Mechanical cooling and squeezing using optimal control

TL;DR

This paper develops a complete formalism for optimally controlling mechanical oscillators via continuous measurement and feedback, emphasizing the importance of exact models over approximations for cooling and squeezing.

Contribution

It introduces a comprehensive formalism that avoids standard approximations, providing accurate predictions for mechanical cooling and squeezing under optimal control.

Findings

Exact solutions differ significantly from approximate ones.

Conditional and unconditional states cannot coincide in typical control schemes.

Complete models are crucial for accurate predictions in mechanical control.

Abstract

A mechanical system can be optimally controlled through continuous measurements of its position followed by feedback. We revisit the complete formalism for predicting the performance of such as system without invoking the standard rotating wave approximations and the adiabatic approximation. Using this formalism we deduce both the conditional and unconditional state of a mechanical oscillator using the optimal control and feedback that leads to mechanical cooling and mechanical squeezing. We find large discrepancies between the exact solutions and the approximate solutions stressing the importance of using the complete model. We also highlight the importance of distinguishing between the conditional and unconditional state by demonstrating that these two cannot coincide in a typical control scheme, even with infinite feedback strength.