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arXiv:gr-qc/0207075 · Classical and Quantum Gravity

Properties of a monolithic sapphire parametric transducer: prospects of measuring the standard quantum limit

Clayton R. Locke, Michael Edmund Tobar, Eugene N. Ivanov

Published Mar 19, 2002• 7 citations
arXivHTMLPDF

Abstract

To measure the standard quantum limit (SQL) a high quality transducer must be coupled to a high quality mechanical system. Due to its monolithic nature, the monolithic sapphire transducer (MST) has high quality factors for both types of resonances. Single loop suspension is shown to yield a mechanical quality factor of 6.10^8 at 4 K. From standard analysis we show the MST has the potential to measure noise fluctuations of the mechanical oscillator at the SQL. also, we point out a new way to determine if the transducer back action is quantum limited. We show that if the fluctuations are at the quantum limit, then the amplitude of the oscillation will be amplified by the ratio of the ringdown time to the measurement time, which is an inherently easier measurement.

DOI
10.1088/0264-9381/19/7/388

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To measure the standard quantum limit (SQL) a high quality transducer must be coupled to a high quality mechanical system. Due to its monolithic nature, the monolithic sapphire transducer (MST) has high quality factors for both types of resonances. Single loop suspension is shown to yield a mechanical quality factor of 6.10^8 at 4 K. From standard analysis we show the MST has the potential to measure noise fluctuations of the mechanical oscillator at the SQL. also, we point out a new way to determine if the transducer back action is quantum limited. We show that if the fluctuations are at the quantum limit, then the amplitude of the oscillation will be amplified by the ratio of the ringdown time to the measurement time, which is an inherently easier measurement.
The construction and operation of a high-quality factor microwave sapphire resonator transducer coupled to a 1 kHz niobium membrane acoustic oscillator are presented in this paper. A four-stage passive vibration isolation system was included in the design to permit the measurement of the transducer’s parametric properties. The isolation system was shown to sufficiently suppress mechanical noise above 100 Hz and an upper limit to the displacement sensitivity of the transducer was measured to be 3.0±0.6×10−16 m/√Hz. The parametric behavior of the transducer with a single pump readout was measured for several transducer configurations, and the results were found to be in good agreement with theory. The measurements presented here display for the first time the complete parametric behavior in a high electrical Q system, where the transducer’s bandwidth is less than the mechanical oscillator’s frequency. The high stability and low losses of our system may allow the transducer to be configured as a back-action evasion or quantum nondemolition device.
The high-sensitivity quantum detection of a resonant classical force acting on a quantum harmonic oscillator can be significantly improved by employing a resonant optical parametric transducer. This technique leverages the unique properties of parametric interactions to enhance the response of the measurement system while maintaining quantum-limited performance. We demonstrate that such a configuration not only enables quantum back-action evading (BAE) measurements, surpassing the Standard Quantum Limit (SQL) of sensitivity, it also provides a mechanism for noiseless amplification of the classical signal. The key to this enhancement lies in the ability of the parametric transducer to generate and separately measure the upper and lower modulation sidebands induced by the external force. By decoupling and analyzing these sidebands independently, the system becomes capable of amplifying the signal without introducing additional noise, effectively circumventing quantum measurement constraints.
An optomechanical sensor suitable for the study of quantum effects has been developed and characterized. The sensor reads out the vibrations of a microfabricated miniature silicon mechanical oscillator which forms one end mirror of a high finesse Fabry-P\'erot cavity. The mechanical quality factor is up to Q=300000Q=300000Q=300000 at 300 K and rises up to $Q=4\ifmmode\times\else\texttimes\fi{}{10}^{6}$ at 4 K. The thermal noise of the oscillator has been measured in the time and frequency domains at room temperature and at 4.5 K. The prospects for observing the standard quantum limit are discussed.
