Harvesting entropy and quantifying the transition from noise to chaos in a photon-counting feedback loop

TL;DR

This paper experimentally investigates how entropy and chaotic dynamics emerge from noise in a photon-counting feedback system, revealing a transition from shot noise to chaos as photon rate increases and how entropy rate reflects system unpredictability.

Contribution

It introduces an experimental analysis of entropy generation and chaos transition in a photon-counting feedback loop, linking noise, chaos, and entropy rate.

Findings

Dynamics shift from shot noise to chaos with increasing photon rate

Entropy rate varies with sampling rate and resolution, reflecting system unpredictability

System demonstrates the emergence of deterministic chaos from discrete noise

Abstract

Some physical processes, including the intensity fluctuations of a chaotic laser, the detection of single photons, and the Brownian motion of a microscopic particle in a fluid are unpredictable, at least on long timescales. This unpredictability can be due to a variety of physical mechanisms, but it is quantified by an entropy rate. This rate describes how quickly a system produces new and random information, is fundamentally important in statistical mechanics and practically important for random number generation. We experimentally study entropy generation and the emergence of deterministic chaotic dynamics from discrete noise in a system that applies feedback to a weak optical signal at the single-photon level. We show that the dynamics qualitatively change from shot noise to chaos as the photon rate increases, and that the entropy rate can reflect either the deterministic or noisy aspects of the system depending on the sampling rate and resolution.