Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems

Abstract

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 (DCTWA). 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 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 non-classical 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.

arXiv comment16 pages, 5 figures

References in corpus (28)

• Quantum information with Rydberg atoms
• Efficient simulation of one-dimensional quantum many-body systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• A Rydberg Quantum Simulator
• Phase space representation of quantum dynamics
• Keldysh Field Theory for Driven Open Quantum Systems
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Dynamical quantum noise in Bose-Einstein condensates
• Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Variational principle for steady states of dissipative quantum many-body systems
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
• Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation
• Wigner Functions for Arbitrary Quantum Systems
• Steady-state crystallization of Rydberg excitations in an optically driven lattice gas
• Spin squeezing with short-range spin-exchange interactions
• A generalized phase space approach for solving quantum spin dynamics
• Simulation of Quantum Spin Dynamics by Phase Space Sampling of BBGKY Trajectories
• Discrete truncated Wigner approach to dynamical phase transitions in Ising models after a quantum quench
• Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems
• Phase-Space Methods for Simulating the Dissipative Many-Body Dynamics of Collective Spin Systems
• Driven-dissipative criticality within the discrete truncated Wigner approximation
• Analysis of continuous and discrete Wigner approximations for spin dynamics
• Quenches near criticality of the quantum Ising chain---power and limitations of the discrete truncated Wigner approximation
• Performance evaluation of the discrete truncated Wigner approximation for quench dynamics of quantum spin systems with long-range interactions
• Continuous phase-space methods on discrete phase spaces

Cited by in corpus (21)

• Universality in driven open quantum matter
• Dissipative time crystals with long-range Lindbladians
• Collective Radiative Interactions in the Discrete Truncated Wigner Approximation
• Predicting correlations in superradiant emission from a cascaded quantum system
• Far from equilibrium field theory for strongly coupled light and matter: dynamics of frustrated multi-mode cavity QED
• User-friendly TWA for dissipative spin dynamics
• Quantum speed limits in arbitrary phase spaces
• Motional decoherence in ultracold Rydberg atom quantum simulators of spin models
• Effects of retardation on many-body superradiance in chiral waveguide QED
• Photon-mediated dipole-dipole interactions as a resource for quantum science and technology in cold atoms
• Crossover from the discontinuous to continuous phase transitions in dissipative spin system with collective decay
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Symmetry based efficient simulation of dissipative quantum many-body dynamics in subwavelength quantum emitter arrays
• Prethermalization of light and matter in cavity-coupled Rydberg arrays
• Discrete-phase-space method for driven-dissipative dynamics of strongly interacting bosons in optical lattices
• Cluster truncated Wigner approximation for bond-disordered Heisenberg spin models
• Two-dimensional correlation propagation dynamics with a cluster discrete phase-space method
• Polytopes of Absolutely Wigner Bounded Spin States
• Phase-Space Methods for Many-Body Quantum Optics
• Magnon Nesting in Driven Two-Dimensional Quantum Magnets
• Path-Integral Formulation of Bosonic Markovian Open Quantum Dynamics with Monte Carlo stochastic trajectories using the Glauber-Sudarshan P, Wigner, and Husimi Q Functions and Hybrids