Dispersive optomechanics: a membrane inside a cavity

Jayich, A. M.; Sankey, J. C.; Zwickl, Benjamin M.; Yang, Cheng; Thompson, J. D.; Girvin, S. M.; Clerk, Aashish A.; Marquardt, Florian; Harris, Jack

doi:10.1088/1367-2630/10/9/095008

Cited by 409 publications

(536 citation statements)

References 37 publications

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“…Recently, the Yale group of Jack Harris introduced a novel optomechanical setup Jayich et al, 2008), where a thin dielectric membrane is placed in the middle of a cavity with two fixed, high finesse mirrors. Beside the technological advances offered by this setup, it also leads to a different coupling of the mechanical displacement of the oscillating membrane to the cavity, which is advantageous for the aim of Fock state detection.…”

Section: Towards Fock-state Detectionmentioning

confidence: 99%

Optomechanics

Kubala¹,

Ludwig²,

Marquardt³

2009

NATO Science for Peace and Security Series B: Physics and Biophysics

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Section: Towards Fock-state Detectionmentioning

confidence: 99%

Optomechanics

Kubala¹,

Ludwig²,

Marquardt³

2009

NATO Science for Peace and Security Series B: Physics and Biophysics

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“…Measuring an appropriate quadrature of the output light field, we would get fewer fluctuations than that of the vacuum state, which makes it possible to detect weak forces far below the SQL. Furthermore, since we pump and probe different resonant optical modes, the effective optomechanical coupling is enhanced, and thus the pump power requirement for achieving the best sensitivity is lowered substantially.We consider a high finesse Fabry-Perot cavity with a dielectric mirror in the middle [17,18] [ Fig. 1(a)].…”

mentioning

confidence: 99%

“…The middle mirror has a nonzero transmission, which allows the exchange of light between these two subcavities and thus leads to an effective coupling between the left and right cavity modes [19]. Further, the coupling will shift the resonant frequencies of two coupled cavity modes and leads to the so-called normal mode splitting effect [20,21].Following [18,22], the normal mode splitting in the presence of the middle mirror can be calculated by assuming a transfer matrix with a high reflectivity r d . For simplicity, we assuming the middle membrane to be exactly at the middle point of the FP cavity initially, dividing the cavity into two subcavities with the same length L, and the normal mode splitting when the middle mirror is at a new position x is given by Ω = c L arccos(|r d | cos(2kx)) [ Fig.…”

mentioning

confidence: 99%

“…We consider a high finesse Fabry-Perot cavity with a dielectric mirror in the middle [17,18] [ Fig. 1(a)].…”

mentioning

confidence: 99%

“…Following [18,22], the normal mode splitting in the presence of the middle mirror can be calculated by assuming a transfer matrix with a high reflectivity r d . For simplicity, we assuming the middle membrane to be exactly at the middle point of the FP cavity initially, dividing the cavity into two subcavities with the same length L, and the normal mode splitting when the middle mirror is at a new position x is given by Ω = c L arccos(|r d | cos(2kx)) [ Fig.…”

mentioning

confidence: 99%

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Squeezing in a coupled two-mode optomechanical system for force sensing below the standard quantum limit

Taylor

2014

Phys. Rev. A

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Optomechanics allows the transduction of weak forces to optical fields, with many efforts approaching the standard quantum limit. We consider force-sensing using a mirror-in-the-middle setup and use two coupled cavity modes originated from normal mode splitting for separating pump and probe fields. We find that this two-mode model can be reduced to an effective single-mode model, if we drive the pump mode strongly and detect the signal from the weak probe mode. The optimal force detection sensitivity at zero frequency (DC) is calculated and we show that one can beat the standard quantum limit by driving the cavity close to instability. The best sensitivity achievable is limited by mechanical thermal noise and by optical losses. We also find that the bandwidth where optimal sensitivity is maintained is proportional to the cavity damping in the resolved sideband regime. Finally, the squeezing spectrum of the output signal is calculated, and it shows almost perfect squeezing at DC is possible by using a high quality factor and low thermal phonon-number mechanical oscillator.Dramatic progress in coupling mechanics to light [1][2][3][4] suggests that such devices may be used in a wide variety of settings to explore quantum effects in macroscopic systems. Furthermore, such systems can be exquisitely sensitive to small perturbations, such as forces induced either by acceleration as in accelerometer [5] or by, e.g., coupling to surfaces or fields as in atomic force microscopy [6]. For such force measurements, a high quality factor (Q) mechanical oscillator acts as a test mass, transducing a force into a time-dependent displacement of the oscillator [7,8]. By using interferometric techniques to monitor the position of the oscillator, one can infer the force via optical signals. However, the radiation pressure coupling between the mechanical mode and optical mode has three consequences: photon shot noise, quantum backaction and dynamical backaction [1,9]. The dynamical backaction modifies the oscillator dynamics [10] and makes laser cooling [11,12] or amplification of phonons [13] in the mechanical system possible. Photon shot noise and quantum backaction, the former decreases with increasing input laser power while the latter increases with increasing input laser power, introduce two sources of noise on the displacement readout of the oscillator motion. An optimal compromise between these two noise sources leads to the standard quantum limit (SQL) in force sensing [7].The SQL, however, is itself not a fundamental limit. By using squeezed states of light [14], employing quantum nondemolition (QND) measurement [15], or by cavity detuning [16], the SQL can be surpassed. Here we show that in a coupled two-mode optomechanical system, if we drive it appropriately, the interaction between cavity photons and the mechanical oscillator will generate squeezed states of the output light. Measuring an appropriate quadrature of the output light field, we would get fewer fluctuations than that of the vacuum state, which makes it possib...

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A short walk through quantum optomechanics

Meystre¹

2012

Annalen der Physik

408

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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Dispersive optomechanics: a membrane inside a cavity

Cited by 409 publications

References 37 publications

Optomechanics

Optomechanics

Squeezing in a coupled two-mode optomechanical system for force sensing below the standard quantum limit

A short walk through quantum optomechanics

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