The quantum transduction of an rf/microwave signal to the optical domain, and vice versa, paves the way for technologies that exploit the advantages of each domain to perform quantum operations. Since electro-optomechanical devices implement a simultaneous coupling of a mechanical oscillator to both an rf/microwave field and an optical field, they are suitable for the realization of a quantum transducer. The membrane-in-the-middle setup is a possible solution, once its vibrational mode is cooled down to ultra cryogenic temperature for achieving quantum operation. This work is focused on the mechanical characterization via an optical interferometric probe, down to T = 18 mK , of a loss-shielded metalized membrane designed for this purpose. A stroboscopic technique has been exploited for revealing a mechanical quality factor up to 64 × 10 6 at the lowest temperature. In fact, with continuous illumination and a cryostat temperature below 1 K , the heat due to optical absorption is not efficiently dissipated anymore, and the membrane remains hotter than its environment.

In this work, we present an Opto-Electro-Mechanical Modulator (OEMM) for RF-to-optical transduction realized via an ultra-coherent nanomembrane resonator capacitively coupled to an rf injection circuit made of a microfabricated read-out able to improve the electro-optomechanical interaction. This device configuration can be embedded in a Fabry–Perot cavity for electromagnetic cooling of the LC circuit in a dilution refrigerator exploiting the opto-electro-mechanical interaction. To this aim, an optically measured steady-state frequency shift of 380 Hz was seen with a polarization voltage of 30 V and a Q-factor of the assembled device above (Formula presented.) at room temperature. The rf-sputtered titanium nitride layer can be made superconductive to develop efficient quantum transducers.

Thermal noise is a major obstacle to observing quantum behavior in macroscopic systems. To mitigate its effect, quantum optomechanical experiments are typically performed in a cryogenic environment. However, this condition represents a considerable complication in the transition from fundamental research to quantum technology applications. It is therefore interesting to explore the possibility of achieving the quantum regime in room-temperature experiments. In this work we test the limits of sideband-cooling vibration modes of a SiN membrane in a cavity optomechanical experiment. We obtain an effective temperature of a few millikelvins, corresponding to a phononic occupation number of around 100. We show that further cooling is prevented by the excess classical noise of our laser source, and we outline the road toward the achievement of ground state cooling.

Feedback-based control techniques are useful tools in precision measurements as they allow us to actively shape the mechanical response of high quality factor oscillators used in force detection measurements. In this paper, we implement a feedback technique on a high-stress low-loss SiN membrane resonator, exploiting the charges trapped on the dielectric membrane. A properly delayed feedback force (dissipative feedback) enables the narrowing of the thermomechanical displacement variance in a similar manner to the cooling of the normal mechanical mode down to an effective temperature Teff. In the experiment reported here, we started from room temperature and gradually increasing the feedback gain, we were able to cool down the first normal mode of the resonator to a minimum temperature of about 124mK. This limit is imposed by our experimental setup and, in particular, by the injection of the read-out noise into the feedback. We discuss the implementation details and possible improvements to the technique.

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 3N 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.

We present a complete theory for laser cooling of a macroscopic radio-frequency LC electrical circuit by means of an optoelectromechanical system, consisting of an optical cavity dispersively coupled to a nanomechanical oscillator, which is in turn capacitively coupled to the LC circuit of interest. The driven optical cavity cools the mechanical resonator, which in turn sympathetically cools the LC circuit. We determine the optimal parameter regime where the LC resonator can be cooled down to its quantum ground state, which requires a large optomechanical cooperativity, and a larger electromechanical cooperativity. Moreover, comparable optomechanical and electromechanical coupling rates are preferable for reaching the quantum ground state.

Abstract: 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 abstract: [Figure not available: see fulltext.].

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.

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.

Cavity optomechanics has achieved the major breakthrough of the preparation and observation of macroscopic mechanical oscillators in non-classical 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 sideband 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.

A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated to a minimal uncertainty in position measurements, which is encoded in deformed commutation relations. Once applied in the Heisenberg dynamics, they give effects potentially detectable in low energy experiments. For instance, an isolated harmonic oscillator becomes intrinsically nonlinear and its dynamics shows a dependence of the oscillation frequency on the amplitude, as well as the appearance of higher harmonics. Here we analyze the free decay of micro and nano-oscillators, spanning a wide range of masses, and we place upper limits to the parameters quantifying the commutator deformation.

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.

