Theory of Mechanical Displacement Measurement Using a Multiple Cavity Mode Transducer

Dobrindt, Jens M.; Kippenberg, Tobias J.

doi:10.1364/cleo.2010.jthe38

Cited by 2 publications

(3 citation statements)

References 3 publications

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“…The term 1 + 4Ω 2 /κ 2 is due to a less efficient transduction of the motion into phase shift for Fourier frequencies beyond the cavity cutoff (which can, in principle, be avoided using multiple cavity modes (Dobrindt and Kippenberg (2009))).…”

Section: Quantum Noisementioning

confidence: 99%

Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators

Schließer

Kippenberg

2010

Advances in Atomic, Molecular, and Optical Physics

114

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Parametric coupling of optical and mechanical degrees of freedom forms the basis of many ultra-sensitive measurements of both force and mechanical displacement. An optical cavity with a mechanically compliant boundary enhances the optomechanical interaction, which gives rise to qualitatively new behavior which can modify the dynamics of the mechanical motion. As early as 1967, in a pioneering work, V. Braginsky analyzed theoretically the role of radiation pressure in the interferometric measurement process, but it has remained experimentally unexplored for many decades. Here, we use whispering-gallery-mode optical microresonators to study these radiation pressure phenomena. Optical microresonators simultaneously host optical and mechanical modes, which are systematically analyzed and optimized to feature ultra-low mechanical dissipation, photon storage times exceeding the mechanical oscillation period (i.e. the "resolved-sideband regime") and large optomechanical coupling. In this manner, it is demonstrated for the first time that dynamical backaction can be employed to cool mechanical modes, i.e., to reduce their thermally excited random motion. Utilizing this novel technique together with cryogenic pre-cooling of the mechanical oscillator, the phonon occupation of mechanical radial-breathing modes could be reduced to n = 63 ± 20 excitation quanta. The corresponding displacement fluctuations are monitored interferometrically with a sensitivity at the level of 1 · 10 −18 m/ √ Hz, which is below the imprecision at the standard quantum limit (SQL). This implies that the readout is already in principle sufficient to measure the quantum mechanical zero-point position fluctuations of the mechanical mode. Moreover, it is shown that optical measurement techniques employed here are operating in a near-ideal manner according to the principles of quantum measurement, displaying a backaction-imprecision product close to the quantum limit.

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Section: Quantum Noisementioning

confidence: 99%

Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators

Schließer

Kippenberg

2010

Advances in Atomic, Molecular, and Optical Physics

114

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“…Spherical WGM resonators have been used to increase the frequency up to 1 GHz [7]. Further increase of the acoustic frequency is problematic because this opto-mechanical system includes one optical WGM and one mechanical mode, so the Q-factor of the optical mode must be low enough to accommodate both the pumping and the Stokes (reddetuned) waves, and lowering the Q-factor results in a reduction of the interaction efficiency.Higher frequency interaction accompanied by increased interaction efficiency is possible if the Stokes (or anti-Stokes) light is scattered to a different high-Q WGM [8,9]. Phase matching between optical and acoustic modes represents a major difficulty in this case.…”

mentioning

confidence: 99%

“…Higher frequency interaction accompanied by increased interaction efficiency is possible if the Stokes (or anti-Stokes) light is scattered to a different high-Q WGM [8,9]. Phase matching between optical and acoustic modes represents a major difficulty in this case.…”

mentioning

confidence: 99%

Optomechanics with Surface-Acoustic-Wave Whispering-Gallery Modes

Matsko¹,

Savchenkov²,

Ilchenko³

et al. 2009

Phys. Rev. Lett.

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A surface acoustic wave (SAW) creates its own high-Q ultra-small volume whispering gallery modes (WGMs), different from usual bulk acoustic WGMs, in an optical dielectric WGM resonator. We show that it is possible to realize an externally controllable, efficient triply-resonant opto-mechanical interaction between two optical WGMs and the SAW WGM and to use such an interaction in various sensor applications.The prediction of surface acoustic waves (SAWs) [1] and the study of whispering gallery modes (WGM) in acoustic resonators [2] are amongst numerous contributions of Lord Rayleigh, nee John William Strutt, to physics of waves. In the hundred or so years that followed the inception of these branches of acoustics, SAWs have been extensively studied and widely used in various electronic applications, particularly as sensors, oscillators, and filters. The notion of WGM resonators has been extended to photonics to serve as a tool in many applications in linear and nonlinear optics. With the advent of cavity opto-mechanics in recent years (see [3,4] for review) it is natural to ask if there is a way to devise a system where optical WGMs interact, or lead to, mechanical SAWs. At first glance it might be concluded that optical and SAW WGMs do not interact efficiently because SAWs do not change the volume of the resonator. In this work we describe a system of three WGMs in a dielectric resonator, whereby two optical modes combine to generate and control a mechanical SAW. The resulting acoustic wave is of extremely high quality factor (Q) and can be optically cooled to quantum level. Such a system, interesting from the scientific point of view, can have important applications in quantum technologies and will significantly enhance the sensitivity of SAW sensors. As an example of these applications, we describe a high sensitivity "absolute temperature" thermometer capable of operation outside the controlled environment of metrological laboratories.Opto-mechanics relies on interacting high-Q optical and mechanical modes [3,4] that can be used for manipulation of both classical and quantum states of the optical as well as mechanical modes. For instance, the dynamic back action of light onto a long lived mechanical mode of a resonator allows either a significant reduction of the mode temperature or an efficient transfer of the optical energy to the mechanical mode, depending on the experimental conditions. The temperature reduction results from conversion of thermal phonons populating the mechanical mode into optical domain, similar to the case of laser cooling in atomic systems. Hence cooling occurs when frequency of light increases as a result of interaction with the mechanical mode. Enforced decrease of frequency of the scattered light results in heating and oscillation of the mechanical mode.The basic practical task of cavity opto-mechanics is related to fabrication and integration of resonant micromechanical and optical elements, which interact efficiently. The efficiency of the interaction increases with an increase of ...

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Theory of Mechanical Displacement Measurement Using a Multiple Cavity Mode Transducer

Cited by 2 publications

References 3 publications

Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators

Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators

Optomechanics with Surface-Acoustic-Wave Whispering-Gallery Modes

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