Stochastic Langevin propagation for classical and quantum optomechanics

TL;DR

This paper introduces a two-timescale stochastic Langevin propagation method for simulating quantum optomechanical systems, capturing correlations and nonlinear effects more accurately than traditional frequency-domain approaches.

Contribution

The authors develop a novel T2SL method that efficiently simulates time-domain correlations and nonlinear phenomena in quantum optomechanics, surpassing standard stochastic techniques.

Findings

T2SL accurately reproduces ponderomotive squeezing.

The method captures cavity sideband structures below quantum noise floor.

It agrees with analytical master equation results in certain regimes.

Abstract

Interesting experimental signatures of quantum cavity optomechanics arise because the quantum back-action induces correlations between incident quantum shot noise and the cavity field. While the quantum linear theory of optomechanics (QLT) has provided vital understanding across many experimental platforms, in certain new set-ups it may be insufficient: analysis in the time domain may be needed, but QLT obtains only spectra in frequency space; and nonlinear behavior may be present. Direct solution of the stochastic equations of motion in time is an alternative, but unfortunately standard methods do not preserve the important optomechanical correlations. We introduce two-timescale stochastic Langevin (T2SL) propagation as an efficient and straightforward method to obtain time traces with the correct correlations. We show that T2SL, in contrast to standard stochastic simulations, can efficiently simulate correlation phenomena such as ponderomotive squeezing and reproduces accurately cavity sideband structures on the scale of the applied quantum noise and even complicated features entirely submerged below the quantum shot noise imprecision floor. We investigate nonlinear regimes and find where comparison is possible, that the method agrees with analytical results obtained with master equations at low temperatures and in perturbative regimes.