our setup. We characterize the spatial dependence of the tweezer Rabi frequency which is suppressed by a factor of 19(3) in the immediate surrounding of the ion. We investigate the effects of optical forces and coherent population trapping on the ion. Finally, we show that the challenges posed by these forces can be overcome, and that the number of tweezers can be easily scaled up to reach several ions by using a spatial light modulator.

Quantum states that are symmetric under particle exchange play a crucial role in fields such as quantum metrology and quantum error correction. We use a variational circuit composed of global one-axis twisting and global rotations to efficiently prepare arbitrary symmetric states, i.e. any superposition of Dicke states. The circuit does not require local addressability or ancilla qubits and thus can be readily implemented in a variety of experimental platforms including trapped-ion quantum simulators and cavity QED systems. We provide analytic and numerical evidence that any $N$-qubit symmetric state can be prepared in $2N/3$ steps. We demonstrate the utility of our protocol by preparing (i) metrologically useful $N$-qubit Dicke states of up to $N = 300$ qubits in $\mathcal{O}(1)$ gate steps with theoretical infidelities $1-\mathcal{F} < 10^{-3}$, (ii) the $N = 9$ Ruskai codewords in $P = 4$ gate steps with $1-\mathcal{F} < 10^{-4}$, and (iii) the $N = 13$ Gross codewords in $P = 7$ gate steps with $1-\mathcal{F} < 10^{-4}$. Focusing on trapped-ion platforms, for the $N = 9$ Ruskai and $N = 13$ Gross codewords we estimate that the protocol achieves fidelities $\gtrsim 95\%$ in the presence of typical experimental noise levels, thus providing a pathway to the preparation of a wide range of useful highly-entangled quantum states.

We combine quantum optimal control with a variational ansatz based on non-Gaussian states for fast, non-adiabatic preparation of quantum many-body states. We demonstrate this on the example of the spin-boson model, and use a multi-polaron ansatz to prepare near-critical ground states. For one mode, we achieve a reduction in infidelity of up to $\approx 60$ ($\approx 20$) times compared to linear (optimised local adiabatic) ramps respectively; for many modes we achieve a reduction in infidelity of up to $\approx 5$ times compared to non-adiabatic linear ramps. Further, we show that the typical control quantity, the leakage from the variational manifold, provides only a loose bound on the state's fidelity. Instead, in analogy to the bond dimension of matrix product states, we suggest a controlled convergence criterion based on the number of polarons. Finally, motivated by the possibility of realizations in trapped ions, we study the dynamics of a system with bath properties going beyond the paradigm of (sub/super) Ohmic couplings. We apply the ansatz to the study of the out-of-time-order-correlator (OTOC) of the bath modes in a non-perturbative regime. The scrambling time is found to be a robust feature only weakly dependent on the details of the coupling between the bath and the spin.

We consider the implementation of quantum logic gates in trapped ions using tightly focused optical tweezers. Strong polarization gradients near the tweezer focus lead to qubit-state dependent forces on the ion. We show that these may be used to implement quantum logic gates on pairs of ion qubits in a crystal. The qubit-state dependent forces generated by this effect live on the plane perpendicular to the direction of propagation of the laser beams opening new ways of coupling to motional modes of an ion crystal. The proposed gate does not require ground state cooling of the ions and does not rely on the Lamb-Dicke approximation, although the waist of the tightly focused beam needs to be comparable with its wavelength in order to achieve the needed field curvature. Furthermore, the gate can be performed on both ground state and magnetic field insensitive clock state qubits without the need for counter-propagating laser fields. This simplifies the setup and eliminates errors due to phase instabilities between the gate laser beams. Finally, we show that imperfections in the gate execution, in particular pointing errors $<30$ nm in the tweezers reduce the gate fidelity from $\mathcal F\gtrsim 0.99998$ to $\gtrsim 0.999$.

We theoretically investigate the trap-assisted formation of complexes in atom-ion collisions and their impact on the stability of the trapped ion. The time-dependent potential of the Paul trap facilitates the formation of temporary complexes by reducing the energy of the atom, which gets temporarily stuck in the atom-ion potential. As a result, those complexes significantly impact termolecular reactions leading to molecular ion formation via three-body recombination. We find that complex formation is more pronounced in systems with heavy atoms, but the mass has no influence on the lifetime of the transient state. Instead, the complex formation rate strongly depends on the amplitude of the ion's micromotion. We also show that complex formation persists even in the case of a time-independent harmonic trap. In this case, we find higher formation rates and longer lifetimes than the Paul trap, indicating that the atom-ion complex plays an essential role in atom-ion mixtures in optical traps.

