Coherent scattering 2D cooling in levitated cavity optomechanics

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. Delić 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 $n_x+n_y\lesssim 1$ 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.

17 pages; 6 figures

References in corpus (3)

• Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion
• Observation of strong coupling between a micromechanical resonator and an optical cavity field
• Motional Quantum Ground State of a Levitated Nanoparticle from Room Temperature