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Mechanical resonators are gradually becoming available as new quantum systems. Quantum optics in combination with optomechanical interactions (quantum optomechanics) provides a particularly helpful toolbox for generating and controlling mechanical quantum states. We highlight some of the current challenges in the field by discussing two of our recent experiments.

Mechanical resonators are gradually becoming available as new quantum systems. Quantum optics in combination with optomechanical interactions (quantum optomechanics) provides a particularly helpful toolbox for generating and controlling mechanical quantum states. We highlight some of the current challenges in the field by discussing two of our recent experiments.

Entangling a mechanical oscillator with an optical mode is an enticing and yet a very challenging goal in cavity optomechanics. Here we consider a pulsed scheme to create Einstein-Podolsky-Rosen-type entanglement between a traveling-wave light pulse and a mechanical oscillator. The entanglement can be verified unambiguously by a pump-probe sequence of pulses. In contrast to schemes that work in a steady-state regime under a continuous-wave drive, this protocol is not subject to stability requirements that normally limit the strength of achievable entanglement. We investigate the protocol's performance under realistic conditions, including mechanical decoherence, in full detail. We discuss the relevance of a high mechanical Qf product for entanglement creation and provide a quantitative statement on which magnitude of the Qf product is necessary for a successful realization of the scheme. We determine the optimal parameter regime for its operation and show it to work in current state-of-the-art systems.

We present a two-dimensional array of nearest-neighbor coupled waveguides that is the optical analog of a quantum optomechanical system. We show that the quantum model predicts the appearance of effective column isolation, diagonal-coupling and other non-trivial couplings in the two-dimensional photonic lattice under a standard approximation from ion-trap cavity electrodynamics. We provide an approximate impulse function for the case of effective column isolation and compare it with exact numerical propagation in the photonic lattice.

Rapid experimental progress has recently allowed the use of light to prepare macroscopic mechanical objects into nearly pure quantum states. This research field of quantum optomechanics opens new doors toward testing quantum mechanics, and possibly other laws of physics, in new regimes. In the first part of this paper, I will review a set of techniques of quantum measurement theory that are often used to analyze quantum optomechanical systems. Some of these techniques were originally designed to analyze how a classical driving force passes through a quantum system, and can eventually be detected with optimal signal-to-noise ratio --- while others focus more on the quantum state evolution of a mechanical object under continuous monitoring. In the second part of this paper, I will review a set of experimental concepts that will demonstrate quantum mechanical behavior of macroscopic objects --- quantum entanglement, quantum teleportation, and the quantum Zeno effect. Taking the interplay between gravity and quantum mechanics as an example, I will review a set of speculations on how quantum mechanics can be modified for macroscopic objects, and how these speculations --- and their generalizations --- might be tested by optomechanics.

We analyze a quantum force sensor that uses coherent quantum noise cancellation (CQNC) to beat the Standard Quantum Limit (SQL). This sensor, which allows for the continuous, broad-band detection of feeble forces, is a hybrid dual-cavity system comprised of a mesoscopic mechanical resonator optically coupled to an ensemble of ultracold atoms. In contrast to the stringent constraints on dissipation typically associated with purely optical schemes of CQNC, the dissipation rate of the mechanical resonator only needs to be matched to the decoherence rate of the atomic ensemble -- a condition that is experimentally achievable even for the technologically relevant regime of low frequency mechanical resonators with large quality factors. The modular nature of the system further allows the atomic ensemble to aid in the cooling of the mechanical resonator, thereby combining atom-mediated state preparation with sensing deep in the quantum regime.

The interaction between a high-frequency dilational mode of a thin dielectric film and an optical cavity field is studied theoretically in the membrane-in-the-middle setup. A derivation from first principles leads to a multi-mode optomechanical Hamiltonian where multiple cavity modes are coupled by the thickness variation of the membrane. For membrane thicknesses on the order of one micron, the frequency of this dilational mode is in the GHz range. This can be matched to the free spectral range of the optical cavity, such that the mechanical oscillator will resonantly couple cavity modes at different frequencies. Furthermore, such a large mechanical frequency also means that the quantum ground state of motion can be reached with conventional refrigeration techniques. Estimation of the coupling strength with realistic parameters suggests that optomechanical effects can be observable with this dilational mode. It is shown how this system can be used as a quantum limited optical amplifier. The dilational motion can also lead to quantum correlations between cavity modes at different frequencies, which is quantified with an experimentally accessible two-mode squeezing spectrum. Finally, an explicit signature of radiation pressure shot noise in this system is identified.