According to quantum mechanics, if we keep observing a continuous variable we generally disturb its evolution. For a class of observables, however, it is possible to implement a so-called quantum nondemolition measurement: by confining the perturbation to the conjugate variable, the observable is estimated with arbitrary accuracy, or prepared in a well-known state. For instance, when the light bounces on a movable mirror, its intensity is not perturbed (the effect is just seen on the phase of the radiation), but the radiation pressure allows one to trace back its fluctuations by observing the mirror motion. In this work, we implement a cavity optomechanical experiment based on an oscillating micromirror, and we measure correlations between the output light intensity fluctuations and the mirror motion. We demonstrate that the uncertainty of the former is reduced below the shot-noise level determined by the corpuscular nature of light.

Optomechanical SiN nano-oscillators in high-finesse Fabry-Perot cavities can be used to investigate the interaction between mechanical and optical degree of freedom for ultra-sensitive metrology and fundamental quantum mechanical studies. In this paper, we present a nano-oscillator made of a high-stress round-shaped SiN membrane with an integrated on-chip 3-D acoustic shield properly designed to reduce mechanical losses. This oscillator works in the range of 200 kHz to 5 MHz and features a mechanical quality factor of Q ≃ 10⁷ and a Q-frequency product in excess of 6.2 × 10¹² Hz at room temperature, fulfilling the minimum requirement for quantum ground-state cooling of the oscillator in an optomechanical cavity. The device is obtained by MEMS deep reactive-ion etching (DRIE) bulk micromachining with a two-side silicon processing on a silicon-on-insulator wafer. The microfabrication process is quite flexible such that additional layers could be deposited over the SiN membrane before the DRIE steps, if required for a sensing application. Therefore, such oscillator is a promising candidate for quantum sensing applications in the context of the emerging field of quantum technologies. 

Normal-mode splitting is the most evident signature of strong coupling between two interacting subsystems. It occurs when two subsystems exchange energy between themselves faster than they dissipate it to the environment. Here we experimentally show that a weakly coupled optomechanical system at room temperature can manifest normal-mode splitting when the pump field fluctuations are antisquashed by a phase-sensitive feedback loop operating close to its instability threshold. Under these conditions the optical cavity exhibits an effectively reduced decay rate, so that the system is effectively promoted to the strong coupling regime.

In this contribution, we discuss the implementation of a novel microelectromechanical-systems (MEMS)-based energy harvester (EH) concept within the technology platform available at the ISAS Institute (TU Vienna, Austria). The device, already presented by the authors, exploits the piezoelectric effect to convert environmental vibrations energy into electricity, and presents multiple resonant modes in the frequency range of interest (i.e. below 10 kHz). The experimental characterisation of a sputter deposited aluminium nitride piezoelectric thin-film layer is reported, leading to the extraction of material properties parameters. Such values are then incorporated in the finite element method model of the EH, implemented in Ansys Workbench™, in order to get reasonable estimates of the converted power levels achievable by the proposed device solution. Multiphysics simulations indicate that extracted power values in the range of several µW can be addressed by the EH-MEMS concept when subjected to mechanical vibrations up to 10 kHz, operating in closed-loop conditions (i.e. piezoelectric generator connected to a 100 kΩ resistive load). This represents an encouraging result, opening up the floor to exploitations of the proposed EH-MEMS device in the field of wireless sensor networks and zero-power sensing nodes.

We realise a feedback-controlled optical Fabry-Pérot cavity in which the transmitted cavity output is used to modulate the input amplitude fluctuations. The resulting phase-dependent fluctuations of the in-loop optical field, which may be either sub-shot or super-shot noise, can be engineered to favourably affect the optomechanical interaction with a nanomechanical membrane placed within the cavity. Here we show that in the super-shot-noise regime ('anti-squashed light') the in-loop field has a strongly reduced effective cavity linewidth, corresponding to an increased optomechanical cooperativity. In this regime, feedback improves the simultaneous resolved-sideband cooling of two nearly degenerate membrane mechanical modes by one order of magnitude.

We realize a phase-sensitive closed-loop control scheme to engineer the fluctuations of the pump field which drives an optomechanical system and show that the corresponding cooling dynamics can be significantly improved. In particular, operating in the counterintuitive "antisquashing" regime of positive feedback and increased field fluctuations, sideband cooling of a nanomechanical membrane within an optical cavity can be improved by 7.5 dB with respect to the case without feedback. Close to the quantum regime of reduced thermal noise, such feedback-controlled light would allow going well below the quantum backaction cooling limit.

In the context of a recoil damping analysis, we have designed and produced a membrane resonator equipped with a specific on-chip structure working as a "loss shield" for a circular membrane. In this device the vibrations of the membrane, with a quality factor of 107, reach the limit set by the intrinsic dissipation in silicon nitride, for all the modes and regardless of the modal shape, also at low frequency. Guided by our theoretical model of the loss shield, we describe the design rationale of the device, which can be used as effective replacement of commercial membrane resonators in advanced optomechanical setups, also at cryogenic temperatures.