Collective Radiative Interactions in the Discrete Truncated Wigner Approximation

Abstract

Interfaces of light and matter serve as a platform for exciting many-body physics and photonic quantum technologies. Due to the recent experimental realization of atomic arrays at sub-wavelength spacings, collective interaction effects such as superradiance have regained substantial interest. Their analytical and numerical treatment is however quite challenging. Here we develop a semiclassical approach to this problem that allows to describe the coherent and dissipative many-body dynamics of interacting spins while taking into account lowest-order quantum fluctuations. For this purpose we extend the discrete truncated Wigner approximation, originally developed for unitarily coupled spins, to include collective, dissipative spin processes by means of truncated correspondence rules. This maps the dynamics of the atomic ensemble onto a set of semiclassical, numerically inexpensive stochastic differential equations. We benchmark our method with exact results for the case of Dicke decay, which shows excellent agreement. For small arrays we compare to exact simulations and a second order cumulant expansion, again showing good agreement at early times and at moderate to strong driving. We conclude by studying the radiative properties of a spatially extended three-dimensional, coherently driven gas and compare the coherence of the emitted light to experimental results.

25 pages, 5 figures

References in corpus (4)

• The density-matrix renormalization group in the age of matrix product states
• Storage and control of optical photons using Rydberg polaritons
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Bopp operators and phase-space spin dynamics: Application to rotational quantum brownian motion

Cited by in corpus (19)

• Directional superradiance in a driven ultracold atomic gas in free-space
• Predicting correlations in superradiant emission from a cascaded quantum system
• User-friendly TWA for dissipative spin dynamics
• Superradiance of Strongly Interacting Dipolar Excitons in Moiré Quantum Materials
• Unraveling superradiance: Entanglement and mutual information in collective decay
• 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
• Symmetry based efficient simulation of dissipative quantum many-body dynamics in subwavelength quantum emitter arrays
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Fate of the Mollow triplet in strongly-coupled atomic arrays
• Towards nonlinear optics with Mössbauer nuclei using x-ray cavities
• Path-Integral Formulation of Truncated Wigner Approximation for Bosonic Markovian Open Quantum Systems
• Genuine Quantum effects in Dicke-type Models at large atom numbers
• Polytopes of Absolutely Wigner Bounded Spin States
• nuHOPS: A quantum trajectory method for highly excited environments in non-Markovian open quantum dynamics
• Emergence of second-order coherence in superfluorescence
• Phase-Space Methods for Many-Body Quantum Optics
• Exact Many-body Quantum Dynamics in One-Dimensional Baths via Collective Spins
• 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