The quantum dynamics of optomechanical systems was mostly studied for their fluctuations around classical steady states. We present a theoretical approach to determining the system observables of optomechanical systems as genuine quantum objects, for example, a coupled quantum mechanical oscillator to a cavity single photon. In this approach we study the dynamics of such systems in strong coupling regime. We find that, under strong optomechanical coupling, steady quantum states of optomechanical systems driven by continuous-wave single photons exhibit periodic oscillation and cavity noise considerably affects system observables.

This paper gives an brief review of the basic physics of quantum optomechanics and provides an overview of some of its recent developments and current areas of focus. It first outlines the basic theory of cavity optomechanical cooling and gives a brief status report of the experimental state-of-the-art. It then turns to the deep quantum regime of operation of optomechanical oscillators and cover selected aspects of quantum state preparation, control and characterization, including mechanical squeezing and pulsed optomechanics. This is followed by a discussion of the "bottom-up" approach that exploits ultracold atomic samples instead of nanoscale systems. It concludes with an outlook that concentrates largely on the functionalization of quantum optomechanical systems and their promise in metrology applications.

We propose a new method for optomechanical quantum non-demolition (QND) detection of phonon number, based on a "shelving" style measurement. The scheme uses a two-mode optomechanical system where the frequency splitting of the two photonic modes is near-resonant with the mechanical frequency. The combination of a strong optical drive and the underlying nonlinear optomechanical interaction gives rise to spin-like dynamics which facilitate the measurement. This approach allows phonon number measurement to be accomplished parametrically faster than in other schemes which are restricted to weak driving. The ultimate power of the scheme is controlled by the size of the single photon optomechanical cooperativity.

This article is from Nature Communications , volume 3 . Abstract The coupling of distinct systems underlies nearly all physical phenomena. A basic instance is that of interacting harmonic oscillators, giving rise to, for example, the phonon eigenmodes in a lattice. Of particular importance are the interactions in hybrid quantum systems, which can combine the benefits of each part in quantum technologies. Here we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with closely spaced frequencies around 32 MHz and no direct interaction. We record the first evidence of tripartite optomechanical mixing, implying that the eigenmodes are combinations of one photonic and two phononic modes. We identify an asymmetric dark mode having a long lifetime. Simultaneously, we operate the nearly macroscopic mechanical modes close to the motional quantum ground state, down to 1.8 thermal quanta, achieved by back-action cooling. These results constitute an important advance towards engineering of entangled motional states.

We show that in the strong coupling linear regime, the dispersive opto-mechanical Hamiltonian system can undergo a Dicke-Hepp-Lieb superradiant phase transition with two critical points. The higher critical point is the usual second order Dicke superradiant phase transition while the lower critical point is a new effect showing similarity to the usual Dicke superradiance. We also show that the mechanical mode near its quantum ground state completely decouples from the optical mode and the optical mode shows similarity to the Bogoluibov like excitations.

We present an approach for exponentially enhancing the single-photon coupling strength in an optomechanical system using only additional linear resources. It allows one to reach the quantum nonlinear regime of optomechanics, where nonlinear effects are observed at the single photon level, even if the bare coupling strength is much smaller than the mechanical frequency and cavity damping rate. Our method is based on using a large amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical setup, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities.

The cavity-optomechanical radiation pressure interaction provides the means to create entanglement between a mechanical oscillator and an electromagnetic field interacting with it. Here we show how we can utilize this entanglement within the framework of time-continuous quantum control, in order to engineer the quantum state of the mechanical system. Specifically, we analyze how to prepare a low-entropy mechanical state by (measurement-based) feedback cooling operated in the blue detuned regime, the creation of bipartite mechanical entanglement via time-continuous entanglement swapping, and preparation of a squeezed mechanical state by time-continuous teleportation. The protocols presented here are feasible in optomechanical systems exhibiting a cooperativity larger than 1.

We investigate the cavity optomechanical properties of an antiferromagnetic Bose-Einstein con- densate, where the role of the mechanical element is played by spin-wave excitations. We show how this system can be described by a single rotor that can be prepared deep in the quantum regime under realizable experimental conditions. This system provides a bottom-up realization of dispersive rotational optomechanics, and opens the door to the direct observation of quantum spin fluctuations.

