Quantum-optical realization of an Ornstein-Uhlenbeck-type process via simultaneous action of white noise and feedback

Based on a Heisenberg equation of motion description of the feedback dynamics in quantum optics, we discuss the impact of phase noise on the excitation dynamics and provide examples in which noise itself is not detrimental but supports and enhances typical features of quantum feedback such as self-stabilization of the electronic population. We furthermore establish a connection between coherent quantum feedback and an Ornstein-Uhlenbeck-type process in quantum optics in the presence of phase noise. The interfering and time-shifted amplitudes introduce a finite memory kernel which, convoluted with a white noise process, results in a resonance fluorescence dynamics of a damped random walk.