Quantum stochastic equations for an opto-mechanical oscillator with radiation pressure interaction and non-Markovian effects

TL;DR

This paper develops a quantum stochastic model for an opto-mechanical system with radiation pressure, incorporating non-Markovian effects and scattering processes, and demonstrates how the reflected light spectrum can serve as a temperature probe.

Contribution

It introduces a quantum stochastic framework that includes non-Markovian dynamics and scattering processes for an opto-mechanical oscillator, advancing physical modeling capabilities.

Findings

The model captures non-Markovian dissipation effects.

Scattering processes are essential for accurate description.

Reflected light spectrum can be used as a temperature probe.

Abstract

The quantum stochastic Schroedinger equation or Hudson-Parthasareathy (HP) equation is a powerful tool to construct unitary dilations of quantum dynamical semigroups and to develop the theory of measurements in continuous time via the construction of output fields. An important feature of such an equation is that it allows to treat not only absorption and emission of quanta, but also scattering processes, which however had very few applications in physical modelling. Moreover, recent developments have shown that also some non-Markovian dynamics can be generated by suitable choices of the state of the quantum noises involved in the HP-equation. This paper is devoted to an application involving these two features, non-Markovianity and scattering process. We consider a micro-mirror mounted on a vibrating structure and reflecting a laser beam, a process giving rise to a radiation-pressure force on the mirror. We show that this process needs the scattering part of the HP-equation to be described. On the other side, non-Markovianity is introduced by the dissipation due to the interaction with some thermal environment which we represent by a phonon field, with a nearly arbitrary excitation spectrum, and by the introduction of phase noise in the laser beam. Finally, we study the full power spectrum of the reflected light and we show how the laser beam can be used as a temperature probe.