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

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.

Figures (2)

• Figure 1: Calculation of the squeezing ratio for the optimum angle of local oscillator in the absence of an optical reservoir as a function of propagation distance using three different methods: PPR (red), TWA (blue), and $\mathrm{PPR}_{\mathrm{D}}$ (black). Shaded regions indicate sampling error. The total atomic densities are (a) $\rho = 2.65 \times10^{21}\,\mathrm{m^{-3}}$, (b) $\rho = 1.33\times10^{22}\,\mathrm{m^{-3}}$, and (c) $\rho = 3.7\times10^{22}\,\mathrm{m^{-3}}$. The number of stochastic trajectories used is approximately $2\times10^{5}$ for PPR, $2\times10^{4}$–-$5\times10^{4}$ for $\mathrm{PPR}_{\mathrm{DR}}$, and $5\times10^{3}$ for TWA.
• Figure 2: Comparison of three methods, i.e, PPR, TWA, and $\mathrm{PPR}_{\text{D}}$. The figure shows the evolution of the squeezed field quadratures within the waveguide in presence of optical reservoir; $\kappa=1\times 10^{-6}$ m$^{-1}$ for three different atom density: (a) $\rho = 2.65\times10^{21}\,\mathrm{m^{-3}}$, (b) $\rho = 1.33\times10^{22}\,\mathrm{m^{-3}}$, and (c) $\rho = 3.7\times10^{22}\,\mathrm{m^{-3}}$. The number of stochastic trajectories used is approximately $3\times10^{5}$ for PPR, $5\times10^{4}$ for $\mathrm{PPR}_{\mathrm{DR}}$, and $5\times10^{3}$ for TWA.