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Some predictions of quantum mechanics are in contrast with the macroscopic realm of everyday experience, in particular those originated by the Heisenberg uncertainty principle, encoded in the non-commutativity of some measurable operators. Nonetheless, in the last decade opto-mechanical experiments have actualized macroscopic mechanical oscillators exhibiting such non-classical properties. A key indicator is the asymmetry in the strength of the motional sidebands generated in an electromagnetic field that measures interferometrically the oscillator position. This asymmetry is a footprint of the quantum motion of the oscillator, being originated by the non-commutativity between its ladder operators. A further step on the path highlighting the quantum physics of macroscopic systems is the realization of strongly non-classical states and the consequent observation of a distinct quantum behavior. Here we extend indeed the analysis to a squeezed state of a macroscopic mechanical oscillator embedded in an optical cavity, produced by parametric effect originated by a suitable combination of optical fields. The motional sidebands assume a peculiar shape, related to the modified system dynamics, with asymmetric features revealing and quantifying the quantum component of the squeezed oscillator motion.
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We experimentally investigate a mechanical squeezed state realized in a parametrically-modulated membrane resonator embedded in an optical cavity. We demonstrate that a quantum characteristic of the squeezed dynamics can be revealed and quantified even in a moderately warm oscillator, through the analysis of motional sidebands. We provide a theoretical framework for quantitatively interpreting the observations and present an extended comparison with the experiment. A notable result is that the spectral shape of each motional sideband provides a clear signature of a quantum mechanical squeezed state without the necessity of absolute calibrations, in particular in the regime where residual fluctuations in the squeezed quadrature are reduced below the zero-point level.
Quantum enhanced sensing is a powerful technique in which nonclassical states are used to improve the sensitivity of a measurement. For enhanced mechanical displacement sensing, squeezed states of light have been shown to reduce the photon counting noise that limits the measurement noise floor. It has long been predicted, however, that suppressing the noise floor with squeezed light should produce an unavoidable increase in radiation pressure noise that drives the mechanical system. Such nonclassical radiation pressure forces have thus far been hidden by insufficient measurement strengths and residual thermal mechanical motion. Since the ultimate measurement sensitivity relies on the delicate balance between these two noise sources, the limits of the quantum enhancement have not been observed. Using a microwave cavity optomechanical system, we observe the nonclassical radiation pressure noise that necessarily accompanies any quantum enhancement of the measurement precision. By varying both the magnitude and phase of the squeezing, we optimize the fundamental trade-off between mechanical imprecision and backaction noise in accordance with the Heisenberg uncertainty principle. As the strength of the measurement is further increased, radiation pressure forces eventually dominate the mechanical motion. In this regime, the optomechanical interaction can be exploited as an efficient quantum nondemolition (QND) measurement of the amplitude fluctuations of the light field. By overwhelming mechanical thermal noise with radiation pressure by two orders of magnitude, we demonstrate a mechanically-mediated measurement of the squeezing with an effective homodyne efficiency of 94%. Thus, with strong radiation pressures forces, mechanical motion enhances the measurement of nonclassical light, just as nonclassical light enhances the measurement of the motion.
We propose a protocol for coherently transferring non-Gaussian quantum states from optical field to a mechanical oscillator. The open quantum dynamics and continuous-measurement process, which can not be treated by the stochastic-master-equation formalism, are studied by a new path-integral-based approach. We obtain an elegant relation between the quantum state of the mechanical oscillator and that of the optical field, which is valid for general linear quantum dynamics. We demonstrate the experimental feasibility of such protocol by considering the cases of both large-scale gravitational-wave detectors and small-scale cavity-assisted optomechanical devices.
Quantum fluctuations in the radiation pressure of light can excite stochastic motions of mechanical oscillators thereby realizing a linear quantum opto-mechanical coupling. When performing a precise measurement of the position of an oscillator, this coupling results in quantum radiation pressure noise. Up to now this effect has not been observed yet. Generally speaking, the strength of radiation pressure noise increases when the effective mass of the oscillator is decreased or when the power of the reflected light is increased. Recently, extremely light SiN membranes with high mechanical Q-values at room temperature have attracted attention as low thermal noise mechanical oscillators. However, the power reflectance of these membranes is much lower than unity which makes the use of advanced interferometer recycling techniques to amplify the radiation pressure noise in a standard Michelson interferometer inefficient. Here, we propose and theoretically analyze a Michelson-Sagnac interferometer that includes the membrane as a common end mirror for the Michelson interferometer part. In this new topology, both, power- and signal-recycling can be used even if the reflectance of the membrane is much lower than unity. In particular, signal-recycling is a useful tool because it does not involve a power increase at the membrane. We derive the formulas for the quantum radiation pressure noise and the shot-noise of an oscillator position measurement and compare them with theoretical models of the thermal noise of a SiN membrane with a fundamental resonant frequency of 75 kHz and an effective mass of 125 ng. We find that quantum radiation pressure noise should be observable with a power of 1 W at the central beam splitter of the interferometer and a membrane temperature of 1 K.
We analyze an optomechanical system that can be used to efficiently transfer a quantum state between an optical cavity and a distant mechanical oscillator coupled to a second optical cavity. We show that for a moderate mechanical Q-factor it is possible to achieve a transfer efficiency of $99.4%$ by using adjustable cavity damping rates and destructive interference. We also show that the quantum mechanical oscillator can be used as a quantum memory device with an efficiency of $96%$ employing a pulsed optomechanical coupling. Although the mechanical dissipation slightly decreases the efficiency, its effect can be significantly reduced by designing a high-Q mechanical oscillator.
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