Chaos due to parametric excitation: phase space symmetry and photon correlations

TL;DR

This paper explores how a nonlinear Kerr resonator exhibits dissipative chaos with phase space symmetries and nonclassical photon correlations, revealing quantum-to-classical transition features and the impact of chaos on photon statistics.

Contribution

It demonstrates the presence of phase space symmetry and nonclassical photon correlations in a parametrically driven Kerr resonator, highlighting quantum-classical correspondence violations in chaos regimes.

Findings

Strange attractors with two-fold symmetry in phase space.

Quantum-to-classical correspondence is violated in chaotic regimes.

Photon correlations decrease and squeezing diminishes in chaos.

Abstract

We discuss dissipative chaos showing symmetries in the phase space and nonclassical statistics for a parametrically driven nonlinear Kerr resonator (PDNR). In this system an oscillatory mode is created in the process of degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. For chaotic regime we demonstrate, that the Poincar\'e section showing a strange attractor, as well as the resonator mode contour plots of the Wigner functions display two-fold symmetry in the phase space. We show that quantum-to-classical correspondence is strongly violated for some chaotic regimes of the PDNR. Considering the second-order correlation function we show that the high-level of photons correlation leading to squeezing in the regular regime strongly decreases if the system transits to the chaotic regime. Thus, observation of the photon-number correlation allows to extract information about the chaotic regime.