Quantum displacement sensing and cooling in 3D levitated cavity optomechanics

TL;DR

This paper explores 3D quantum displacement sensing and cooling in levitated cavity optomechanics, revealing hybridisation effects and interference phenomena that influence ground-state cooling and sensing capabilities.

Contribution

It demonstrates that 3D hybridisation effects are crucial in levitated nanoparticle optomechanics and introduces a sympathetic cooling mechanism to enhance mode cooling.

Findings

Hybridisation effects significantly impact 3D cooling and sensing.

Interference can suppress or enhance 3D effects near the SQL.

Sympathetic cooling improves weakly coupled mode cooling.

Abstract

Ultra-high sensitivity detection of quantum-scale displacements in cavity optomechanics optimises the combined errors from measurement back-action and imprecisions from incoming quantum noises. This sets the well-known Standard Quantum Limit (SQL). Normal quantum cavity optomechanics allows cooling and detection of a single degree of freedom, along the cavity axis. However, a recent breakthrough that allows quantum ground-state cooling of levitated nanoparticles [Delic et al, arxiv:1911.04406], is uniquely 3D in character, with coupling along the $x$, $y$ and $z$ axes. We investigate current experiments and show that the underlying behaviour is far from the addition of independent 1D components and that ground-state cooling and sensing analysis must consider- to date neglected- 3D hybridisation effects. We characterise the additional 3D spectral contributions and find direct and indirect hybridising pathways can destructively interfere suppressing of 3D effects at certain parameters in order to approach, and possibly surpass, the SQL. We identify a sympathetic cooling mechanism that can enhance cooling of weaker coupled modes, arising from optomechanically induced correlations.