Counting statistics of chaotic resonances at optical frequencies: theory and experiments

TL;DR

This study investigates the statistical properties of chaotic resonances in optical microcavities, combining experiments and models to test fractal Weyl laws and understand resonance behavior at different frequencies.

Contribution

It introduces a novel experimental approach to analyze chaotic resonances using high-Q whispering-gallery modes and compares multiple theoretical models for interpretation.

Findings

Semiclassical RMT best describes experimental data at visible frequencies.

RMT alone is sufficient for infrared frequency analysis.

High-Q modes enable indirect measurement of chaotic resonances.

Abstract

A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes (WGMs) directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling. Three different models [classical, Random-Matrix-Theory (RMT) based, semiclassical] to interpret the experimental data are discussed. On the basis of least-squares analysis, theoretical estimates of Ehrenfest time, and independent measurements, we find that a semiclassically modified RMT-based expression best describes the experiment in all its realizations, particularly when the resonator is coupled to visible light, while RMT alone still works quite well in the infrared. In this work we reexamine and substantially extend the results of a short paper published earlier [L. Wang, D. Lippolis, Z.-Y. Li, X.-F. Jiang, Q. Gong, and Y.-F. Xiao, Phys. Rev. E 93, 040201(R) (2016)].