Phase-Space Methods for Many-Body Quantum Optics
arXiv:2608.00341 · doi:10.1016/bs.aamop.2025.04.003
Abstract
Many-body quantum-optical systems, where a collection of emitters interacts through a common electromagnetic reservoir, exhibit rich out-of-equilibrium behavior and hold promise for applications in quantum technologies. However, exact numerical simulations of their dynamics quickly become unfeasible due to the exponential growth of the Hilbert space with system size. Semiclassical, phase-space approaches -- such as the Truncated Wigner approximation (TWA) -- provide computationally efficient alternatives by capturing leading-order quantum fluctuations. In this paper, we present a comprehensive overview of how to tackle problems in many-body quantum optics using phase-space methods. We derive the exact partial differential equation governing many-body dissipative evolution in any phase-space representation and discuss the approximations that yield the dissipative TWA proposed by Mink and Fleischhauer [SciPost Phys. 15, 233 (2023)]. We find that and distributions are generally suboptimal for many-body quantum optics. Additionally, we extend the formalism to calculate multi-time correlation functions, thereby broadening the scope of phase-space simulations of open spin systems to include coherence and spectral properties, as well as directional correlations of collectively radiating emitters. These developments provide valuable tools for investigating exotic light sources driven by collective dissipation, driven-dissipative phase transitions, and a wealth of many-body phenomena arising in state-of-the-art experimental platforms.
51 pages, 12 figures
References in corpus (70)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- The density-matrix renormalization group in the age of matrix product states
- Probing many-body dynamics on a 51-atom quantum simulator
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Search for New Physics with Atoms and Molecules
- The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
- Logical quantum processor based on reconfigurable atom arrays
- An Optical Lattice Clock with Accuracy and Stability at the Level
- Quantum trajectories and open many-body quantum systems
- An atom-by-atom assembler of defect-free arbitrary 2d atomic arrays
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
- Phase space representation of quantum dynamics
- Implementation of Cavity Squeezing of a Collective Atomic Spin
- Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
- Resolving the gravitational redshift within a millimeter atomic sample
- Prospects for a mHz-linewidth laser
- Subradiance in a Large Cloud of Cold Atoms
- Quantum Optics of Chiral Spin Networks
- A subradiant optical mirror formed by a single structured atomic layer
- In situ single-atom array synthesis by dynamic holographic optical tweezers
- Super-radiance reveals infinite-range dipole interactions through a nanofiber
- Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
- Collective atomic scattering and motional effects in a dense coherent medium
- Seconds-scale coherence in a tweezer-array optical clock
- Quantum dynamics of propagating photons with strong interactions: a generalized input-output formalism
- Universality of Dicke superradiance in arrays of quantum emitters
- An omniscient Maxwell's demon
- Steady-state superradiance with alkaline earth atoms
- Realizing spin squeezing with Rydberg interactions in a programmable optical clock
- Subradiant states of quantum bits coupled to a one-dimensional waveguide
- Coherent control of a symmetry-engineered multi-qubit dark state in waveguide quantum electrodynamics
- Scalable spin squeezing in a dipolar Rydberg atom array
- Input-Output Formalism for Few-Photon Transport: A Systematic Treatment Beyond Two Photons
- Storage and release of subradiant excitations in a dense atomic cloud
- A non-equilibrium superradiant phase transition in free space
- Einstein-Podolsky-Rosen correlations via dissociation of a molecular Bose-Einstein condensate
- QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems
- Controlling dipole-dipole frequency shifts in a lattice-based optical atomic clock
- Collective shift in resonant light scattering by a one-dimensional atomic chain
- Dicke superradiance in ordered lattices: dimensionality matters
- Simulating open quantum systems by applying SU(4) to quantum master equations
- Many-body superradiance and dynamical mirror symmetry breaking in waveguide QED
- Canonical Bose gas simulations with stochastic gauges
- Generation of macroscopic singlet states in atomic ensembles
- Dynamics of correlations in two-dimensional quantum spin models with long-range interactions: A phase-space Monte-Carlo study
- A generalized phase space approach for solving quantum spin dynamics
- Characterizing superradiant dynamics in atomic arrays via a cumulant expansion approach
- Beyond lowest order mean field theory for light interacting with atom arrays
- Theoretical study of early time superradiance for atom clouds and arrays
- Superradiance and subradiance in inverted atomic arrays
- Nonequilibrium dynamics of spin-boson models from phase space methods
- Dicke superradiance in ordered arrays of multilevel atoms
- Control of Localized Multiple Excitation Dark States in Waveguide QED
- 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
- Spin squeezing and many-body dipolar dynamics in optical lattice clocks
- Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems
- Multimode Fock states with large photon number: effective descriptions and applications in quantum metrology
- Subradiant-to-Subradiant Phase Transition in the Bad Cavity Laser
- Collective Radiative Interactions in the Discrete Truncated Wigner Approximation
- Dynamic population of multiexcitation subradiant states in incoherently excited atomic arrays
- From superradiance to subradiance: exploring the many-body Dicke ladder
- Bopp operators and phase-space spin dynamics: Application to rotational quantum brownian motion
- Directional superradiance in a driven ultracold atomic gas in free-space
- Dicke superradiance requires interactions beyond nearest-neighbors
- Exact Real Time Dynamics of Quantum Spin Systems Using the Positive-P Representation
- Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space Techniques
- Predicting correlations in superradiant emission from a cascaded quantum system
- Algebraic solution of the Lindblad equation for a collection of multilevel systems coupled to independent environments