Coherent scattering 2D cooling in levitated cavity optomechanics

TL;DR

This paper explores the theoretical conditions and configurations for achieving efficient quantum 2D cooling of a levitated nanoparticle's in-plane motion using coherent scattering in cavity optomechanics, including optimal parameters and mode hybridization effects.

Contribution

It identifies optimal trap and cavity parameters for 2D cooling, analyzes mode hybridization effects, and provides a geometric interpretation of bright/dark modes in levitated cavity optomechanics.

Findings

Efficient 2D cooling to near ground state is achievable with specific trap ellipticity and cavity parameters.

Optimal cooling occurs within a 'Goldilocks' zone balancing coupling strength and mode detuning.

Hybridization of modes influences the cooling dynamics and sensing capabilities.

Abstract

The strong light-matter optomechanical coupling offered by Coherent Scattering (CS) set-ups have allowed the experimental realisation of quantum ground state cavity cooling of the axial motion of a levitated nanoparticle [U. Deli\'{c} et al., Science 367, 892 (2020)]. An appealing milestone is now quantum 2D cooling of the full in-plane motion, in any direction in the transverse plane. By a simple adjustment of the trap polarisation, one obtains two nearly equivalent modes, with similar frequencies $\omega_{x}\sim\omega_{y}$ and optomechanical couplings $g_{x}\simeq g_{y}$ -- in this experimental configuration we identify an optimal trap ellipticity, nanosphere size and cavity linewidth which allows for efficient 2D cooling. Moreover, we find that 2D cooling to occupancies $n_{x}+n_{y}\lesssim1$ at moderate vacuum ($10^{-6}$ mbar) is possible in a "Goldilocks" zone bounded by $\sqrt{\kappa\Gamma/4}\lesssim g_{x},g_{y}\lesssim|\omega_{x}-\omega_{y}|\lesssim\kappa$, where one balances the need to suppress dark modes whilst avoiding far-detuning of either mode or low cooperativities, and $\kappa$ ($\Gamma$) is the cavity decay rate (motional heating rate). With strong-coupling regimes $g_{x},g_{y}\gtrsim\kappa$ in view one must consider the genuine three-way hybridisation between $x$, $y$ and the cavity light mode resulting in hybridized bright/dark modes. Finally, we show that bright/dark modes in the levitated set-up have a simple geometrical interpretation, related by rotations in the transverse plane, with implications for directional sensing.