We present a quantum theory for a fully coupled hybrid optomechanical system where all mutual couplings between a two-level atom, a confined photon mode and a mechanical oscillator mode are considered. In such a configuration, new quantum interference effects and correlations arise due to the interplay and competition between the different physical interactions. We present an analytical diagonalization of the related fully coupled Hamiltonian, showing the nature and energy spectra of the tripartite dressed excitations. We determine the driven-dissipative dynamics of such hybrid systems and study phonon blockade effects under resonant excitation. We also study the statistical properties of the photon emission obtained under incoherent pumping of the two-level atom, which is particularly relevant for experiments with solid-state two-level emitters.

We propose to use the intrinsic two-level system (TLS) defect states found naturally in integrated optomechanical devices for exploring cavity QED-like phenomena with localized phonons. The Jaynes-Cummings-type interaction between TLS and mechanics can reach the strong coupling regime for existing nano-optomechanical systems, observable via clear signatures in the optomechanical output spectrum. These signatures persist even at finite temperature, and we derive an explicit expression for the temperature at which they vanish. Further, the ability to drive the defect with a microwave field allows for realization of phonon blockade, and the available controls are sufficient to deterministically prepare non-classical states of the mechanical resonator.

The Casimir effect results from the optomechanical coupling between field fluctuations and mirrors in quantum vacuum. This contribution to the 20th International Conference on Laser Spectroscopy (ICOLS 2011) discusses the current status in the comparison between theory and experiments.

Amplifier is at the heart of almost all experiment carrying out the precise measurement of a weak signal. An idea amplifier should have large gain and minimum added noise simultaneously. Here, we consider the quantum measurement properties of a hybrid nonlinear cavity with the Kerr and OPA nonlinear media to amplify an input signal. We show that our hybrid-nonlinear-cavity amplifier has large gain in the single-value stable regime and achieves quantum limit unconditionally.

We consider how a single photon can probe the quantum nature of a moving mirror in the context of quantum optomechanics. In particular, we demonstrate how the single-photon spectrum reveals resonances that depend on how many phonons are created as well as on the strength of the mirror-photon interaction. A dressed-state picture is used to explain positions and relative strengths of those resonances. The time-dependent spectrum shows how the resonances are built up over time by the photon interacting with the moving mirror.

We consider how a single photon can probe the quantum nature of a moving mirror in the context of quantum optomechanics. In particular, we demonstrate how the single-photon spectrum reveals resonances that depend on how many phonons are created as well as on the strength of the mirror-photon interaction. A dressed-state picture is used to explain positions and relative strengths of those resonances. The time-dependent spectrum shows how the resonances are built up over time by the photon interacting with the moving mirror.

We consider the dynamics of a movable mirror (cantilever) of a cavity coupled through radiation pressure to the light scattered from ultracold atoms in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the displacement spectrum of the cantilever. We show that for large pump intensities the steady state displacement of the cantilever shows bistable behaviour. Due to atomic back-action, the displacement spectrum of the cantilever is modified and depends on the position of the condensate in the Brillouin zone. We further analyze the occurrence of splitting of the normal mode into three modes due to mixing of the mechanical motion with the fluctuations of the cavity field and the fluctuations of the condensate with finite atomic two-body interaction. The present system offers a novel scheme to coherently control ultracold atoms as well as cantilever dynamics.

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

Studying mechanical resonators via radiation pressure offers a rich avenue for the exploration of quantum mechanical behavior in a macroscopic regime. However, quantum state preparation and especially quantum state reconstruction of mechanical oscillators remains a significant challenge. Here we propose a scheme to realize quantum state tomography, squeezing and state purification of a mechanical resonator using short optical pulses. The scheme presented allows observation of mechanical quantum features despite preparation from a thermal state and is shown to be experimentally feasible using optical microcavities. Our framework thus provides a promising means to explore the quantum nature of massive mechanical oscillators and can be applied to other systems such as trapped ions.

