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Optics and Spectroscopy

Compensation of fluctuational back action and detection of mechanical squeezing in the regime of strongly detuned pumping of an optical displacement sensor

Sergey P. Vyatchanin, A. A. Demchenko

Published Apr 1, 2014• 0 citations
Publisher

Abstract

Measurement of the position of an oscillator by means of a Fabry-Perot resonator with one moving mirror (oscillator mass) pumped by a laser in the regime of strongly detuned pumping is analyzed. Compensation of fluctuational back action in the reflected wave is demonstrated. However, this does not allow overcoming the standard quantum limit due to the dynamic back action. Additionally, the possibility of detecting mechanical squeezing under parametric action on a mechanical oscillator is analyzed.

DOI
10.1134/s0030400x14040250

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Measurement of the position of an oscillator by means of a Fabry-Perot resonator with one moving mirror (oscillator mass) pumped by a laser in the regime of strongly detuned pumping is analyzed. Compensation of fluctuational back action in the reflected wave is demonstrated. However, this does not allow overcoming the standard quantum limit due to the dynamic back action. Additionally, the possibility of detecting mechanical squeezing under parametric action on a mechanical oscillator is analyzed.
We consider the simple model of measurement of mechanical oscillator position via Fabry-Pero cavity pumped by detuned laser (end mirror of cavity is mass of oscillator) in resolved sideband regime when laser is detuned from cavity's frequency by frequency of mechanical oscillator ±ωm\pmω_m±ωm​ and relaxation rate γγγ of cavity is small: γ≪ωmγ\ll ω_mγ≪ωm​. We demonstrate fluctuation back action cancellation in reflected wave. However, it does not allow to circumvent Standard Quantum Limit, the reason of it is the dynamic back action.
Summary form only given.We present an optomechanical system consisting of a Fabry-Perot cavity with a movable mirror, which has the essential features to allow the observation of quantum backaction in the measurement of a macroscopic system. The Fabry-Perot cavity consists of a rigid in-coupling mirror and a torsional oscillator fabricated from a highly polished silicon wafer. At cryogenic temperatures, the mechanical Q factor of the oscillator's torsional mode at 25 kHz exceeds 2/spl middot/10/sup 6/. The finesse of the cavity is /spl Ffr/=13,000, and a diode-pumped monolithic Nd:YAG laser is employed as laser source, with typical laser powers incident onto the cavity /spl sim/5 mW. The laser frequency is locked to the cavity, using a standard FM technique. The change in the cavity's length caused by the motion of the torsional oscillator is detected by reading out the error signal of the feedback loop at the oscillator's resonance frequency. The Brownian random motion of the oscillator at room temperature is shown. At cryogenic temperatures (4.5 K), we measured a rms displacement of /spl Delta/x=1.4/spl middot/10/sup -14/ m, in agreement with the theory of Brownian noise. We demonstrated the operation of the cryogenic high-finesse interferometric force sensor. With planned improvements of the finesse and a reduction of the laser's amplitude and phase noise, our sensor opens up the possibility of observing, for the first time, the standard quantum limit of position measurement in interferometry.
The structure of optimal receiver is discussed for optical sensor measuring a small displacement of probe mass. Due to nonlinear interaction of the field and the mirror, a reflected wave is in squeezed state (natural squeezing), two quadratures of which are correlated and therefore one can increase signal-to-noise ratio and overcome the SQL. A measurement procedure realizing such correlation processing of two quadratures is clarified. The required combination of quadratures can be produced via mixing of pump field reflected from the mirror with local oscillator phase modulated field in duel-detector homodyne scheme. Such measurement procedure could be useful not only for resonant bar gravitational detector but for laser longbase interferometric detectors as well.
The sensitivity of the displacement transducer pumped with a train of high-intensity laser pulses is estimated. Due to the multicomponent character of the pump a consideration of transformations of the signal and the noises between optical modes plays an important role in estimation of the potential sensitivity. An expression for the minimal detectable external classical force resembles those for the continuous wave pumping with substitution of the laser power by a time averaged power of pulsed laser. Possible scheme for back action noise compensation for such transducers is considered. For full suppression of back action noise the field of local oscillator has to be pulsed with the same time dependence as the pump field.
We study the quantum measurement of a cantilever using a parametrically coupled electromagnetic cavity which is driven at the two sidebands corresponding to the mechanical motion. This scheme, originally due to Braginsky et al (Braginsky V, Vorontsov Y I and Thorne K P 1980 Science 209 547), allows a back-action free measurement of one quadrature of the cantilever's motion, and hence the possibility of generating a squeezed state. We present a complete quantum theory of this system, and derive simple conditions on when the quantum limit on the added noise can be surpassed. We also study the conditional dynamics of the measurement, and discuss how such a scheme (when coupled with feedback) can be used to generate and detect squeezed states of the oscillator. Our results are relevant to experiments in optomechanics, and to experiments in quantum electromechanics employing stripline resonators coupled to mechanical resonators.
The sensitivity of the displacement transducer pumped with a train of high-intensity laser pulses is estimated. Due to the multicomponent character of the pump a consideration of transformations of the signal and the noises between optical modes plays an important role in estimation of the potential sensitivity. An expression for the minimal detectable external classical force resembles those for the continuous wave pumping with substitution of the laser power by a time-averaged power of pulsed laser. A possible scheme for back-action noise compensation for such transducers is considered. For full suppression of back-action noise the field of local oscillator has to be pulsed with the same time dependence as the pump field.