Cooling and squeezing via quadratic optomechanical coupling

Nunnenkamp, Andreas; Børkje, Kjetil; Harris, Jack; Girvin, S. M.

doi:10.1103/physreva.82.021806

Cited by 247 publications

(254 citation statements)

References 36 publications

(62 reference statements)

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“…This is what we expect for the PSD of the squared displacement [5,9], the physical meaning of which will become more apparent when we look at the quantum case in Section VI B.…”

Section: A Classicalmentioning

confidence: 87%

“…(2) provides a good approximation for the solution of the damped harmonic oscillator given by Eq. (5). From this point forward, we will assume we are in the small damping limit, as this is the case of interest for most nanomechanical systems.…”

Section: B Classical Damped Harmonic Oscillatormentioning

confidence: 99%

“…However, there are situations where it is useful to measure the square of the position directly [3,[5][6][7][8], in which case we need to consider the second-order PSD for the oscillator. In this section, we shall determine this quadratic PSD for both the quantum and classical cases.…”

Section: Second-order Power Spectral Densitymentioning

confidence: 99%

“…For moderate coupling, a simple linear model suffices, such that monitoring the * Electronic address: bhauer@ualberta.ca † Electronic address: jdavis@ualberta.ca electromagnetic field provides a readout of the linear motion of the oscillating mechanical device. However, as the interaction strength between the two systems increases, nonlinear coupling begins to occur, requiring that higherorder terms be added to the Hamiltonian [3][4][5][6][7][8][9]. This provides a method by which one can obtain direct access to higher-order powers of the mechanical resonator's motion.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, a number of experiments have demonstrated direct coupling to the square of the oscillator's displacement [3,4,[9][10][11]. These types of measurements have generated significant interest, as they have been proposed as a method to perform quantum nondemolition (QND) measurements [12,13] of a mesoscopic quantum system [2,3,6,[14][15][16][17], as well as other exotic two-phonon processes, such as mechanical cooling/squeezing [5] and optomechanically induced transparency [7,8].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear power spectral densities for the harmonic oscillator

2015

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In this paper, we discuss a general procedure by which nonlinear power spectral densities (PSDs) of the harmonic oscillator can be calculated in both the quantum and classical regimes. We begin with an introduction of the damped and undamped classical harmonic oscillator, followed by an overview of the quantum mechanical description of this system. A brief review of both the classical and quantum autocorrelation functions (ACFs) and PSDs follow. We then introduce a general method by which the kth-order PSD for the harmonic oscillator can be calculated, where k is any positive integer. This formulation is verified by first reproducing the known results for the k = 1 case of the linear PSD. It is then extended to calculate the second-order PSD, useful in the field of quantum measurement, corresponding to the k = 2 case of the generalized method. In this process, damping is included into each of the quantum linear and quadratic PSDs, producing realistic models for the PSDs found in experiment. These quantum PSDs are shown to obey the correspondence principle by matching with what was calculated for their classical counterparts in the high temperature, high-Q limit. Finally, we demonstrate that our results can be reproduced using the fluctuation-dissipation theorem, providing an independent check of our resultant PSDs.

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“…This is what we expect for the PSD of the squared displacement [5,9], the physical meaning of which will become more apparent when we look at the quantum case in Section VI B.…”

Section: A Classicalmentioning

confidence: 87%

Section: B Classical Damped Harmonic Oscillatormentioning

confidence: 99%

Section: Second-order Power Spectral Densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear power spectral densities for the harmonic oscillator

2015

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A short walk through quantum optomechanics

Meystre¹

2012

Annalen der Physik

397

361

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A short walk through quantum optomechanics P. MeystreThis paper gives an brief review of the basic physics of quantum optomechanics and provides an overview of some of its recent developments and current areas of focus. It first outlines the basic theory of cavity optomechanical cooling and gives a brief status report of the experimental state-of-the-art. It then turns to the deep quantum regime of operation of optomechanical oscillators and cover selected aspects of quantum state preparation, control and characterization, including mechanical squeezing and pulsed optomechanics. This is followed by a discussion of the "bottom-up" approach that exploits ultracold atomic samples instead of nanoscale systems. It concludes with an outlook that concentrates largely on the functionalization of quantum optomechanical systems and their promise in metrology applications. IntroductionBroadly speaking, quantum optomechanics provides a universal tool to achieve the quantum control of mechanical motion [1]. It does that in devices spanning a vast range of parameters, with mechanical frequencies from a few Hertz to GHz, and with masses from 10 −20 g to several kilos. At a fundamental level, it offers a route to determine and control the quantum state of truly macroscopic objects and paves the way to experiments that may lead to a more profound understanding of quantum mechanics; and from the point of view of applications, quantum optomechanical techniques in both the optical and microwave regimes will provide motion and force detection near the fundamental limit imposed by quantum mechanics. While many of the underlying ideas of quantum optomechanics can be traced back to the study of gravitational wave detectors in the 1970s and 1980s [2,3], the spectacular developments of the last few years rely largely on two additional developments: From the top down, it is the availability of advanced micromechanical and nanomechanical devices capable of probing extremely tiny forces, often with spatial resolution at the atomic scale. And from the bottom-up, we have gained a detailed understanding of the mechanical effects of light and how they can be exploited in laser trapping and cooling. These developments open a path to the realization of macroscopic mechanical systems that operate deep in the quantum regime, with no significant thermal noise remaining.As a result, they offer both knowledge and control of the quantum state of a macroscopic object, and increased sensitivity, precision, and accuracy in the measurement of feeble forces and fields.It was Arthur Ashkin [4] who first suggested and demonstrated that small dielectric balls can be accelerated and trapped using the radiation-pressure forces associated with focused laser beams. In later experiments these particles, weighting on the order of a microgram, were levitated against the Earth gravitational field. This advance led to the realization of optical tweezers, whose applications in biological science have become ubiquitous. In parallel, the use of the strong enhancement prov...

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Quantum synchronization of two Van der Pol oscillators

2014

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We study synchronization of two dissipatively coupled Van der Pol oscillators in the quantum regime. Due to quantum noise strict frequency locking is absent and is replaced by a crossover from weak to strong frequency entrainment. We discuss the differences to the behavior of one quantum Van der Pol oscillator subject to an external drive. Moreover, we describe a possible experimental realization of two coupled quantum van der Pol oscillators in an optomechanical setting.

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Cooling and squeezing via quadratic optomechanical coupling

Cited by 247 publications

References 36 publications

Nonlinear power spectral densities for the harmonic oscillator

Nonlinear power spectral densities for the harmonic oscillator

A short walk through quantum optomechanics

Quantum synchronization of two Van der Pol oscillators

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