Experimental setups that study laser-cooled ions immersed in baths of ultracold atoms merge the two exciting and well-established fields of quantum gases and trapped ions. These experiments benefit both from the exquisite read-out and control of the few-body ion systems as well as the many-body aspects, tunable interactions, and ultracold temperatures of the atoms. However, combining the two leads to challenges both in the experimental design and the physics that can be studied. Nevertheless, these systems have provided insights into ion-atom collisions, buffer gas cooling of ions and quantum effects in the ion-atom interaction. This makes them promising candidates for ultracold quantum chemistry studies, creation of cold molecular ions for spectroscopy and precision measurements, and as test beds for quantum simulation of charged impurity physics. In this review we aim to provide an experimental account of recent progress and introduce the experimental setup and techniques that enabled the observation of quantum effects.

The ability to program and control interactions provides the key to implementing large-scale quantum simulation and computation in trapped ion systems. Adding optical tweezers, which can tune the phonon spectrum and thus modify the phonon-mediated spin-spin interaction, was recently proposed as a way of programming quantum simulators for a broader range of spin models [Arias Espinoza et al., Phys. Rev. A {\bf 103}, 052437]. In this work we study the robustness of our findings in the presence of experimental imperfections: micromotion, local stress, and intensity noise. We show that the effects of micromotion can be easily circumvented when designing and optimizing tweezer patterns to generate a target interaction. Furthermore, while local stress, whereby the tweezers apply small forces on individual ions, may appear to enable further tuning of the spin-spin interactions, any additional flexibility is negligible. We conclude that optical tweezers are a useful method for controlling interactions in trapped ion quantum simulators in the presence of micromotion and imperfections in the tweezer alignment, but require intensity stabilization on the sub-percent level.

We measure chemical reactions between a single trapped $^{174}$Yb$^+$ ion immersed in an ultracold bath of $^6$Li atoms containing trace amounts of Li$_2$ dimers. This produces LiYb$^+$ molecular ions that we detect via mass spectrometry. We explain the reaction rates by modelling the dimer density as a function of the magnetic field and obtain excellent agreement when we assume the reaction to follow the Langevin rate. Our results present a novel approach towards the creation of cold molecular ions and point to the exploration of ultracold chemistry in ion molecule collisions. What is more, with a detection sensitivity below molecule densities of $10^{14}\,\mathrm{m}^{-3}$, we provide a new method to detect low-density molecular gases.

For exploration of quantum effects with hybrid atom-ion systems, reaching ultracold temperatures is the major limiting factor. In this work, we present results on numerical simulations of trapped ion buffer gas cooling using an ultracold atomic gas in a large number of experimentally realistic scenarios. We explore the suppression of micromotion-induced heating effects through optimization of trap parameters for various radio-frequency (rf) traps and rf driving schemes including linear and octupole traps, digital Paul traps, rotating traps and hybrid optical/rf traps. We find that very similar ion energies can be reached in all of them even when considering experimental imperfections that cause so-called excess micromotion. Moreover we look into a quantum description of the system and show that quantum mechanics cannot save the ion from micromotion-induced heating in an atom-ion collision. The results suggest that buffer gas cooling can be used to reach close to the ion's groundstate of motion and is even competitive when compared to some sub-Doppler cooling techniques such as Sisyphus cooling. Thus, buffer gas cooling is a viable alternative for ions that are not amenable to laser cooling, a result that may be of interest for studies into quantum chemistry and precision spectroscopy.

We study the quantum dynamics of an ion confined in a radiofrequency trap in interaction with either a Bose or spin-polarized Fermi gas. To this end, we derive quantum optical master equations in the limit of weak coupling and the Lamb-Dicke approximations. For the bosonic bath, we also include the so-called "Lamb-shift" correction to the ion trap due to the coupling to the quantum gas as well as the extended Fröhlich interaction within the Bogolyubov approximation that have been not considered in previous studies. We calculate the ion kinetic energy for various atom-ion scattering lengths as well as gas temperatures by considering the intrinsic micromotion and we analyse the damping of the ion motion in the gas as a function of the gas temperature. We find that the ion's dynamics depends on the quantum statistics of the gas and that a fermionic bath enables to attain lower ionic energies.

