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arXiv:2602.17660 · Physical Review Research

Benchmarking quantum phase-space methods for near-resonant light propagation

Mojdeh S. Najafabadi, Joel F. Corney, Luis Sanchez Soto, Gerd Leuchs

quant-phmath-phSubmitted Feb 19, 2026• Announced Feb 20, 2026• 0 citations• Revised Jun 30, 2026 (v3)
v1 · Feb 19, 2026v2 · Jun 29, 2026v3 · Jun 30, 2026
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Abstract

We study the dynamics of light interacting with a near-resonant atomic medium using the truncated Wigner and positive P phase-space representations. The atomic degrees of freedom are described using the Jordan-Schwinger mapping. The dynamics is first analyzed under unitary evolution and subsequently in the presence of an optical reservoir. While both approaches capture the main features of the light-matter dynamics, we find that the truncated Wigner approximation exhibits noticeable deviations for stronger interaction strengths and when reservoir-induced noise becomes significant.

Journal reference
Phys. Rev. Research 8, 023353, 2026
DOI
10.1103/xc3m-hsyx
Comments
9 pages, 2 figures

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We study the dynamics of light interacting with a near-resonant atomic medium using the truncated Wigner and positive P phase-space representations. The atomic degrees of freedom are described using the Jordan-Schwinger mapping. The dynamics is first analyzed under unitary evolution and subsequently in the presence of an optical reservoir. While both approaches capture the main features of the light-matter dynamics, we find that the truncated Wigner approximation exhibits noticeable deviations for stronger interaction strengths and when reservoir-induced noise becomes significant.
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Non-Gaussian correlations in a pure state are inextricably linked with certain nonclassical features, such as a non-positive-definite Wigner function. In a commonly used simulation technique in ultracold atoms and quantum optics, known as the truncated Wigner method, the quantum dynamics is mapped to stochastic trajectories in phase space, governed by a positive approximation to the true Wigner distribution. The question thus arises: How accurate is this approach in predicting truly nonclassical behavior? In this article, we benchmark the ability of the truncated Wigner phase-space method to reproduce the non-Gaussian statistics of the single-mode anharmonic oscillator. We find that the this method can reliably predict departures from Gaussian statistics over a wide range of particle numbers, whereas the positive-PPP representation, which involves no approximations, is limited by rapidly growing statistical uncertainty. The truncated Wigner function, furthermore, is able to reproduce the non-Gaussian correlations while satisfying the condition for purity.