Arghavan Safavi-Naini

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.

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.

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 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.

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.

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 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.

We study, both experimentally and theoretically, electromagnetically induced transparency cooling of the drumhead modes of planar 2-dimensional arrays with up to $N\approx 190$ Be${}^+$ ions stored in a Penning trap. Substantial sub-Doppler cooling is observed for all $N$ drumhead modes. Quantitative measurements for the center-of-mass mode show near ground state cooling with motional quantum numbers of $\bar{n} = 0.3\pm0.2$ obtained within $200~μs$. The measured cooling rate is faster than that predicted by single particle theory, consistent with a quantum many-body calculation. For the lower frequency drumhead modes, quantitative temperature measurements are limited by apparent damping and frequency instabilities, but near ground state cooling of the full bandwidth is strongly suggested. This advancement will greatly improve the performance of large trapped ion crystals in quantum information and quantum metrology applications.

Penning traps, with their ability to control planar crystals of tens to hundreds of ions, are versatile quantum simulators. Thermal occupations of the motional drumhead modes, transverse to the plane of the ion crystal, degrade the quality of quantum simulations. Laser cooling using electromagnetically induced transparency (EIT cooling) is attractive as an efficient way to quickly initialize the drumhead modes to near ground-state occupations. We numerically investigate the efficiency of EIT cooling of planar ion crystals in a Penning trap, accounting for complications arising from the nature of the trap and from the simultaneous cooling of multiple ions. We show that, in spite of challenges, the large bandwidth of drumhead modes (hundreds of kilohertz) can be rapidly cooled to near ground-state occupations within a few hundred microseconds. Our predictions for the center-of-mass mode include a cooling time constant of tens of microseconds and an enhancement of the cooling rate with increasing number of ions. Successful experimental demonstrations of EIT cooling in the NIST Penning trap [E. Jordan, K. A. Gilmore, A. Shankar, A. Safavi-Naini, M. J. Holland, and J. J. Bollinger, "Near ground-state cooling of two-dimensional trapped-ion crystals with more than 100 ions", (2018), submitted.] validate our predictions.

The coupling of spins to long-wavelength bosonic modes is a prominent means to engineer long-range spin-spin interactions, and has been realized in a variety of platforms, such as atoms in optical cavities and trapped ions. To date, much of the experimental focus has been on the realization of long-range Ising models, but generalizations to other spin models are highly desirable. In this work, we explore a previously unappreciated connection between the realization of an XY model by off-resonant driving of single sideband of boson excitation (i.e.~a single-beam Mølmer-Sørensen scheme) and a boson-mediated Ising simulator in the presence of a transverse field. In particular, we show that these two schemes have the same effective Hamiltonian in suitably defined rotating frames, and analyze the emergent effective XY spin model through truncated Magnus series and numerical simulations. In addition to XY spin-spin interactions that can be non-perturbatively renormalized from the naive Ising spin-spin coupling constants, we find an effective transverse field that is dependent on the thermal energy of the bosons, as well as other spin-boson couplings that cause spin-boson entanglement not to vanish at any time. In the case of a boson-mediated Ising simulator with transverse field, we discuss the crossover from transverse-field Ising-like to XY-like spin behavior as a function of field strength.

Controllable arrays of ions and ultra-cold atoms can simulate complex many-body phenomena and may provide insights into unsolved problems in modern science. To this end, experimentally feasible protocols for quantifying the buildup of quantum correlations and coherence are needed, as performing full state tomography does not scale favorably with the number of particles. Here we develop and experimentally demonstrate such a protocol, which uses time reversal of the many-body dynamics to measure out-of-time-order correlation functions (OTOCs) in a long-range Ising spin quantum simulator with more than 100 ions in a Penning trap. By measuring a family of OTOCs as a function of a tunable parameter we obtain fine-grained information about the state of the system encoded in the multiple quantum coherence spectrum, extract the quantum state purity, and demonstrate the buildup of up to 8-body correlations. Future applications of this protocol could enable studies of many-body localization, quantum phase transitions, and tests of the holographic duality between quantum and gravitational systems.

The global coupling of few-level quantum systems ("spins") to a discrete set of bosonic modes is a key ingredient for many applications in quantum science, including large-scale entanglement generation, quantum simulation of the dynamics of long-range interacting spin models, and hybrid platforms for force and spin sensing. We present a general numerical framework for treating the out-of-equilibrium dynamics of such models based on matrix product states. Our approach applies for generic spin-boson systems: it treats any spatial and operator dependence of the two-body spin-boson coupling and places no restrictions on relative energy scales. We show that the full counting statistics of collective spin measurements and infidelity of quantum simulation due to spin-boson entanglement, both of which are difficult to obtain by other techniques, are readily calculable in our approach. We benchmark our method using a recently developed exact solution for a particular spin-boson coupling relevant to trapped ion quantum simulators. Finally, we show how decoherence can be incorporated within our framework using the method of quantum trajectories, and study the dynamics of an open-system spin-boson model with spatially non-uniform spin-boson coupling relevant for trapped atomic ion crystals in the presence of molecular ion impurities.