Observation and Interpretation of Motional Sideband Asymmetry in a Quantum Electromechanical Device

Weinstein, A. J.; Lei, Chan U; Wollman, Emma E.; Suh, Junho; Metelmann, A.; Clerk, Aashish A.; Schwab, Keith

doi:10.1103/physrevx.4.041003

Cited by 100 publications

(199 citation statements)

References 25 publications

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“…In the context of optomechanics, these processes are strongly tied to Stokes/anti-Stokes Raman scattering whereby phonons can be created/annihilated via interaction with cavity photons [2]. Furthermore, the asymmetry of these peaks leads to distinctly non-classical effects at low phonon number, such as motional sideband asymmetry, which has recently been observed experimentally [23,31].…”

Section: B Quantummentioning

confidence: 99%

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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Section: B Quantummentioning

confidence: 99%

Nonlinear power spectral densities for the harmonic oscillator

2015

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“…In a heterodyne detector, they manifest as motional sideband asymmetry [304][305][306][307]. Differences between these effects arise from the details of how meter fluctuations are converted to a classical signal by the detection process [145,305,308,309].…”

Section: Quantum Correlations In Measurement-based Controlmentioning

confidence: 99%

“…Cross-correlations observed using linear detectors (linear optomechanical interaction followed by linear detection of the optical field) do not involve any contribution from the vacuum fluctuations of the mechanical oscillator [305,315].…”

Section: Origin Of Sideband Asymmetrymentioning

confidence: 99%

“…Firstly, characteristic of linear detection, deviation of R from unity in the ideal case (C qq = 0 = C pp ) is due to correlations developed between the quantum-back-action driven mechanical motion and the detection process [305,318]. When C qq and C pp are finite, classical correlations are established that affect R. The response of the cavity (for Δ/κ ≈ 0) ensures that excess classical correlations due to input amplitude noise lead to an enhanced asymmetry, whereas those arising from input phase noise lead to a common increase in the sideband noise power.…”

Section: Origin Of Sideband Asymmetrymentioning

confidence: 99%

“…Note that we explicitly "tag" the commutator so as to follow its contribution to the measured quantities [305]; in reality ε a = 1.…”

Section: Contribution Of Excess Noise For Resonant Probingmentioning

confidence: 99%

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Quantum Limits on Measurement and Control of a Mechanical Oscillator

Sudhir

2018

Springer Theses

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PAR Vivishek SUDHIR JOSEPH CONRAD, Heart of DarknessExperimental physics demands a certain degree of manual dexterity, the patience to tolerate the mundane, and an inexhaustible supply of optimism. Tobias hired me to work on an immensely sophisticated experiment despite any proof of my possessing these qualities; I am indebted to him for the belief he has placed in me. I would also like to acknowledge his dedication to fostering an environment where the pursuit of science is unencumbered by other worldly concerns. Stefan, Ewold and Samuel bore the brunt of a theorist trying to perform delicate experiments; the stern, yet encouraging, stewardship of this trio ensured that I enjoyed the culture shock. Dal Wilson was more than a colleague and a post-doc; his pragmatic approach to physics provided the ideal counter-point in our attempts to forge a deeper understanding of things ranging from vibration isolation to the subtleties of quantum mechanics. Without the patient efforts of Amir, Ryan and Hendrik in designing, fabricating, and testing of devices, none of the results reported here would have been possible. I hope I have been able to bequeath a better vision of the future of our experiment to Sergey. Conversations with Alexey, Daniel and Nathan have enabled me to vicariously learn how to measure microwave "photons". John Jost once taught me how to decorate a Christmas tree; since then he has imparted some wisdom on frequency metrology, and some on atomic physics. Together with Dal, Victor and Caroline have probably spent the most time with me outside the lab; it was fun to exercise an air of social normalcy with this bunch. Christophe has been an amazing sparring partner on every subject capable of being brought under scientific scrutiny.The personal space required for the pursuit of science comes through the sacrifice of many people. My family back home in India -parents, sister, grand-parents -have had to patiently wait for the brief interludes when I go home. No words can do justice to this and the very many other pleasures they have surrendered over the years for my sake. Before physics attracted me, I was charmed by someone else; I am lucky to have married her. Long time friends, mentorsAjith and Subeesh -have played pivotal roles in my being able to engage in physics; I hope to repay this enormous debt, some day.It was a privilege to have learnt from a few great teachers during my formative years. Their vision of an indelible unity in nature continues to motivate my study of physics. vii AbstractThe precision measurement of position has a long-standing tradition in physics. Cavendish's verification of the universal law of gravitation using a torsion pendulum, Perrin's confirmation of the atomic hypothesis via the precise measurement of the Brownian motion, and, the verification of the mechanical effect of electromagnetic radiation, all belong to this classical heritage. Quantum mechanics posits that the measurement of position results in an uncertain momentum; an idea developed to full maturity within the ...

