Coherent-scattering two-dimensional cooling in levitated cavity optomechanics
Marko Toroš, Uroš Delić, Fagin Hales, T. S. Monteiro
Abstract
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)]. 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 \nω \nx \n∼ \nω \ny \n and optomechanical couplings \ng \nx \n≃ \ng \ny \n—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 \nn \nx \n+ \nn \ny \n≲ \n1 \n at moderate vacuum ( \n10 \n− \n6 \n mbar) is possible in a “Goldilocks” zone bounded by \n√ \nκ \nΓ \n/ \n4 \n≲ \ng \nx \n, \ng \ny \n≲ \n∣ \n∣ \nω \nx \n− \nω \ny \n∣ \n∣ \n≲ \nκ \n, where one balances the need to suppress dark modes while avoiding far-detuning of either mode or low cooperativities, and \nκ \n ( \nΓ \n) is the cavity decay rate (motional heating rate). With strong-coupling regimes \ng \nx \n, \ng \ny \n≳ \nκ \n in view one must consider the genuine three-way hybridization between \nx \n, \ny \n 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.