Statistics of Chaotic Resonances in an Optical Microcavity

TL;DR

This paper investigates the statistical distribution of chaotic resonances in an optical microcavity with mixed dynamics, combining theoretical predictions and experimental validation to understand resonance behavior in open chaotic systems.

Contribution

It introduces a method to analyze chaotic resonances in optical microcavities by counting regular modes and compares experimental results with semiclassical and random matrix theory predictions.

Findings

Experimental data agree with semiclassical predictions.

Deviations from random matrix theory are observed.

Ballistic decay within Ehrenfest time influences resonance statistics.

Abstract

Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify classical-to-quantum correspondence. Here, we study, both theoretically and experimentally, the statistics of chaotic resonances in an optical microcavity with a mixed phase space of both regular and chaotic dynamics. Information on the number of chaotic modes is extracted by counting regular modes, which couple to the former via dynamical tunneling. The experimental data are in agreement with a known semiclassical prediction for the dependence of the number of chaotic resonances on the number of open channels, while they deviate significantly from a purely random-matrix-theory-based treatment, in general. We ascribe this result to the ballistic decay of the rays, which occurs within Ehrenfest time, and importantly, within the timescale of transient chaos. The present approach may provide a general tool for the statistical analysis of chaotic resonances in open systems.