We propose a new scalable architecture for trapped ion quantum computing that combines optical tweezers delivering qubit state-dependent local potentials with oscillating electric fields. Since the electric field allows for long-range qubit-qubit interactions mediated by the center-of-mass motion of the ion crystal alone, it is inherently scalable to large ion crystals. Furthermore, our proposed scheme does not rely on either ground state cooling or the Lamb-Dicke approximation. We study the effects of imperfect cooling of the ion crystal, as well as the role of unwanted qubit-motion entanglement, and discuss the prospects of implementing the state-dependent tweezers in the laboratory.

We propose a new method for generating programmable interactions in one- and two-dimensional trapped-ion quantum simulators. Here we consider the use of optical tweezers to engineer the sound-wave spectrum of trapped ion crystals. We show that this approach allows us to tune the interactions and connectivity of the ion qubits beyond the power-law interactions accessible in current setups. We demonstrate the experimental feasibility of our proposal using realistic tweezer settings and experimentally relevant trap parameters to generate the optimal tweezer patterns to create target spin-spin interaction patterns in both one- and two-dimensional crystals. Our approach will advance quantum simulation in trapped-ion platforms as it allows them to realize a broader family of quantum spin Hamiltonians.

The so-called aromatic infrared bands are attributed to emission of polycyclic aromatic hydrocarbons. The observed variations toward different regions in space are believed to be caused by contributions of different classes of PAH molecules, i.e. with respect to their size, structure, and charge state. Laboratory spectra of members of these classes are needed to compare them to observations and to benchmark quantum-chemically computed spectra of these species. In this paper we present the experimental infrared spectra of three different PAH dications, naphthalene$^{2+}$, anthracene$^{2+}$, and phenanthrene$^{2+}$, in the vibrational fingerprint region 500-1700~cm$^{-1}$. The dications were produced by electron impact ionization of the vapors with 70 eV electrons, and they remained stable against dissociation and Coulomb explosion. The vibrational spectra were obtained by IR predissociation of the PAH$^{2+}$ complexed with neon in a 22-pole cryogenic ion trap setup coupled to a free-electron infrared laser at the Free-Electron Lasers for Infrared eXperiments (FELIX) Laboratory. We performed anharmonic density-functional theory calculations for both singly and doubly charged states of the three molecules. The experimental band positions showed excellent agreement with the calculated band positions of the singlet electronic ground state for all three doubly charged species, indicating its higher stability over the triplet state. The presence of several strong combination bands and additional weaker features in the recorded spectra, especially in the 10-15~$μ$m region of the mid-IR spectrum, required anharmonic calculations to understand their effects on the total integrated intensity for the different charge states. These measurements, in tandem with theoretical calculations, will help in the identification of this specific class of doubly-charged PAHs as carriers of AIBs.

Conditional multi-qubit gates are a key component for elaborate quantum algorithms. In a recent work, Rasmussen et al. (Phys. Rev. A 101, 022308) proposed an efficient single-step method for a prototypical multi-qubit gate, a Toffoli gate, based on a combination of Ising interactions between control qubits and an appropriate driving field on a target qubit. Trapped ions are a natural platform to implement this method, since Ising interactions mediated by phonons have been demonstrated in increasingly large ion crystals. However, the simultaneous application of these interactions and the driving field required for the gate results in undesired entanglement between the qubits and the motion of the ions, reducing the gate fidelity. In this work, we propose a solution based on adiabatic switching of these phonon mediated Ising interactions. We study the effects of imperfect ground state cooling, and use spin-echo techniques to undo unwanted phase accumulation in the achievable fidelities. For gates coupling to all axial modes of a linear crystal, we calculate high fidelities ($>$ 99%) $N$-qubit rotations with $N=$ 3-7 ions cooled to their ground state of motion and a gate time below 1~ms. The high fidelities obtained also for large crystals could make the gate competitive with gate-decomposed, multi-step variants of the $N$-qubit Toffoli gate, at the expense of requiring ground state cooling of the ion crystal.

We theoretically investigate the possibility of creating phonon-mediated spin-spin interactions between neutral atoms trapped in optical tweezers. By laser coupling the atoms to Rydberg states, collective modes of motion appear. We show that these can be used to mediate effective spin-spin interactions or quantum logic gates between the atoms in analogy to schemes employed in trapped ions. In particular, we employ Rydberg dressing in a novel scheme to induce the needed interaction, and we show that it is possible to replicate the working of the Mølmer-Sørensen entanglement scheme. The Mølmer-Sørensen gate is widely used in emerging quantum computers using trapped ion qubits and currently features some of the highest fidelities of any quantum gate under consideration. We find arbitrarily high fidelity for the coherent time evolution of the two-atom state even at non-zero temperature.

