We consider a generic optomechanical system, consisting of a driven optical cavity and a movable mirror attached to a cantilever. Systems of this kind (and analogues) have been realized in many recent experiments. It is well known that those systems can exhibit an instability towards a regime where the cantilever settles into self-sustained oscillations. In this paper, we briefly review the classical theory of the optomechanical instability, and then discuss the features arising in the quantum regime. We solve numerically a full quantum master equation for the coupled system, and use it to analyze the photon number, the cantilever's mechanical energy, the phonon probability distribution and the mechanical Wigner density, as a function of experimentally accessible control parameters. We observe and discuss the quantum-to-classical transition as a function of a suitable dimensionless quantum parameter.
Conditional dynamics due to continuous optical measurements has successfully been applied for state reconstruction and feedback cooling in optomechanical systems. In this article, we show that the same measurement techniques can be used to unravel nonclassicality in optomechanical limit cycles. In contrast to unconditional dynamics, our approach gives rise to nonclassical limit cycles even in the sideband-unresolved regime, where the cavity decay rate exceeds the mechanical frequency. We predict a significant reduction of the mechanical amplitude fluctuations for realistic experimental paramet…
In the past few years, coupling strengths between light and mechanical motion in optomechanical setups have improved by orders of magnitude. Here we show that, in the standard setup under continuous laser illumination, the steady state of the mechanical oscillator can develop a non-classical, strongly negative Wigner density if the optomechanical coupling is large at the single-photon level. Because of its robustness, such a Wigner density can be mapped using optical homodyne tomography. These features are observed near the onset of the instability towards self-induced oscillations. We show th…
Cavity optomechanical phenomena, such as cooling, amplification or optomechanically induced transparency, emerge due to a strong imbalance in the dissipation rates of the parametrically coupled electromagnetic and mechanical resonators. Here we analyze the reversed dissipation regime where the mechanical energy relaxation rate exceeds the energy decay rate of the electromagnetic cavity. We demonstrate that this regime allows for mechanically-induced amplification (or cooling) of the electromagnetic mode. Gain, bandwidth, and added noise of this electromagnetic amplifier are derived and compare…
Optomechanical systems have been shown both theoretically and experimentally to exhibit an analogon to atomic electromagnetically induced transparency, with sharp transmission features that are controlled by a second laser beam. Here we investigate these effects in the regime where the fundamental nonlinear nature of the optomechanical interaction becomes important. We demonstrate that pulsed transistor-like switching of transmission still works even in this regime. We also show that optomechanically induced transparency at the second mechanical sideband could be a sensitive tool to see first …
Classical optomechanical systems feature self-sustained oscillations, where multiple periodic orbits at different amplitudes coexist. We study how this multistability is realized in the quantum regime, where new dynamical patterns appear because quantum trajectories can move between different classical orbits. We explain the resulting quantum dynamics from the phase space point of view, and provide a quantitative description in terms of autocorrelation functions. In this way we can identify clear dynamical signatures of the crossover from classical to quantum mechanics in experimentally access…
We present a scheme for cooling mechanical motion to the ground state in an optomechanical system. Unlike standard sideband cooling, this scheme applies to the so-called unresolved sideband regime, where the resonance frequency of the mechanical mode is much smaller than the cavity linewidth. Ground state cooling becomes possible when assuming the presence of an additional, auxiliary mechanical mode and exploiting the effect of optomechanically induced transparency. We first consider a system where one optical cavity interacts with two mechanical modes, and show that ground state cooling of th…
Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation pressure interaction. Here we show that it is not necessary to reach the single-photon strong-coupling regime in order to realize significant optomechanical nonlinearities. Instead, nonlinearities at the few quanta level can be achieved, even with weak-coupling, in a two-mode optomechanical system driven near instability. In this limit, we establish a new fi…
We study how quantum and thermal noise affects synchronization of two optomechanical limit-cycle oscillators. Classically, in the absence of noise, optomechanical systems tend to synchronize either in-phase or anti-phase. Taking into account the fundamental quantum noise, we find a regime where fluctuations drive transitions between these classical synchronization states. We investigate how this "mixed" synchronization regime emerges from the noiseless system by studying the classical-to-quantum crossover and we show how the time scales of the transitions vary with the effective noise strength…
