Thermometry of levitated nanoparticles in a hybrid electro-optical trap

There have been recent rapid developments in stable trapping of levitated nanoparticles in high vacuum. Cooling of nanoparticles, from phonon occupancies of 107 down to 100 - 1000 phonons, have already been achieved by several groups. Prospects for quantum ground-state cooling seem extremely promising. Cavity-cooling without added stabilisation by feedback cooling remains challenging, but trapping at high vacuum in a cavity is now possible through the addition of a Paul trap. However, the Paul trap has been found to qualitatively modify the cavity output spectrum, with the latter acquiring an atypical 'split-sideband' structure, of different form from the displacement spectrum, and which depends on N, the optical well at which the particle localises. In the present work we investigate the N-dependence of the dynamics, in particular with respect to thermometry: we show that in strong cooling regions N 100 , the temperature may still be reliably inferred from the cavity output spectra. We also explain the N-dependence of the mechanical frequencies and optomechanical coupling showing that these may be accurately estimated. We present a simple 'fast-cavity' model for the cavity output and test all our findings against full numerical solutions of the nonlinear stochastic equations of motion for the system.