Tracing the dynamics of a quantum system using a mesoscopic device is an important topic of interest nowadays. Here we show how a mesoscopic mechanical oscillator steers the dynamics of a coupled two-atom system and gives rise to a two-qubit SWAP gate. We have theoretically studied a generic hybrid atom-optomechanical system where two identical atoms in $\Lambda$ configuration are trapped inside the cavity and the cavity mode mediates the interaction between the atoms and the mechanical oscillator. Adiabatic elimination of the lossy channels is adopted which in turn gives rise to an effective Hamiltonian that is responsible for a two-atom SWAP gate controlled by the mechanical motion of the oscillator. The validity of the proposal for successful implementation is assessed using presently available experimental parameters.

Mechanical resonators are macroscopic quantum objects with great potential. They couple to many different quantum systems such as spins, optical photons, cold atoms, and Bose Einstein condensates. It is however difficult to measure and manipulate the phonon state due to the tiny motion in the quantum regime. On the other hand, microwave resonators are powerful quantum devices since arbitrary photon state can be synthesized and measured with a quantum tomography. We show that a linear coupling, strong and controlled with a gate voltage, between the mechanical and the microwave resonators enables to create quantum phonon states, manipulate hybrid entanglement between phonons and photons and generate entanglement between two mechanical oscillators. In circuit quantum optomechanics, the mechanical resonator acts as a quantum transducer between an auxiliary quantum system and the microwave resonator, which is used as a quantum bus.

We use a microscopic model, the Mirror-Oscillator-Field (MOF) model proposed by Galley, Behunin and Hu [Phys. Rev. A 87, 043832 (2013)], to describe the quantum entanglement between a mirror's center of mass (CoM) motion and a field. In contrast with the conventional approach where the mirror-field entanglement is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror's CoM, the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. The major advantage in this approach is that it provides a self-consistent treatment of the three pertinent subsystems (the mirror's CoM motion, its internal degrees of freedom and the field) including their back-actions on each other, thereby giving a more accurate account of the quantum correlations between the individual subsystems. The optical and the mechanical properties of a mirror arising from its dynamical interaction with a quantum field are obtained without imposing any boundary conditions on the field additionally, as is done in the conventional way. As one of the new physical features that arise from this self-consistent treatment of the coupled optics and mechanics behavior we observe a coherent transfer of quantum correlations from the field to the mirror via its internal degrees of freedom. We find the quantum entanglement between the optical field and the mirror's center of mass motion upon coarse-graining over the internal degree of freedom. Further, we show that in certain parameter regimes the mirror-field entanglement is enhanced when the field interacts resonantly with the mirror's internal degree of freedom, a new result which highlights the importance of including the internal structure of the mirror in quantum optomechanical studies.

The control of quantum systems requires the ability to change and read-out the phase of a system. The non-commutativity of canonical conjugate operators can induce phases on quantum systems, which can be employed for implementing phase gates and for precision measurements. Here we study the phase acquired by a radiation field after its radiation pressure interaction with a mechanical oscillator, and compare the classical and quantum contributions. The classical description can reproduce the nonlinearity induced by the mechanical oscillator and the loss of correlations between mechanics and optical field at certain interaction times. Such features alone are therefore insufficient for probing the quantum nature of the interaction. Our results thus isolate genuine quantum contributions of the optomechanical interaction that could be probed in current experiments.

We study cavity optomechanics of a mixture of ultracold atoms with tunable nonlinear collisions. We show that atomic collisions provide linear couplings between fictitious condensate oscillators, leading to possibilities of achieving a globally coupled quantum optomechanical network with an integrated atom chip. Potential applications range from simulating collective nonequilibrium dynamics in fields well past physics to probing unique properties of quantum mixtures.

We review the physics of hybrid optomechanical systems consisting of a mechanical oscillator interacting with both a radiation mode and an additional matter-like system. We concentrate on the cases embodied by either a single or a multi-atom system (a Bose-Einstein condensate, in particular) and discuss a wide range of physical effects, from passive mechanical cooling to the set-up of multipartite entanglement, from optomechanical non-locality to the achievement of non-classical states of a single mechanical mode. The reviewed material showcases the viability of hybridised cavity optomechanical systems as basic building blocks for quantum communication networks and quantum state-engineering devices, possibly empowered by the use of quantum and optimal control techniques. The results that we discuss are instrumental to the promotion of hybrid optomechanical devices as promising experimental platforms for the study of non-classicality at the genuine mesoscopic level.