With an increasing coupling between light and mechanics, nonlinearities begin to play an important role in optomechanics. We solve the quantum dynamics of an optomechanical system in the multi-photon strong coupling regime retaining nonlinear terms. This is achieved by performing a Schrieffer-Wolff transformation on the Hamiltonian including driving terms. The approach is valid away from the red- and blue-sideband drive. We show that the mechanical resonator displays self-sustained oscillations in regimes where the linearized model predicts instabilities, and that the amplitude of these oscill…
We investigate a hybrid electro-optomechanical system that allows us to obtain controllable strong Kerr nonlinearities in the weak-coupling regime. We show that when the controllable electromechanical subsystem is close to its quantum critical point, strong photon-photon interactions can be generated by adjusting the intensity (or frequency) of the microwave driving field. Nonlinear optical phenomena, such as the appearance of the photon blockade and the generation of nonclassical states (e.g., Schrödinger cat states), are predicted in the weak-coupling regime, which is feasible for most curre…
We identify signatures of the intrinsic nonlinear interaction between light and mechanical motion in cavity optomechanical systems. These signatures are observable even when the cavity linewidth exceeds the optomechanical coupling rate. A strong laser drive red-detuned by twice the mechanical frequency from the cavity resonance frequency makes two-phonon processes resonant, which leads to a nonlinear version of optomechanically induced transparency. This effect provides a new method of measuring the average phonon number of the mechanical oscillator. Furthermore, we show that if the strong las…
Laser cooling of mesoscopic mechanical resonators is of great interest for both fundamental studies and practical applications. We provide a general framework to describe the cavity-assisted backaction cooling in the strong coupling regime. By studying the cooling dynamics, we find that the temporal evolution of mean phonon number oscillates as a function of the optomechanical coupling strength depending on frequency mixing. The further analytical result reveals that the optimal cooling limit is obtained when the system eigenmodes satisfy the frequency matching condition. The reduced instantan…
A pulsed scheme for generating robust optical entanglement via the coupling of two optical modes to a mechanical oscillator is proposed. This scheme is inspired by the Sørensen-Mølmer approach for entangling trapped ions in a thermal environment and is based on the use of optical driving pulses that are slightly detuned from the respective sideband resonance. We show that for certain pulse durations, the optomechanical interaction can return the mechanical oscillator to its initial state. The corresponding entanglement generation is robust against thermal mechanical noise in the weak as well a…
We propose to use cavity optomechanical systems in the regime of optical bistability for the detection of weak harmonic forces. Due to the optomechanical coupling an external force on the mechanical oscillator modulates the resonance frequency of the cavity and consequently the switching rates between the two bistable branches. A large difference in the cavity output fields then leads to a strongly amplified homodyne signal. We determine the switching rates as a function of the cavity detuning from extensive numerical simulations of the stochastic master equation as appropriate for continuous …
We realise a simple and robust optomechanical system with a multitude of long-lived ($Q>10^7$) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate ($96~\mathrm{kHz}$) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures ($10\,\mathrm{K}$). Reaching this quantum regime entails, i.~a., quantum measurement backaction exceeding thermal forces, and thus detectable optomechanical quantum correlations. In particular, we observe ponderomotive squeez…
We study a dissipative, mechanically coupled optomechanical system that accommodates gain and loss. The gain (loss) is engineered by driven a purely dispersive optomechanical cavity with a blue-detuned (red-detuned) electromagnetic field. By taking into account the dissipative coupling, the Exceptional Point (EP), which is the $\mathcal{PT}-$symmetry phase transition, occurs at low threshold driving strength compared to the purely dispersive system. In the linear regime, the $\mathcal{PT}-$symmetry is unbroken and the dissipative coupling induces strong coupling between the mechanical resonato…
Optomechanical systems driven by an effective blue detuned laser can exhibit self-sustained oscillations of the mechanical oscillator. These self-oscillations are a prerequisite for the observation of synchronization. Here, we study the synchronization of the mechanical oscillations to an external reference drive. We study two cases of reference drives: (1) An additional laser applied to the optical cavity; (2) A mechanical drive applied directly to the mechanical oscillator. Starting from a master equation description, we derive a microscopic Adler equation for both cases, valid in the classi…
