Optical Bistability in a Low Photon-Density Regime

TL;DR

This paper provides a microscopic analysis of optical bistability at low photon densities, revealing unique spectral and dynamical properties distinct from classical regimes, and introduces an efficient numerical method for such quantum systems.

Contribution

It develops a novel numerical algorithm to analyze quantum master equations in low photon-density regimes, characterizing optical bistability microscopically and comparing it with high photon-density behavior.

Findings

Bistability characterized by double peak resonance spectrum.

Relaxation times grow exponentially with system size.

Hysteresis depends on system size and sweep rate.

Abstract

We give a microscopic description of the optical bistability, where the transmission coefficient has two different values as a function of input light intensity, and the system exhibits a discontinuous jump with a hysteresis loop. We developed an efficient numerical algorithm to treat the quantum master equation for hybridized systems of many photons and a large number of two-level atoms. By using this method, we characterize the bistability from the viewpoint of eigenmodes and eigenvalues of the time evolution operator of the quantum master equation. We investigate the optical bistability within the low photon-density regime, where the hybridization of photon and atom degrees of freedom occurs and the resonance spectrum has a double peak structure. We compared it with the standard optical bistability between the low photon-density regime and the high photon-density regime, where the photons can be treated as a classical electromagnetic field and the resonance spectrum has a single peak structure. We discuss the steady-state properties of the optical bistability: dependencies of the photon number density on the intensity and the double peak structure of the photon number distribution inside the bistable region. As for the dynamical properties, we find that the relaxation timescale shows an exponential growth with the system size, and reveal how the hysteresis loop of the optical bistability depends on the size of the system and the sweeping rate of the driving amplitude. Finally, by investigating the effects of detuning frequency of the input field, we clarify the characteristic properties of the present optical bistability within the low photon-density regime, which are qualitatively different from the standard optical bistable phenomena.