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Collective Radiative Interactions in the Discrete Truncated Wigner Approximation
by Christopher D. Mink, Michael Fleischhauer
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Christopher Mink |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202311_00024v1 (pdf) |
| Date accepted: | 2023-11-27 |
| Date submitted: | 2023-11-14 08:48 |
| Submitted by: | Mink, Christopher |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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, again showing good agreement at early times and at moderate to strong driving, and to a second order cumulant expansion. 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.
Author comments upon resubmission
Based on these reports, as well as further feedback from interested readers, we have carefully revised and significantly improved the manuscript.
List of changes
-Replaced the notation starting at around Eq. (21) (formerly 19) such that the coefficients do not use the letter 'J' anymore
-Expanded explanations for the sampling of initial states and the calculation of expectation values
-Sec. 6.2, which demonstrates a failure of our method, now contains comparisons to a second order cumulant expansion
-Pointed out the differences between this work and the previous single-particle decay, see e.g. after Eq. (49)
-Entirely reworked Sec. 6.3. We now compare our method to an actual experimental report on a dissipative phase transition in a driven gas and have replaced the unreferenced spin squeezing graph by a much more relevant calculation of g^(2) correlation functions.
Published as SciPost Phys. 15, 233 (2023)