The Hitomi results for the Perseus cluster have shown that accurate atomic models are essential to the success of X-ray spectroscopic missions, and just as important as knowledge on instrumental calibration and astrophysical modeling. Preparing the models requires a multifaceted approach, including theoretical calculations, laboratory measurements, and calibration using real observations. In a previous paper, we presented a calculation of the electron impact cross sections on the transitions forming the Fe-L complex. In the present work, we systematically test the calculation against cross sections of ions measured in an electron beam ion trap experiment. A two-dimensional analysis in the electron beam energies and X-ray photon energies is utilized to disentangle radiative channels following dielectronic recombination, direct electron-impact excitation, and resonant excitation processes in the experimental data. The data calibrated through laboratory measurements are further fed into global modeling of the Chandra grating spectrum of Capella. We investigate and compare the fit quality, as well as sensitivity of the derived physical parameters to the underlying atomic data and the astrophysical plasma modeling. We further list the potential areas of disagreement between the observation and the present calculations, which in turn calls for renewed efforts in theoretical calculations and targeted laboratory measurements.

We theoretically study the dynamics of a trapped ion that is immersed in an ultracold gas of weakly bound atomic dimers created by a Feshbach resonance. Using quasi-classical simulations, we find a crossover from dimer dissociation to molecular ion formation depending on the binding energy of the dimers. The location of the crossover strongly depends on the collision energy and the time-dependent fields of the Paul trap. Deeply bound dimers lead to fast molecular ion formation, with rates approaching the Langevin collision rate $Γ'_\text{L}\approx4.8\times10^{-9}\,$cm$^3$s$^{-1}$. The kinetic energies of the created molecular ions have a median below $1\,$mK, such that they will stay confined in the ion trap. We conclude that interacting ions and Feshbach molecules may provide a novel approach towards the creation of ultracold molecular ions with applications in precision spectroscopy and quantum chemistry.

We describe and characterize an experimental apparatus that has been used to study interactions between ultracold lithium atoms and ytterbium ions. The preparation of ultracold clouds of Li atoms is described as well as their subsequent transport and overlap with Yb$^+$ ions trapped in a Paul trap. We show how the kinetic energy of the ion after interacting with the atoms can be obtained by laser spectroscopy. From analyzing the dynamics of the ion in the absence of atoms, we conclude that background heating, due to electric field noise, limits attainable buffer gas cooling temperatures. We suspect that this effect can be mitigated by noise reduction and by increasing the density of the Li gas, in order to improve its cooling power. Imperfections in the Paul trap lead to so-called excess micromotion, which poses another limitation to the buffer gas cooling. We describe in detail how we measure and subsequently minimize excess micromotion in our setup. We measure the effect of excess micromotion on attainable ion temperatures after buffer gas cooling and compare this to molecular dynamics simulations which describe the observed data very well.

Quantum logic gates with many control qubits are essential in many quantum algorithms, but remain challenging to perform in current experiments. Trapped ion quantum computers natively feature a different type of entangling operation, namely the Molmer-Sorensen (MS) gate which effectively applies an Ising interaction to all qubits at the same time. We consider a sequence of equal all-to-all MS operations, interleaved with single qubit gates that act only on one special qubit. Using a connection with quantum signal processing techniques, we find that it is possible to perform an arbitray SU(2) rotation on the special qubit if and only if all other qubits are in the state |1>. Such controlled rotation gates with N-1 control qubits require 2N applications of the MS gate, and can be mapped to a conventional Toffoli gate by demoting a single qubit to ancilla.

With the long-term goal of studying models of quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in the recent traversable wormhole constructions of [1,2]: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of teleportation by size to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semi-classical holographic wormhole corresponds to a rather special property of the operator-size distribution we call size winding. For more general systems (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversable wormhole phenomenon. In addition, a form of signalling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole, but rather to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations feasible with current technology in two experimental platforms: Rydberg atom arrays and trapped ions.