We study the optical bistability of an optomechanical system in which the position of a mechanical oscillator modulates the cavity frequency. The steady-state mean-field equation of the optical mode is identical to the one for a Kerr medium, and thus we expect it to have the same characteristic behavior with a lower, a middle, and an upper branch. However, the presence of position fluctuations of the mechanical resonator leads to a new feature: the upper branch will become unstable at sufficiently strong driving in certain parameter regimes. We identify the appropriate parameter regime for the…
In this paper, we study the full statistics of photons transmitted through an optical cavity coupled to nanomechanical motion. We analyze the entire temporal evolution of the photon correlations, the Fano factor, and the effects of strong laser driving, all of which show pronounced features connected to the mechanical backaction. In the regime of single-photon strong coupling, this allows us to predict a transition from sub-Poissonian to super-Poissonian statistics for larger observation time intervals. Furthermore, we predict cascades of transmitted photons triggered by multi-photon transitio…
Preparing and manipulating quantum states of mechanical resonators is a highly interdisciplinary undertaking that now receives enormous interest for its far-reaching potential in fundamental and applied science. Up to now, only nanoscale mechanical devices achieved operation close to the quantum regime. We report a new micro-optomechanical resonator that is laser cooled to a level of 30 thermal quanta. This is equivalent to the best nanomechanical devices, however, with a mass more than four orders of magnitude larger (43 ng versus 1 pg) and at more than two orders of magnitude higher environm…
We demonstrate optomechanical quantum control of the internal electronic states of a diamond nitrogen vacancy (NV) center in the resolved-sideband regime by coupling the NV to both optical fields and surface acoustic waves via a phonon-assisted optical transition and by taking advantage of the strong excited-state electron-phonon coupling of a NV center. Optomechanically-driven Rabi oscillations as well as quantum interferences between the optomechanical sideband and the direct dipole-optical transitions have been realized. These studies open the door to using resolved-sideband optomechanical …
A pertinent question in cavity optomechanics is whether reaching the regime of large single-photon cooperativity, where the single-photon coupling rate exceeds the geometric mean of the cavity and mechanical decay rates, can enable any new phenomena. We show that in some multimode optomechanical systems, the single-photon cooperativity can indeed be a figure of merit. We first study a system with one cavity mode and two mechanical oscillators which combines the concepts of levitated optomechanics and coherent scattering with standard dispersive optomechanics. Later, we study a more complicated…
Freestanding photonic crystals can be used to trap both light and mechanical vibrations. These "optomechanical crystal" structures have already been experimentally demonstrated to yield strong coupling between a photon mode and a phonon mode, co-localized at a single defect site. Future devices may feature a regular superlattice of such defects, turning them into "optomechanical arrays". In this letter we predict that tailoring the optomechanical band structure of such arrays can be used to implement Dirac physics of photons and phonons, to create a photonic gauge field via mechanical vibratio…
We present a scheme for ground-state cooling of a mechanical resonator by simultaneously coupling it to a superconducting qubit and a cavity field. The Hamiltonian describing the hybrid system dynamics is systematically derived. The cooling process is driven by a red-detuned ac drive on the qubit and a laser drive on the optomechanical cavity. We have investigated cooling in the weak and the strong coupling regimes for both the individual system, i.e., qubit assisted cooling and optomechanical cooling, and compared them with the effective hybrid cooling. It is shown that hybrid cooling is more…
We have observed nonlinear transduction of the thermomechanical motion of a nanomechanical resonator when detected as laser transmission through a sideband unresolved optomechanical cavity. Nonlinear detection mechanisms are of considerable interest as special cases allow for quantum nondemolition measurements of the mechanical resonator's energy. We investigate the origin of the nonlinearity in the optomechanical detection apparatus and derive a theoretical framework for the nonlinear signal transduction, and the optical spring effect, from both nonlinearities in the optical transfer function…
We propose to use the resonant enhancement of the parametric instability in an optomechanical system of two optical modes coupled to a mechanical oscillator to prepare mechanical states with sub-Poissonian phonon statistics. Strong single photon coupling is not required. The requirements regarding sideband resolution, circulating cavity power and environmental temperature are in reach with state of the art parameters of optomechanical crystals. Phonon antibunching can be verfied in a Hanburry-Brown-Twiss measurement on the output field of the optomechanical cavity.
