Aranas, Erika B.; (2018) Levitated optomechanics with periodically driven fields. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Levitated optomechanics offers a route to high-Q, low frequency oscillators by all-optical trapping in high vacuum, although progress has been hampered by particle loss at ∼ 1 mbar. Combining an optical cavity with a Paul trap yielded promising results, showing stable trapping and strong cavity cooling of 200 nm silica nanoparticles up to ∼ 10−5−10−6 mbar, in addition to interesting nonlinear effects. However, the time-periodic fields of the Paul trap gave rise to atypical “split-sideband” spectra which we found to be correlated with the cooling dynamics of the nanoparticle: twin peaks around the mechanical frequency plus a dominant signal at the second harmonic indicated weak cooling, while a complete suppression of one of the split-sidebands showed strong cooling. Presented first in this thesis are the analytical and numerical models used to describe the dynamics of a nanoparticle in a hybrid electro-optical trap. The split-sideband spectra is a result of simultaneous, outof-phase oscillations in g and ωM, and is, in fact, a generic feature of any optically trapped particle where an auxiliary field causes a harmonic excursion in the equilibrium position. Split-sideband asymmetry and thermometry are further discussed for a generic, doublymodulated optomechanical system. A suitably normalised cavity output probing a splitdisplacement spectra still gives the correct steady-state temperature. Analytical formulas are also derived for the complete split-sideband suppression, which may offer additional diagnostic of the quantum regime. Finally, a matrix algorithm to accurately calculate the measured quantum spectra of linear optomechanical systems with arbitrary periodicity is devised to verify the results obtained thus far. In addition, the algorithm allows a systematic calculation of the non-stationary components of the spectra, which are usually averaged out, but are shown to be experimentally accessible via heterodyne detection. In summary, this thesis aims to contribute to the analysis of levitated optomechanics with periodically driven fields, motivated in part by modelling the hybrid electro-optical experiments in UCL.

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