# Rapid cooling of a strain-coupled oscillator by optical phaseshift measurement

## TL;DR

This paper proposes a method to rapidly cool a cantilever by using optical phase shift measurements on an ensemble of ions, enabling active feedback control to reduce thermal fluctuations effectively.

## Contribution

It introduces a theoretical framework and numerical simulations for optically measuring and actively cooling a strain-coupled oscillator via phase shift detection.

## Key findings

- Rapid reduction of cantilever's position and momentum uncertainty.
- Effective cooling towards a low-entropy, conditioned state.
- Feasibility of active feedback to eliminate thermal fluctuations.

## Abstract

We consider an optical probe that interacts with an ensemble of rare earth ions doping a materialin the shape of a cantilever. By optical spectral hole burning, the inhomogeneously broadenedtransition in the ions is prepared to transmit the probe field within a narrow window, but bendingof the cantilever causes strain in the material which shifts the ion resonances. The motion of thecantilever may thus be registered by the phase shift of the probe. By continuously measuringthe optical field we induce a rapid reduction of the position and momentum uncertainty of thecantilever. Doing so, the probing extracts entropy and thus effectively cools the thermal state ofmotion towards a known, conditional oscillatory motion with strongly reduced thermal fluctuations.Moreover, as the optical probe provides a force on the resonator proportional to its intensity, it ispossible to exploit the phase shift measurements in order to create an active feedback loop, whicheliminates the thermal fluctuations of the resonator. We describe this system theoretically, andprovide numerical simulations which demonstrate the rapid reduction in resonator position andmomentum uncertainty, as well as the implementation of the active cooling protocol.