Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

Abstract

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of matter. A nonlinear coupling offers access to rich new physics, in both the quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising of a nanosphere levitated and cooled in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere to millikelvin temperatures for indefinite periods of time in high vacuum. We observe cooling of the linear and non-linear motion, leading to a 10 5 fold reduction in phonon number np, attaining final occupancies of np = 100 − 1000. This work puts cavity cooling of a levitated object to the quantum ground-state firmly within reach.Cavity optomechanics, the cooling and coherent manipulation of mechanical oscillators using optical cavities, has undergone rapid progress in recent years [1], with many experimental milestones realized. These include cooling to the quantum level [2,3], optomechanically induced transparency (OMIT) [4], and the transduction [5][6][7] and squeezing [8] of light. These important processes are due to a linear light-matter interaction; linear in both the position of the oscillatorx and the amplitude of the optical fieldâ.Nonlinear optomechanical interactions open up a new range of applications which are so far largely unexplored. In principle, they allow quantum nondemolition (QND) measurements of energy and thus the possibility of monitoring quantum jumps in a macroscopic system [1,9]. They also offer the prospect of observing phonon quantum shot noise [10], nonlinear OMIT [11,12], and the preparation of macroscopic nonclassical states [13]. To achieve a nonlinear interaction one can use optical means, which require strong single-photon coupling to the mechanical system [11,12] but are a considerable experimental challenge. Nonlinearities can also arise from spatial, mechanical effects, by engineering, for example, a light-matter interaction of the form (â+â † )(G 1x +G 2x 2 ). Previous studies investigated the static shift in the cavity resonant frequency [9,14,15] or the quadratic optical spring effect [15] arising from a nonlinear coupling. However, these studies identified the problem of a residual linear G 1 contribution to the coupling. Not only can G 1 allow unwanted back-action, but a large G 2 1 contribution (e.g. [14]) can mask the signatures of true nonlinear G 2 coupling.In this work, we study a nanosphere levitated in a hybrid system formed from a Paul trap and an optical cavity [16] as shown in fig 1. The output of the cavity is used to access the linear and nonlinear dynamics of the particle. We are able to tune the G 1 : G 2 ratio to reach G 2 G 1 , isolating the true nonlinear dynamics. Further, due to the dynamic nature of this experiment, we are able to observe the cooling, in time, of the nonlinear contribution to motion. To ...

Arbitrary multimode Gaussian operations on mechanical cluster states

“…This will necessitate involving a non-Gaussian element in the network, whether taking advantage of a non-Gaussian measurement, a non-linear optomechanical dynamics, or an already prepared nonGaussian resource. Promisingly in this direction, it has been shown that opto-and electro-mechanical systems can intrinsically host non-linearities in various settings [33,36,76,77], and this possibility has been suggested for engineering non-Gaussian states, dynamics, and measurements [32,[78][79][80][81][82][83][84][85]. The latter could potentially be exploited to unlock the universality of computation and this shall be the topic of future work.…”

Imaging Correlations in Heterodyne Spectra for Quantum Displacement Sensing

“…The r-heterodyne technique may also have further practical applications for optomechanical systems with non-stationary cavity dynamics [26][27][28].…”

Millikelvin cooling of the center-of-mass motion of a levitated nanoparticle

“…The amplitude of the micromotion is proportional to the Paul trap voltage, the number of charges on the particle and the well number N. Cavity cooling of a nanoparticle in the hybrid trap has been demonstrated. 1,3 There are a number of important improvements that are required to reach the ground state. These include improvements in the Paul trap as well as the reduction of the major noise sources.…”

“…The particle-light coupling is highly nonlinear and both linear and quadratic couplings have been reported. 1 The particle micromotion in the Paul trap at the drive frequency ω d leads to some excursion of the particle away from the antinode where there is a non vanishing linear optomechanical coupling. The amplitude of the micromotion is proportional to the Paul trap voltage, the number of charges on the particle and the well number N. Cavity cooling of a nanoparticle in the hybrid trap has been demonstrated.…”