A quantum optical realization of the Ornstein-Uhlenbeck process via simultaneous action of white noise and feedback

TL;DR

This paper demonstrates how quantum feedback and noise can produce an Ornstein-Uhlenbeck process in quantum optics, revealing that noise can sometimes enhance quantum feedback effects like self-stabilization.

Contribution

It establishes a link between quantum feedback and the Ornstein-Uhlenbeck process, showing how uncorrelated noise influences quantum emitter dynamics.

Findings

Energy level fluctuations lead to Ornstein-Uhlenbeck process in populations

Phase noise can support quantum feedback effects

Noise can enhance self-stabilization in quantum systems

Abstract

We establish an important connection between coherent quantum feedback and the Ornstein-Uhlenbeck process in quantum optics. We show that an emitter with fluctuating energy levels in front of a mirror results in an Ornstein-Uhlenbeck process for electronic populations, although the fluctuation of the energy levels is assumed to be uncorrelated in time and space. Based on a Heisenberg equation of motion description of the quantum feedback dynamics, we discuss additionally the impact of phase noise on the population dynamics and provide examples in which noise itself is not detrimental but supports and enhances typical features of quantum feedback such as self-stabilization.