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Sideband cooling beyond the quantum backaction limit with squeezed light

Clark

Lecocq

Simmonds

et al. 2017

Nature

267

205

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Quantum fluctuations of the electromagnetic vacuum produce measurable physical effects such as Casimir forces and the Lamb shift [1]. Similarly, these fluctuations also impose an observable quantum limit to the lowest temperatures that can be reached with conventional laser cooling techniques [2,3]. As laser cooling experiments continue to bring massive mechanical systems to unprecedented temperatures [4,5], this quantum limit takes on increasingly greater practical importance in the laboratory [6]. Fortunately, vacuum fluctuations are not immutable, and can be "squeezed" through the generation of entangled photon pairs. Here we propose and experimentally demonstrate that squeezed light can be used to sideband cool the motion of a macroscopic mechanical object below the quantum limit. To do so, we first cool a microwave cavity optomechanical system with a coherent state of light to within 15% of this limit. We then cool by more than 2 dB below the quantum limit using a squeezed microwave field generated by a Josephson Parametric Amplifier (JPA). From heterodyne spectroscopy of the mechanical sidebands, we measure a minimum thermal occupancy of 0.19 ± 0.01 phonons. With this novel technique, even low frequency mechanical oscillators can in principle be cooled arbitrarily close to the motional ground state, enabling the exploration of quantum physics in larger, more massive systems.Rapid progress in the control and measurement of massive mechanical oscillators has enabled tests of fundamental physics, as well as applications in sensing and quantum information processing [7]. The noise performance of these experiments, however, is often limited by thermal motion of the mechanical mode. Although the most sophisticated refrigeration technologies can be sufficient for cooling high frequency mechanical structures to the ground state [8,9], observing quantum behavior in lower frequency mechanical systems requires other cooling methods. Recent efforts using active quantum feedback have been remarkably successful in preparing motional states with low entropies [10]. Thus far, however, only laser cooling techniques similar to those that revolutionized the coherent control of atomic systems [11,12] have yielded thermal occupancies below one quantum [4][5][6]. Nevertheless, vacuum fluctuations impose a lowest possible temperature that can be achieved using these techniques [2,3]. This limit is now being encountered in state of the art experiments involving macroscopic oscillators [6].The concept of sideband cooling relies on the removal of mechanical energy by scattering incident drive photons to higher frequencies. In general, however, this photon up-conversion (anti-Stokes) process competes with a downconversion (Stokes) process that adds energy to the mechanical system. In cavity optomechanics [7], a light-matter interaction arises due to a parametric modulation of an optical cavity's resonance frequency with a mechanical oscillator's position. When the cavity is driven at detuning ∆ below its resonance frequency, the dif...

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Observation and Interpretation of Motional Sideband Asymmetry in a Quantum Electromechanical Device

Cited by 100 publications

References 25 publications

Nonlinear power spectral densities for the harmonic oscillator

Nonlinear power spectral densities for the harmonic oscillator

Quantum Limits on Measurement and Control of a Mechanical Oscillator

Sideband cooling beyond the quantum backaction limit with squeezed light

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