Universal power law decay in the dynamic hysteresis of an optical cavity with non-instantaneous photon-photon interactions

TL;DR

This paper demonstrates a universal power law decay in the hysteresis area of an optical cavity with non-instantaneous photon interactions, revealing non-Markovian dynamics and scaling behavior.

Contribution

It introduces a theoretical model with a memory kernel to explain the universal power law decay in optical hysteresis.

Findings

Hysteresis area decays as a power law with exponent -1 near the photon-photon interaction memory time.

The power law exponent is independent of system parameters.

Experimental and theoretical results confirm the universal scaling behavior.

Abstract

We investigate, experimentally and theoretically, the dynamic optical hysteresis of a coherently driven cavity with non-instantaneous photon-photon interactions. By scanning the frequency detuning between the driving laser and the cavity resonance at different speeds across an optical bistability, we find a hysteresis area that is a non-monotonic function of the scanning speed. As the scanning speed increases and approaches the memory time of the photon-photon interactions, the hysteresis area decays following a power law with exponent -1. The exponent of this power law is independent of the system parameters. To reveal this universal scaling behavior theoretically, we introduce a memory kernel for the interaction term in the standard driven-dissipative Kerr model. Our results offer new perspectives for exploring non-Markovian dynamics of light using arrays of bistable cavities with low quality factors, driven by low laser powers, and at room temperature.