Split-sideband spectroscopy in slowly modulated optomechanics

Optomechanical coupling between the motion of a mechanical oscillator and a cavity represents a new arena for experimental investigation of quantum effects on the mesoscopic and macroscopic scale. The motional sidebands of the output of a cavity offer ultra-sensitive probes of the dynamics. We introduce a scheme whereby these sidebands split asymmetrically and show how they may be used as experimental diagnostics and signatures of quantum noise limited dynamics. We show split-sidebands with controllable asymmetry occur by simultaneously modulating the light-mechanical coupling g and the mechanical frequency, ${\omega }_{{\rm{M}}}$—slowly and out-of-phase. Such modulations are generic but already occur in optically trapped set-ups where the equilibrium point of the oscillator is varied cyclically. We analyse recently observed, but overlooked, experimental split-sideband asymmetries; although not yet in the quantum regime, the data suggests that split sideband structures are easily accessible to future experiments

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

Cavity cooling a single charged nanoparticle

The development of laser cooling coupled with the ability to trap atoms and ions in electromagnetic fields, has revolutionised atomic and optical physics, leading to the development of atomic clocks, high-resolution spectroscopy and applications in quantum simulation and processing. However, complex systems, such as large molecules and nanoparticles, lack the simple internal resonances required for laser cooling. Here we report on a hybrid scheme that uses the external resonance of an optical cavity, combined with radio frequency (RF) fields, to trap and cool a single charged nanoparticle. An RF Paul trap allows confinement in vacuum, avoiding instabilities that arise from optical fields alone, and crucially actively participates in the cooling process. This system offers great promise for cooling and trapping a wide range of complex charged particles with applications in precision force sensing, mass spectrometry, exploration of quantum mechanics at large mass scales and the possibility of creating large quantum superpositions

Nonlinear dynamics and strong cavity cooling of levitated nanoparticles

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment