Partial Optomechanical Refrigeration via Multimode Cold-Damping Feedback

TL;DR

This paper presents an analytical approach to partially cool multiple vibrational modes of a quantum resonator using cold-damping feedback, showing that effective refrigeration is achievable across many modes with proper frequency separation.

Contribution

It introduces a fully analytical model for multimode optomechanical cooling via feedback, extending standard single-mode techniques to multiple modes with predictable efficiency.

Findings

Low final phonon occupancies are achievable regardless of the number of modes.

Cooling efficiency depends on the intermode frequency separation.

Designing frequency-resolved resonators enhances refrigeration performance.

Abstract

We provide a fully analytical treatment for the partial refrigeration of the thermal motion of a quantum mechanical resonator under the action of feedback. As opposed to standard cavity optomechanics where the aim is to isolate and cool a single mechanical mode, the aim here is to extract the thermal energy from many vibrational modes within a large frequency bandwidth. We consider a standard cold-damping technique where homodyne read-out of the cavity output field is fed into a feedback loop that provides a cooling action directly applied on the mechanical resonator. Analytical and numerical results predict that low final occupancies are achievable independently of the number of modes addressed by the feedback as long as the cooling rate is smaller than the intermode frequency separation. For resonators exhibiting a few nearly degenerate pairs of modes cooling is less efficient and a weak dependence on the number of modes is obtained. These scalings hint towards the design of frequency resolved mechanical resonators where efficient refrigeration is possible via simultaneous cold-damping feedback.