Coherent-scattering two-dimensional cooling in levitated cavity optomechanics - Marko Toroš; Uroš Delić; Fagin Hales; Tania S. Monteiro (Physical Review Research, 2021)
The strong light-matter optomechanical coupling offered by coherent scattering set-ups have allowed the experimental realization of quantum ground-state cavity cooling of the axial motion of a levitated nanoparticle [U. Delić et al., Science 367, 892 (2020)SCIEAS0036-807510.1126/science.aba3993]. An appealing milestone is now quantum two-dimensional (2D) cooling of the full in-plane motion, in any direction in the transverse plane. By a simple adjustment of the trap polarization, one obtains two nearly equivalent modes, with similar frequencies ω_{x}∼ω_{y} and optomechanical couplings g_{x}≃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}≲1 at moderate vacuum (10^{−6} mbar) is possible in a “Goldilocks” zone bounded by sqrt[κΓ/4]≲g_{x},g_{y}≲|ω_{x}−ω_{y}|≲κ, where one balances the need to suppress dark modes while avoiding far-detuning of either mode or low cooperativities, and κ (Γ) is the cavity decay rate (motional heating rate). With strong-coupling regimes g_{x},g_{y}≳κ in view one must consider the genuine three-way hybridization 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.