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arXiv:1304.6779 · Physical Review A

Optomechanical backaction-evading measurement without parametric instability

Steven Steinke, Keith Schwab, Pierre Meystre

Published Aug 21, 2013• 9 citations
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Abstract

We review a scheme for performing a backaction-evading measurement of one mechanical quadrature in an optomechanical setup. The experimental application of this scheme has been limited by parametric instabilities caused in general by a slight dependence of the mechanical frequency on the electromagnetic energy in the cavity. We find that a simple modification to the optical drive can effectively eliminate the parametric instability even at high intracavity power, allowing realistic devices to achieve sub-zero-point uncertainties in the measured quadrature.

DOI
10.1103/physreva.88.023838

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We review a scheme for performing a backaction-evading measurement of one mechanical quadrature in an optomechanical setup. The experimental application of this scheme has been limited by parametric instabilities caused in general by a slight dependence of the mechanical frequency on the electromagnetic energy in the cavity. We find that a simple modification to the optical drive can effectively eliminate the parametric instability even at high intracavity power, allowing realistic devices to achieve sub-zero-point uncertainties in the measured quadrature.
Quantum mechanics imposes a limit on the precision of a continuous position measurement of a harmonic oscillator, due to backaction arising from quantum fluctuations in the measurement field. This standard quantum limit can be surpassed by monitoring only one of the two non-commuting quadratures of the motion, known as backaction-evading measurement. This technique has not been implemented using optical interferometers to date. Here we demonstrate, in a cavity optomechanical system operating in the optical domain, a continuous two-tone backaction-evading measurement of a localized gigahertz-frequency mechanical mode of a photonic-crystal nanobeam cryogenically and optomechanically cooled close to the ground state. Employing quantum-limited optical heterodyne detection, we explicitly show the transition from conventional to backaction-evading measurement. We observe up to 0.67 dB (14%) reduction of total measurement noise, thereby demonstrating the viability of backaction-evading measurements in nanomechanical resonators for optical ultrasensitive measurements of motion and force.
Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intracavity squeezing, and optomechanical entanglement. We further apply an analogous analysis to the multimode optomechanical system of two mechanical and one cavity mode and find conditional mechanical Einstein-Podolski-Rosen entanglement and genuinely tripartite optomechanical entanglement. Our analysis is of direct relevance for ultrasensitive measurements and measurement-based control in high-cooperativity optomechanical sensors operating beyond the adiabatic limit.
Recently it has been demonstrated that the combination of continuous position detection with detuned parametric driving can lead to significant steady-state mechanical squeezing, far beyond the 3 dB limit normally associated with parametric driving. In this work, we show the close connection between this detuned scheme and quantum non-demolition (QND) measurement of a single mechanical quadrature. In particular, we show that applying an experimentally realistic detuned parametric drive to a cavity optomechanical system allows one to effectively realize a QND measurement despite being in the bad-cavity limit. In the limit of strong squeezing, we show that this scheme offers significant advantages over standard backaction evasion, not only by allowing operation in the weak measurement and low efficiency regimes, but also in terms of the purity of the mechanical state.
When measuring the position of a mechanical oscillator, quantum mechanics imposes a strict limit on the attainable precision: Any reduction of imprecision leads to increased quantum backaction of the measuring probe on the oscillator. This quantum limit can be circumvented, in principle allowing to indefinitely reduce imprecision, by monitoring only a single quadrature of the oscillator. Such backaction-evading measurement has been recently demonstrated in electromechanical oscillators coupled to microwave resonant circuits. Here we demonstrate this technique in a photonic crystal nanomechanical oscillator, cryogenically and optomechanically cooled to a few quanta.
We study theoretically a three-mode optomechanical system where two mechanical oscillators are coupled to a single cavity mode. By using two-tone (i.e., amplitude-modulated) driving of the cavity, it is possible to couple the cavity to a single collective quadrature of the mechanical oscillators. In such a way, a back-action-evading measurement of the collective mechanical quadrature is possible. We discuss how this can allow one to measure both quadratures of a mechanical force beyond the full quantum limit, paying close attention to the role of dissipation and experimental imperfections. We also describe how this scheme allows one to generate steady-state mechanical entanglement; namely, one can conditionally prepare an entangled, two-mode squeezed mechanical state. This entanglement can be verified directly from the measurement record by applying a generalized version of Duan's inequality; we also discuss how feedback can be used to produce unconditional entanglement.
We present the exact analytical solution of the explicitly time-periodic quantum Langevin equation describing the dual-beam backaction-evading measurement of a single mechanical oscillator quadrature due to V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne [Science 209, 547 (1980)] beyond the commonly used rotating-wave approximation. We show that counterrotating terms lead to extra sidebands in the optical and mechanical spectra and to a modification of the main peak. Physically, the backaction of the measurement is due to periodic coupling of the mechanical resonator to a light-field quadrature that only contains cavity-filtered shot noise. Since this fact is independent of other degrees of freedom the resonator might be coupled to, our solution can be generalized, including to dissipatively or parametrically squeezed oscillators, as well as recent two-mode backaction-evading measurements.