We show that a cavity optomechanical system formed by a mechanical resonator simultaneously coupled to two modes of an optical cavity can be used for the implementation of a deterministic quantum phase gate between optical qubits associated with the two intracavity modes. The scheme is realizable for sufficiently strong single-photon optomechanical coupling in the resolved sideband regime, and is robust against cavity losses.

The coupling of distinct systems underlies nearly all physical phenomena and their applications. A basic instance is that of interacting harmonic oscillators, which gives rise to, for example, the phonon eigenmodes in a crystal lattice. Particularly important are the interactions in hybrid quantum systems consisting of different kinds of degrees of freedom. These assemblies can combine the benefits of each in future quantum technologies. Here, we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with closely spaced frequencies around 32 MHz and no direct interaction. We record the first evidence of tripartite optomechanical mixing, implying that the eigenmodes are combinations of one photonic and two phononic modes. We identify an asymmetric dark mode having a long lifetime. Simultaneously, we operate the nearly macroscopic mechanical modes close to the motional quantum ground state, down to 1.8 thermal quanta, achieved by back-action cooling. These results constitute an important advance towards engineering entangled motional states.

The coupling of distinct systems underlies nearly all physical phenomena and their applications. A basic instance is that of interacting harmonic oscillators, which gives rise to, for example, the phonon eigenmodes in a crystal lattice. Particularly important are the interactions in hybrid quantum systems consisting of different kinds of degrees of freedom. These assemblies can combine the benefits of each in future quantum technologies. Here, we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with closely spaced frequencies around 32 MHz and no direct interaction. We record the first evidence of tripartite optomechanical mixing, implying that the eigenmodes are combinations of one photonic and two phononic modes. We identify an asymmetric dark mode having a long lifetime. Simultaneously, we operate the nearly macroscopic mechanical modes close to the motional quantum ground state, down to 1.8 thermal quanta, achieved by back-action cooling. These results constitute an important advance towards engineering entangled motional states.

We present the basic ingredients of continuum optomechanics, i.e. the suitable extension of cavity-optomechanical concepts to the interaction of photons and phonons in an extended waveguide. We introduce a real-space picture and argue which coupling terms may arise in leading order in the spatial derivatives. This picture allows us to discuss quantum noise, dissipation, and the correct boundary conditions at the waveguide entrance. The connections both to optomechanical arrays as well as to the theory of Brillouin scattering in waveguides are highlighted. We identify the 'strong coupling regime' of continuum optomechanics that may be accessible in future experiments.

The promise of innovative applications has triggered the development of many modern technologies capable of exploiting quantum effects. But in addition to future applications, such quantum technologies have already provided us with the possibility of accessing quantum-mechanical scenarios that seemed unreachable just a few decades ago. With this spirit, in this work we show that modern optomechanical setups are mature enough to implement one of the most elusive models in the field of open system dynamics: degenerate parametric oscillation. The possibility of implementing it in nonlinear optical resonators was the main motivation for introducing such model in the eighties, which rapidly became a paradigm for the study of dissipative phase transitions whose corresponding spontaneously broken symmetry is discrete. However, it was found that the intrinsic multimode nature of optical cavities makes it impossible to experimentally study the model all the way through its phase transition. In contrast, here we show that this long-awaited model can be implemented in the motion of a mechanical object dispersively coupled to the light contained in a cavity, when the latter is properly driven with multi-chromatic laser light. We focus on membranes as the mechanical element, showing that the main signatures of the degenerate parametric oscillation model can be studied in state-of-the-art setups, thus opening the possibility of studying spontaneous symmetry breaking and enhanced metrology in one of the cleanest dissipative phase transitions.

Quantum superposition in mechanical systems is not only key evidence for macroscopic quantum coherence, but can also be utilized in modern quantum technology. Here we propose an efficient approach for creating macroscopically distinct mechanical superposition states in a two-mode optomechanical system. Photon hopping between the two cavity modes is modulated sinusoidally. The modulated photon tunneling enables an ultrastrong radiation-pressure force acting on the mechanical resonator, and hence significantly increases the mechanical displacement induced by a single photon. We study systematically the generation of the Yurke-Stoler-like states in the presence of system dissipations. We also discuss the experimental implementation of this scheme.

