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Journal of the Optical Society of America B

Simulating the generation of spin squeezing in a Rydberg atomic array for quantum metrology via a dissipative discrete truncated Wigner approximation

Jingya Wang, Zhongxiao Xu, Donghao Li

Published Feb 28, 2023• 0 citations
Publisher

Abstract

An atomic ensemble with many-body entanglement is desirable for precision measurement. As a type of such quantum state, the spin squeezed state has been pursued in both cold and warm atoms for applications of a quantum-enhanced atomic clock, interferometer, and magnetometer. Here, we report the numerical simulation of many-body dynamics in a Rydberg atomic array with dipole–dipole interaction, and evaluate the generation of spin squeezing. The method builds on the dissipative discrete truncated Wigner approximation, which combines the mean-field dynamics of a spin ensemble with Monte Carlo sampling. By taking into account experimental imperfections such as spin decoherence, we apply this approach to the dynamics in both strontium and rubidium Rydberg atomic arrays with the current available scale. This offers the possibility to accurately simulate the many-body dynamics of interacting quantum systems in achievable platforms for application of quantum simulation and quantum metrology.

DOI
10.1364/josab.484967

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An atomic ensemble with many-body entanglement is desirable for precision measurement. As a type of such quantum state, the spin squeezed state has been pursued in both cold and warm atoms for applications of a quantum-enhanced atomic clock, interferometer, and magnetometer. Here, we report the numerical simulation of many-body dynamics in a Rydberg atomic array with dipole–dipole interaction, and evaluate the generation of spin squeezing. The method builds on the dissipative discrete truncated Wigner approximation, which combines the mean-field dynamics of a spin ensemble with Monte Carlo sampling. By taking into account experimental imperfections such as spin decoherence, we apply this approach to the dynamics in both strontium and rubidium Rydberg atomic arrays with the current available scale. This offers the possibility to accurately simulate the many-body dynamics of interacting quantum systems in achievable platforms for application of quantum simulation and quantum metrology.
We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which combines the mean-field dynamics of a spin ensemble with a Monte Carlo sampling of discrete initial spin values to account for quantum correlations. Here we show how this approach can be generalized for dissipative spin systems by replacing the deterministic mean-field evolution by a stochastic process, which describes the decay of coherences and populations while preserving the length of each spin. We demonstrate the application of this technique for simulating nonclassical spin-squeezing effects or the dynamics and steady states of cavity QED models with 105{10}^{5}105 interacting two-level systems. This opens up the possibility to perform accurate real-scale simulations of a diverse range of experiments in quantum optics or with solid-state spin ensembles under realistic laboratory conditions.
Abstract Numerical techniques to efficiently model out-of-equilibrium dynamics in interacting quantum many-body systems are key for advancing our capability to harness and understand complex quantum matter. Here we propose a new numerical approach which we refer to as generalized discrete truncated Wigner approximation (GDTWA). It is based on a discrete semi-classical phase space sampling and allows to investigate quantum dynamics in lattice spin systems with arbitrary S ≥ 1/2. We show that the GDTWA can accurately simulate dynamics of large ensembles in arbitrary dimensions. We apply it for S > 1/2 spin-models with dipolar long-range interactions, a scenario arising in recent experiments with magnetic atoms. We show that the method can capture beyond mean-field effects, not only at short times, but it also can correctly reproduce long time quantum-thermalization dynamics. We benchmark the method with exact diagonalization in small systems, with perturbation theory for short times, and with analytical predictions made for models which feature quantum-thermalization at long times. We apply our method to study dynamics in large S > 1/2 spin-models and compute experimentally accessible observables such as Zeeman level populations, contrast of spin coherence, spin squeezing, and entanglement quantified by single-spin Renyi entropies. We reveal that large S systems can feature larger entanglement than corresponding S = 1/2 systems. Our analyses demonstrate that the GDTWA can be a powerful tool for modeling complex spin dynamics in regimes where other state-of-the art numerical methods fail.
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We present a systematic approach for the semiclassical treatment of many-body dynamics of interacting, open spin systems. Our approach overcomes some of the shortcomings of the recently developed discrete truncated Wigner approximation (DTWA) based on Monte Carlo sampling in a discrete phase space that improves the classical treatment by accounting for lowest-order quantum fluctuations. We provide a rigorous derivation of the DTWA by embedding it in a continuous phase space, thereby introducing a hybrid discrete-continuous truncated Wigner approximation . We derive a set of operator-differential mappings that yield an exact equation of motion (EOM) for the continuous SU(2) Wigner function of spins. The standard DTWA is then recovered by a systematic neglection of specific terms in this exact EOM. The hybrid approach permits us to determine the validity conditions and to gain a detailed understanding of the quality of the approximation, paving the way for systematic improvements. Furthermore, we show that the continuous embedding allows for a straightforward extension of the method to open spin systems subject to dephasing, losses, and incoherent drive, while preserving the key advantages of the discrete approach, such as a positive definite Wigner distribution of typical initial states. We derive exact stochastic differential equations for processes which cannot be described by the standard DTWA due to the presence of nonclassical noise. We illustrate our approach by applying it to the dissipative dynamics of Rydberg excitation of one-dimensional arrays of laser-driven atoms and compare it to exact results for small systems.
We report on the creation of an array of spin-squeezed ensembles of cesium atoms via Rydberg dressing, a technique that offers optical control over local interactions between neutral atoms. We optimize the coherence of the interactions by a stroboscopic dressing sequence that suppresses super-Poissonian loss. We thereby prepare squeezed states of N=200 atoms with a metrological squeezing parameter ξ^{2}=0.77(9) quantifying the reduction in phase variance below the standard quantum limit. We realize metrological gain across three spatially separated ensembles in parallel, with the strength of squeezing controlled by the local intensity of the dressing light. Our method can be applied to enhance the precision of tests of fundamental physics based on arrays of atomic clocks and to enable quantum-enhanced imaging of electromagnetic fields.
Ultracold Rydberg-atom arrays are an emerging platform for quantum simulation and computing. However, decoherence in these systems remains incompletely understood. Recent experiments [Guardado-Sanchez et al., Phys. Rev. X 8, 021069 (2018)] observed strong decoherence in the quench and longitudinal-field-sweep dynamics of two-dimensional Ising models realized with 6Li^{6}\mathrm{Li}6Li Rydberg atoms in optical lattices. This decoherence was conjectured to arise from the effective spin 12\frac{1}{2}21​ formed by the ground and Rydberg electronic states coupling to atom motion and therefore inducing an effective interaction noise. Here we show that this spin-motion coupling indeed leads to decoherence in qualitative, and often quantitative, agreement with the experimental data, by treating the difficult spin-motion-coupled problem using the discrete truncated Wigner approximation method. We also show that this decoherence will be an important factor to account for in future experiments with Rydberg atoms in optical lattices and microtrap arrays and discuss methods to mitigate the effect of motion, such as using heavier atoms or deeper traps.