The quantum limit for resolution in force measurement using active interferometric optical transducer of displacement is proved to be less than the standard quantum limit (SQL) if one measures not the phase but a specially chosen quadrature amplitude in the output wave, squeezed by a mechanism of ponderomotive nonlinearity. Consideration of two types of active transducer having three-level atoms gain and parametric gain is given. Noises of spontaneous emission, fluctuations due to losses in mirrors and effect of radiative friction are taken into account.
In quantum mechanics, the Heisenberg uncertainty principle places a fundamental limit in the measurement precision for certain pairs of physical quantities, such as position and momentum, time and energy or amplitude and phase. Due to the Heisenberg uncertainty principle, any attempt to extract certain information from a quantum object would inevitably perturbitinanunpredictableway. This raises one question,"What is the precision limit in such quantum measurements?" The answer, standard quantum limit (SQL), has been obtained by Braginsky to figure out the fundamental quantum limits of displacement measurement in the context of gravitational wave detection. To circumvent the unavoidable quantum back-action from the priori measurement, quantum non-demolition measurement (QND) methods were introduced by Braginsky and Thorne. To surpass the SQL of the displacement measurement in an interferometer, one can measure only one quadrature of the mechanical motion while give up the information about the other canonically conjugated quadrature. Such measurements can be performed by periodic driving the mechanical oscillator, i.e. the back-action evading (BAE) measurement. Cavity optomechanics provides an ideal table-top platform for the testing of the quantum measurement theory. Mechanical oscillator is coupled to electromagnetic field via radiation pressure, which is enhanced by an optical micro-cavity. Over the last decade, laser cooling has enabled the preparation of mechanical oscillator in the ground state in both optical and microwave systems. BAE measurements of mechanical motion have been allowed in the microwave electromechanical systems, which led to the observations of mechanical squeezing and entanglement. However, despite the theoretical proposal almost 40 years ago, the sub-SQL measurements still remain elusive. This thesis reports our efforts approach the sub-SQL with a highly sideband-resolved silicon optomechanical crystal (OMC) in a 3He buffer gas environment at 2K. The OMC couples an optical mode at telecommunication wavelengths and a colocalized mechanical mode at GHz frequencies. The Helium3 buffer gas environment allows sufficient thermalization of the OMC despite the drastically decreased silicon thermal conductivity. We observe Floquet dynamics in motional sideband asymmetry measurement when employing multiple probe tones. The Floquet dynamics arises due to presence of Kerr-type nonlinearities and gives rise to an artificially modified motional sideband asymmetry, resulting from a synthetic gauge field among the Fourier modes. We demonstrate the first optical continuous two-tone backaction-evading measurement of a localized GHz frequency mechanical mode of silicon OMC close to the ground state by showing the transition from conventional sideband asymmetry to backaction-evading measurement. We discover a fundamental two-tone optomechanical instability and demonstrate its implications on the back-action evading measurement. Such instability imposes a fundamental limitation on other two-tone schemes, such as dissipative quantum mechanical squeezing. We demonstrate state-of-art laser sideband cooling of the mechanical motion to a mean thermal occupancy of 0.09 quantum, which is 7.4dB of the oscillator's zero-point energy and corresponds to 92% ground state probability. This also enables us to observe the dissipative mechanical squeezing below the zero-point motion for the first time with laser light.
The standard quantum limit (SQL) of a classical mechanical force detection results from quantum back action perturbing evolution of a mechanical system. In this paper we show that usage of a multidimensional optical transducer may enable a broadband quantum back action evading measurement. We study theoretically a corresponding technique of measurement of a resonant signal force acting on a linear mechanical oscillator coupled to a generic optical system with three optical modes with separation nearly equal to the mechanical frequency. The measurement is performed by optical pumping of the central optical mode and analyzing the light escaping the two other modes. By detecting optimal quadrature components of the optical modes and postprocessing the measurement results we are able to exclude the back action in a broad frequency band and characterize the force with sensitivity better than the SQL. We show that the proposed scheme is similar to the multidimensional system containing quantum-mechanics-free subsystems which can evade the SQL using the idea of the so-called negative mass [M. Tsang and C. M. Caves, Phys. Rev. X 2, 031016 (2012).].