We study theoretically interaction of optically-pumped excitons with acoustic waves in planar semiconductor nanostructures in the strongly nonlinear regime. We start with the multimode optomechanical lasing regime for optical pump frequency {above} the exciton resonance and demonstrate broadband chaotic-like lasing spectra. We also predict formation of propagating optomechanical domain walls driven by optomechanical nonlinearity for the optical pump {below} the exciton resonance. Stability conditions for the domain walls are examined analytically and are in agreement with direct numerical simu…
Electromagnetically induced transparency has great theoretical and experimental importance in many physics subjects, such as atomic physics, quantum optics, and more recent cavity optomechanics. Optical delay is the most prominent feature of electromagnetically induced transparency, and in cavity optomechanics optical delay is limited by mechanical dissipation rate of sideband-resolved mechanical modes. Here we demonstrate a cascaded optical transparency scheme by leveraging the parametric phonon-phonon coupling in a multimode optomechanical system, where a low damping mechanical mode in the u…
In cavity optomechanics, nanomechanical motion couples to a localized optical mode. The regime of single-photon strong coupling is reached when the optical shift induced by a single phonon becomes comparable to the cavity linewidth. We consider a setup in this regime comprising two optical modes and one mechanical mode. For mechanical frequencies nearly resonant to the optical level splitting, we find the photon-phonon and the photon-photon interactions to be significantly enhanced. In addition to dispersive phonon detection in a novel regime, this offers the prospect of optomechanical photon …
We study entanglement of the cavity modes in a double-cavity optomechanical system in strong-coupling regime. The system consists of two optomechanical systems coupled by a single photon hopping between them. With the radiation pressure of the photon, entanglement of the cavity modes can be generated. The concurrence between the cavity modes is at least twice larger than that between the mechanical modes. Moreover, when we change the ratio between coupling strength and resonant frequency of mechanical modes, the entanglement in cavity and mechanical modes are influenced differently.
Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly rich and so far remains underexplored. Works devoted to this subject have typically focussed on dissipation constants which are substantially larger than those encountered in current experiments, such that the nonlinear dynamics of weakly dissipative optomechanical systems is almost uncharted waters. In this work, we fill this gap and investigate the regular …
We have explored the nonlinear dynamics of an optomechanical system consisting of an illuminated Fabry-Perot cavity, one of whose end-mirrors is attached to a vibrating cantilever. Such a system can experience negative light-induced damping and enter a regime of self-induced oscillations. We present a systematic experimental and theoretical study of the ensuing attractor diagram describing the nonlinear dynamics, in an experimental setup where the oscillation amplitude becomes large, and the mirror motion is influenced by several optical modes. A theory has been developed that yields detailed …
The combination of low mass density, high frequency, and high quality-factor of mechanical resonators made of two-dimensional crystals such as graphene make them attractive for applications in force sensing/mass sensing, and exploring the quantum regime of mechanical motion. Microwave optomechanics with superconducting cavities offers exquisite position sensitivity and enables the preparation and detection of mechanical systems in the quantum ground state. Here, we demonstrate coupling between a multilayer graphene resonator with quality factors up to 220,000 and a high-$\textit{Q}$ supercondu…
Phonons offer the possibility to connect the microwave and optical domains while being efficiently transduced with electronic and optical signals. Here, we present a multimodal optomechanical platform, consisting of a mechanical-optical-mechanical resonator configuration. The mechanical modes, with frequencies at 265 MHz and 6.8 GHz, can be simultaneously excited into a phonon lasing regime as supported by a stability analysis of the system. Both the MHz and the GHz modes enter a self-sustained oscillation regime, leading to the intermodulation of two frequency combs in the optical field. We c…
The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the quasiharmonic to the relaxational regime occurs via chaotic canard explosions, where large-amplitude relaxation spikes are separated by an irregular number of subthreshold oscillations. We also show that this regime coexists with other periodic attractors, on which the trajectories evolve on a substantially faster time scale. The experimental results are reprodu…
We investigate the collective optomechanics of an ensemble of scatterers inside a Fabry-Perot resonator and identify an optimized configuration where the ensemble is transmissive, in contrast with the usual reflective optomechanics approach. In this configuration, the optomechanical coupling of a specific collective mechanical mode can be several orders of magnitude larger than the single-element case, and long-range interactions can be generated between the different elements since light permeates throughout the array. This new regime should realistically allow for achieving strong single-pho…
Two-photon coherent states are one of the main building pillars of non-linear and quantum optics. It is the basis for the generation of minimum-uncertainty quantum states and entangled photon pairs, applications not obtainable from standard coherent states or one-photon lasers. Here we describe a fully-resonant optomechanical parametric amplifier involving a polariton condensate in a trap lattice quadratically coupled to mechanical modes. The quadratic coupling derives from non-resonant virtual transitions to extended discrete excited states induced by the optomechanical coupling. Non-resonant…