The family of $n$-bit Toffoli gates, with the two-bit Toffoli gate as the figurehead, are of great interest in quantum information as they can be used as universal gates and in quantum error correction, among other things. We present a single-step implementation of arbitrary $n$-bit Toffoli gates (up to a local change of basis), based on resonantly driving a single qubit that has a strong Ising coupling to $n$ other qubits. The setup in the two-qubit case turns out to be identical to the universal Barenco gate. The gate time and error are, in theory, independent of the number of control qubits, scaling better than conventional circuit decompositions. We note that our assumptions, namely strongly coupling $n+1$ qubits and a driving frequency that scales with $n$, may break down for large systems. Still, our protocol could enhance the capabilities of intermediate scale quantum computers, and we discuss the prospects of implementing our protocol on trapped ions, Rydberg atoms, and on superconducting circuits. Simulations of the latter platform show that the Toffoli gate with two control bits attains fidelities of above 0.98 even in the presence of decoherence. We also show how similar ideas can be used to make a series of controlled-\textsc{not}-gates in a single step. We show how these can speed up the implementation of quantum error correcting codes and we simulate the encoding steps of the three-qubit bit-flip code and the seven-qubit Steane code.

Great advances in precision quantum measurement have been achieved with trapped ions and atomic gases at the lowest possible temperatures. These successes have inspired ideas to merge the two systems. In this way one can study the unique properties of ionic impurities inside a quantum fluid or explore buffer gas cooling of the trapped ion quantum computer. Remarkably, in spite of its importance, experiments with atom-ion mixtures remained firmly confined to the classical collision regime. We report a collision energy of 1.15(0.23) times the $s$-wave energy (or 9.9(2.0)~$μ$K) for a trapped ytterbium ion in an ultracold lithium gas. We observed a deviation from classical Langevin theory by studying the spin-exchange dynamics, indicating quantum behavior in the atom-ion collisions. Our results open up numerous opportunities, such as the exploration of atom-ion Feshbach resonances, in analogy to neutral systems.

In order to study interactions of atomic ions with ultracold neutral atoms, it is important to have sub-$μ$m control over positioning ion crystals. Serving for this purpose, we introduce a microfabricated planar ion trap featuring 21 DC electrodes. The ion trap is controlled by a home-made FPGA voltage source providing independently variable voltages to each of the DC electrodes. To assure stable positioning of ion crystals with respect to trapped neutral atoms, we integrate into the overall design a compact mirror magneto optical chip trap (mMOT) for cooling and confining neutral $^{87}$Rb atoms. The trapped atoms will be transferred into an also integrated chipbased Ioffe-Pritchard trap potential formed by a Z-shaped wire and an external bias magnetic field.We introduce the hybrid atom-ion chip, the microfabricated planar ion trap and use trapped ion crystals to determine ion lifetimes, trap frequencies, positioning ions and the accuracy of the compensation of micromotion.

We report on the observation of interactions between ultracold Rydberg atoms and ions in a Paul trap. The rate of observed inelastic collisions, which manifest themselves as charge transfer between the Rydberg atoms and ions, exceeds that of Langevin collisions for ground state atoms by about three orders of magnitude. This indicates a huge increase in interaction strength. We study the effect of the vacant Paul trap's electric fields on the Rydberg excitation spectra. To quantitatively describe the exhibited shape of the ion loss spectra, we need to include the ion-induced Stark shift on the Rydberg atoms. Furthermore, we demonstrate Rydberg excitation on a dipole-forbidden transition with the aid of the electric field of a single trapped ion. Our results confirm that interactions between ultracold atoms and trapped ions can be controlled by laser coupling to Rydberg states. Adding dynamic Rydberg dressing may allow for the creation of spin-spin interactions between atoms and ions, and the elimination of collisional heating due to ionic micromotion in atom-ion mixtures.

We perform numerical simulations of trapped $^{171}$Yb$^+$ ions that are buffer gas cooled by a cold cloud of $^6$Li atoms. This species combination has been suggested to be the most promising for reaching the quantum regime of interacting atoms and ions in a Paul trap. Treating the atoms and ions classically, we compute that the collision energy indeed reaches below the quantum limit for a perfect linear Paul trap. We analyze the effect of imperfections in the ion trap that cause excess micromotion. We find that the suppression of excess micromotion required to reach the quantum limit should be within experimental reach. Indeed, although the requirements are strong, they are not excessive and lie within reported values in the literature. We analyze the detection and suppression of excess micromotion in our experimental setup. Using the obtained experimental parameters in our simulation, we calculate collision energies that are a factor 2-11 larger than the quantum limit, indicating that improvements in micromotion detection and compensation are needed there. We also analyze the buffer-gas cooling of linear and two-dimensional ion crystals. We find that the energy stored in the eigenmodes of ion motion may reach 10-100 $μ$K after buffer-gas cooling under realistic experimental circumstances. Interestingly, not all eigenmodes are buffer-gas cooled to the same energy. Our results show that with modest improvements of our experiment, studying atom-ion mixtures in the quantum regime is in reach, allowing for buffer-gas cooling of the trapped ion quantum platform and to study the occurrence of atom-ion Feshbach resonances.

