Multimode optomechanical dynamics in a cavity with avoided crossings

Lee, D; Underwood, Mitchell; Mason, David; Shkarin, Alexey; Hoch, S. W.; Harris, Jack

doi:10.1038/ncomms7232

Cited by 83 publications

(70 citation statements)

References 44 publications

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“…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.…”

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confidence: 99%

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

et al. 2016

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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 ...

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Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

et al. 2016

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“…[5,6]. More broadly, the particular type of oscillator used here (a Si 3 N 4 membrane) has been shown to be well suited to a range of applications in quantum optomechanics [8,9,[20][21][22][23][24][25][26][27][28].In the experiments described here, both sidebands are produced by a single laser and are measured simultaneously. This is in contrast with most earlier experiments, in which the sidebands were produced using two separate drives applied at once [16,19] or at different times [17,13].…”

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Measurement of the motional sidebands of a nanogram-scale oscillator in the quantum regime

et al. 2015

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We describe measurements of the motional sidebands produced by a mechanical oscillator (with effective mass 43 ng and resonant frequency 705 kHz) that is placed in an optical cavity and cooled close to its quantum ground state. The red and blue sidebands (corresponding to Stokes and anti-Stokes scattering) from a single laser beam are recorded simultaneously via a heterodyne measurement. The oscillator's mean phonon numbern is inferred from the ratio of the sidebands, and reaches a minimum value of 0.84 ± 0.22 (corresponding to a mode temperature T = 28 ± 7 μK). We also infern from the calibrated area of each of the two sidebands, and from the oscillator's total damping. The values ofn inferred from these four methods are in close agreement. The behavior of the sidebands as a function of the oscillator's temperature agrees well with theory that includes the quantum fluctuations of both the cavity field and the mechanical oscillator. Cavity optomechanical systems operating in the quantum regime are expected to play an important role in advancing the control of electromagnetic fields and mechanical oscillators, interfacing disparate quantum systems, detecting gravitational waves, constraining modifications to orthodox quantum mechanics, and testing hypotheses about quantum gravity [1][2][3][4][5][6][7][8][9][10][11]. The utility of optomechanical systems in these areas reflects their particular combination of long relaxation times, unitary coupling to electromagnetic fields in the microwave and near-infrared domains, and access to the quantum behavior of massive objects.Optomechanical experiments have been based primarily on systems in which the mechanical oscillator and the cavity field are prepared in Gaussian states, couple weakly to each other at the quantum level (i.e., the bare optomechanical coupling rate g 0 is much less than the oscillator frequency ω m and the cavity damping rate κ), and are probed via linear measurements of the fields leaving the cavity. (Some optomechanics experiments have demonstrated nonlinear measurements of the cavity fields [12,13], although without resolving non-Gaussian behavior.) Within this paradigm of Gaussian states, weak coupling, and linear measurements, quantum effects can manifest themselves as apparent fluctuations of quantities which, according to classical mechanics, could be noiseless [14]. Depending on the specific type of measurement, these quantum fluctuations may be ascribed to the cavity field, the mechanical oscillator, or both [15,16].One such experiment is a heterodyne measurement of the light leaving an optomechanical cavity that is driven on resonance by a single laser. Classically, the thermal motion of the mechanical oscillator inside the cavity adds modulation sidebands to the laser beam. In the spectrum of the heterodyne signal, the area of these sidebands will be equal, and will be proportional to the oscillator's temperature.In the quantum treatment described in Refs. [15,16] of the same measurement, the heterodyne spectrum arises from four distinct c...

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“…Recent experiments have measured QOC in various optomechanical setups such as membrane in the middle set-up [28][29][30][31], atomic gases trapped in Fabry-Prot cavities [32], microdisk-cantilever systems [33], microsphere-nanostring systems [34], paddle nanocavities [35] and tunable photonic crystal Optomechanical Cavity [36,37]. Among all these schemes the tunable photonic crystal system enabled to yield the value of QOC of 245 Hz [36] and the recent advancement has pushed this limit to the order of kHz [37].…”

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Squeezing of the mechanical motion and beating 3 dB limit using dispersive optomechanical interactions

Sainadh

Kumar

2016

Journal of Modern Optics

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We study an optomechanical system consisting of an optical cavity and movable mirror coupled through dispersive linear optomechanical coupling (LOC) and quadratic optomechanical coupling(QOC). We work in the resolved side band limit with a high quality factor mechanical oscillator in a strong coupling regime. We show that the presence of QOC in the conventional optomechanical system (with LOC alone) modifies the mechanical oscillator's frequency and reduces the back-action effects on mechanical oscillator. As a result of this the fluctuations in mechanical oscillator can be suppressed below standard quantum limit thereby squeeze the mechanical motion of resonator. We also show that either of the quadratures can be squeezed depending on the sign of the QOC. With detailed numerical calculations and analytical approximation we show that in such systems, the 3 dB limit can be beaten.

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Multimode optomechanical dynamics in a cavity with avoided crossings

Cited by 83 publications

References 44 publications

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

Measurement of the motional sidebands of a nanogram-scale oscillator in the quantum regime

Squeezing of the mechanical motion and beating 3 dB limit using dispersive optomechanical interactions

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