Cavity-Assisted Back Action Cooling of Mechanical Resonators

TL;DR

This paper investigates the quantum limits of cavity-assisted back action cooling of mechanical resonators, deriving analytical models and optimizing parameters for ground state cooling in optomechanical systems.

Contribution

It provides a comprehensive analysis including thermal noise effects, derives a master equation, and offers an analytical expression for final mechanical occupancy for optimal cooling.

Findings

Derived the motional master equation using Nakajima-Zwanzig formalism.

Calculated the output spectrum in the optomechanical regime.

Obtained an analytical expression for the final mechanical occupancy.

Abstract

We analyze the quantum regime of the dynamical backaction cooling of a mechanical resonator assisted by a driven harmonic oscillator (cavity). Our treatment applies to both optomechanical and electromechanical realizations and includes the effect of thermal noise in the driven oscillator. In the perturbative case, we derive the corresponding motional master equation using the Nakajima-Zwanzig formalism and calculate the corresponding output spectrum for the optomechanical case. Then we analyze the strong optomechanical coupling regime in the limit of small cavity linewidth. Finally we consider the steady state covariance matrix of the two coupled oscillators for arbitrary input power and obtain an analytical expression for the final mechanical occupancy. This is used to optimize the drive's detuning and input power for an experimentally relevant range of parameters that includes the "ground state cooling" regime.