Photon waiting-time distributions: A keyhole into dissipative quantum chaos

Abstract

Quantum systems, when interacting with their environments, can exhibit complex non-equilibrium states that are tempting to be interpreted as quantum versions of chaotic attractors. Here we propose an approach to open cavity dynamics based on the unraveling of the corresponding master equation into an ensemble of quantum trajectories. By using the concept of "quantum Lyapunov exponents" [I. I. Yusipov et al., arxiv: 1806.09295], we demonstrate that 'chaotic' and 'regular' regimes of the intra-cavity dynamics can be identified. The chaotic regimes are marked by the emergence of power-law intermediate asymptotics in the distribution of photon waiting times. The photon counting statistics can be retrieved by monitoring photon emission in experiment. Therefore, chaotic regimes can be identified without additional measurements (and thus disturbance) of the intra-cavity dynamics.

Chaotic spin-photonic quantum states in an open periodically modulated cavity

“…In our prior work 17 , we found that the transitions to chaotic photonic regimes in an open Kerr-nonlinear cavity are associated with appearance of power-law intermediate asymptotics, PDF(∆t) ∼ ∆t −α , in the corresponding waiting time pdf (which otherwise decays exponentially) 17 . We expect that this effect is generic and will emerge also in the considered spin-photonic model.…”

“…The dynamics of the photonic mode in the periodically modulated in time Kerr-nonlinear cavity 17 serves us a reference case and a background to project our results on. Equations (1)-(4) reproduce this case when we set δ = 0, g = 0, ω = 0.…”

“…Figure 1 shows largest Lyapunov exponent 17 λ as a function of amplitude A and period T . For the relatively small values of the modulation period and amplitude, the system remains in the regular regime characterized by negative LE.…”

“…The chaotic and regular dynamics of the system has been demonstrated by using the idea of maximal Lyapunov exponents for individual trajectories 17 . Measurement of these exponents in an experiment is hardly possible.…”

“…In our recent work 17 we showed that a photonic mode of an open and periodically modulated Kerr-nonlinear cavity can exhibit transitions from regular dynamics to chaos. A degree of chaos is quantified with quantum Lyapunov exponent 12 .…”