Recent optomechanical experiments have observed nonclassical properties in macroscopic mechanical oscillators. A key indicator of such properties is the asymmetry in the strength of the motional sidebands produced in the probe electromagnetic field, which is originated by the noncommutativity between the oscillator ladder operators. Here we extend the analysis to a squeezed state of an oscillator embedded in an optical cavity, produced by the 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.

Cavity optomechanics has achieved the major breakthrough of the preparation and observation of macroscopic mechanical oscillators in peculiarly quantum states. The development of reliable indicators of the oscillator properties in these conditions is important also for applications to quantum technologies. We compare two procedures to infer the oscillator occupation number, minimizing the necessity of system calibrations. The former starts from homodyne spectra, the latter is based on the measurement of the motional sidebands asymmetry in heterodyne spectra. Moreover, we describe and discuss a method to control the cavity detuning, that is a crucial parameter for the accuracy of the latter, intrinsically superior procedure.

Micro- and nanomechanical resonators play a prominent part in many sensing and signal processing platforms due to their capability to pervasively couple with a wide variety of physical systems. Particularly relevant is their embedding in advanced optomechanical setups, which has recently pioneered optically cooled mechanical oscillators toward the quantum regime. A frequently adopted experimental scheme exploits a thin, highly tensioned Si${}_3$ N${}_4$ nanomembrane where the membrane’s vibrations are dispersively coupled to the optical mode of a Fabry–Pérot cavity. A significant effort has been done into realizing high-quality factor membranes, considering that low mechanical loss represents a benchmark to operate in the elusive quantum regime. In this article, we compare two state-of-the-art SiN resonators, realized exploiting the dilution of the material’s intrinsic dissipation and efficient solutions to fully isolate the membrane from the substrate. In particular, we examine and discuss the interplay between the edge and distributed dissipation and propose an analytical approach to evaluate the total intrinsic loss. Also, our analysis delves into the sensitivity of the devices to a point-like force and a uniform-density force field. These results provide meaningful guidelines for designing new ultra-coherent resonating devices.

Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that account for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the basis of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization. Graphical

The extraordinary sensitivity of the output field of an optical cavity to small quantum-scale displacements has led to breakthroughs such as the first detection of gravitational waves and of the motions of quantum ground-state cooled mechanical oscillators. While heterodyne detection of the output optical field of an optomechanical system exhibits asymmetries which provide a key signature that the mechanical oscillator has attained the quantum regime, important quantum correlations are lost. In turn, homodyning can detect quantum squeezing in an optical quadrature but loses the important sideband asymmetries. Here we introduce and experimentally demonstrate a new technique, subjecting the autocorrelators of the output current to filter functions, which restores the lost heterodyne correlations (whether classical or quantum), drastically augmenting the useful information accessible. The filtering even adjusts for moderate errors in the locking phase of the local oscillator. Hence we demonstrate the single-shot measurement of hundreds of different field quadratures allowing the rapid imaging of detailed features from a simple heterodyne trace. We also obtain a spectrum of hybrid homodyne-heterodyne character, with motional sidebands of combined amplitudes comparable to homodyne. Although investigated here in a thermal regime, the method’s robustness and generality represents a promising new approach to sensing of quantum-scale displacements.

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.