We compute the effect of Markovian bulk dephasing noise on the staggered magnetization of the spin-1/2 XXZ Heisenberg chain, as the system evolves after a Néel quench. For sufficiently weak system-bath coupling, the unitary dynamics are found to be preserved up to a single exponential damping factor. This is a consequence of the interplay between $\mathbb{PT}$ symmetry and weak symmetries, which strengthens previous predictions for $\mathbb{PT}$-symmetric Liouvillian dynamics. Requirements are a non-degenerate $\mathbb{PT}$-symmetric generator of time evolution $\hat{\mathcal{L}}$, a weak parity symmetry and an observable that is anti-symmetric under this parity transformation. The spectrum of $\hat{\mathcal{L}}$ then splits up into symmetry sectors, yielding the same decay rate for all modes that contribute to the observable's time evolution. This phenomenon may be realized in trapped ion experiments and has possible implications for the control of decoherence in out-of-equilibrium many-body systems.

We report on spectroscopic results on the $^2S_{1/2} \rightarrow\,^2P_{3/2}$ transition in single trapped Yb$^+$ ions. We measure the isotope shifts for all stable Yb$^+$ isotopes except $^{173}$Yb$^+$, as well as the hyperfine splitting of the $^2P_{3/2}$ state in $^{171}$Yb$^+$. Our results are in agreement with previous measurements but are a factor of 5-9 more precise. For the hyperfine constant $A\left(^2P_{3/2}\right) = 875.4(10)$ MHz our results also agree with previous measurements but deviate significantly from theoretical predictions. We present experimental results on the branching ratios for the decay of the $^2P_{3/2}$ state. We find branching fractions for the decay to the $^2D_{3/2}$ state and $^2D_{5/2}$ state of 0.17(1)% and 1.08(5)%, respectively, in rough agreement with theoretical predictions. Furthermore, we measured the isotope shifts of the $^2F_{7/2} \rightarrow\,^1D\left[5/2\right]_{5/2}$ transition and determine the hyperfine structure constant for the $^1D\left[5/2\right]_{5/2}$ state in $^{171}$Yb$^+$ to be $A\left(^1D\left[5/2\right]_{5/2}\right) = -107(6)$ MHz.

Hybrid systems of laser-cooled trapped ions and ultracold atoms combined in a single experimental setup have recently emerged as a new platform for fundamental research in quantum physics. This paper reviews the theoretical and experimental progress in research on cold hybrid ion-atom systems which aim to combine the best features of the two well-established fields. We provide a broad overview of the theoretical description of ion-atom mixtures and their applications, and report on advances in experiments with ions trapped in Paul or dipole traps overlapped with a cloud of cold atoms, and with ions directly produced in a Bose-Einstein condensate. We start with microscopic models describing the electronic structure, interactions, and collisional physics of ion-atom systems at low and ultralow temperatures, including radiative and non-radiative charge transfer processes and their control with magnetically tunable Feshbach resonances. Then we describe the relevant experimental techniques and the intrinsic properties of hybrid systems. In particular, we discuss the impact of the micromotion of ions in Paul traps on ion-atom hybrid systems. Next, we review recent proposals for using ions immersed in ultracold gases for studying cold collisions, chemistry, many-body physics, quantum simulation, and quantum computation and their experimental realizations. In the last part we focus on the formation of molecular ions via spontaneous radiative association, photoassociation, magnetoassociation, and sympathetic cooling. We discuss applications and prospects of cold molecular ions for cold controlled chemistry and precision spectroscopy.

We theoretically study trapped ions that are immersed in an ultracold gas of Rydberg-dressed atoms. By off-resonant coupling on a dipole-forbidden transition, the adiabatic atom-ion potential can be made repulsive. We study the energy exchange between the atoms and a single trapped ion and find that Langevin collisions are inhibited in the ultracold regime for these repulsive interactions. Therefore, the proposed system avoids recently observed ion heating in hybrid atom-ion systems caused by coupling to the ion's radio frequency trapping field and retains ultracold temperatures even in the presence of excess micromotion.