We study the simplest optomechanical system with a focus on the bistable regime. The covariance matrix formalism allows us to study both cooling and entanglement in a unified framework. We identify two key factors governing entanglement, namely the bistability parameter, i.e. the distance from the end of a stable branch in the bistable regime, and the effective detuning, and we describe the optimum regime where entanglement is greatest. We also show that in general entanglement is a non-monotonic function of optomechanical coupling. This is especially important in understanding the optomechanical entanglement of the second stable branch.

In connection with the 150-th Anniversary of P. N. Lebedev, we present historical aspects of his scientific and organizing activity and recall his famous experimental observations and proof of the existence of light pressure along with other results that essentially influenced the development of physics in Russia and in the whole world as well. We discuss the relationship of these studies of electromagnetic waves and other kinds of vibrational phenomena investigated by P. N. Lebedev to modern studies of the interaction of photons with mirrors, gravitational waves, acoustic waves, nonstationary (dynamical) Casimir effect of photon creation in resonators with vibrating boundaries, and vibrations of voltage and current in superconducting circuits realizing the states of qubits and qudits. We discuss the possibility of existence of the nonstationary Casimir effect for gravitational waves and sound in liquid helium.

We theoretically show that the dipole force of an ensemble of quantum emitters embedded in a dielectric nanosphere can be exploited to achieve near-field optical levitation. The key ingredient is that the polarizability from the ensemble of embedded quantum emitters can be larger than the bulk polarizability of the sphere, thereby enabling the use of repulsive optical potentials and consequently the levitation using optical near-fields. In levitated cavity quantum optomechanics, this could be used to boost the single-photon coupling by combining larger polarizability to mass ratio, larger field gradients, and smaller cavity volumes while remaining in the resolved sideband regime and at room temperature. A case study is done with a nanodiamond containing a high-density of silicon-vacancy color centers that is optically levitated in the evanescent field of a tappered nano-fiber and coupled to a high-finesse microsphere cavity.

An optomechanical interface that converts quantum states between optical fields with distinct wavelengths is proposed. A mechanical mode couples to two optical modes via radiation pressure and mediates the quantum state mapping between the two optical modes. A sequence of optomechanical $\pi/2$ pulses enables state-swapping between optical and mechanical states as well as the cooling of the mechanical mode. Theoretical analysis shows that high fidelity conversion can be realized for states with small photon numbers in systems with experimentally achievable parameters. The pulsed conversion process also makes it possible to maintain high conversion fidelity at elevated bath temperatures.

Interaction with a thermal environment decoheres the quantum state of a mechanical oscillator. When the interaction is sufficiently strong, such that more than one thermal phonon is introduced within a period of oscillation, quantum coherent oscillations are prevented. This is generally thought to preclude a wide range of quantum protocols. Here, we introduce a pulsed optomechanical protocol that allows ground state cooling, general linear quantum non-demolition measurements, optomechanical state swaps, and quantum state preparation and tomography without requiring quantum coherent oscillations. Finally we show how the protocol can break the usual thermal limit for sensing of impulse forces.

The recently increasing explorations for cavity optomechanical coupling assisted by a single atom or an atomic ensemble have opened an experimentally accessible fashion to interface quantum optics and nano (micro) -mechanical systems. In this paper, we study in details such composite quantum dynamics of photon, phonon and atoms, specified by the triple coupling, which only exists in this triple hybrid system: The cavity QED system with a movable end mirror. We exactly diagonalize the Hamiltonian of the triple hybrid system under the parametric resonance condition. We find that, with the rotating-wave approximation, the hybrid system is modeled by a generalized spin-orbit coupling where the orbital angular momentum operator is defined through a Jordan-Schwinger realization with two bosonic modes, corresponding to the mirror oscillation and the single mode photon of the cavity. In the quasi-classical limit of very large angular momentum, this system will behave like a standard cavity-QED system described by the Jaynes-Cummings model as the angular momentum operators are transformed to bosonic operators of a single mode. We test this observation with an experimentally accessible system with the atom in the cavity with a moving mirror.

Coupling electromagnetic waves in a cavity and mechanical vibrations via the radiation pressure of the photons [1,2] is a promising platform for investigations of quantum mechanical properties of motion of macroscopic bodies and thereby the limits of quantum mechanics [3,4]. A drawback is that the effect of one photon tends to be tiny, and hence one of the pressing challenges is to substantially increase the interaction strength towards the scale of the cavity damping rate. A novel scenario is to introduce into the setup a quantum two-level system (qubit), which, besides strengthening the coupling, allows for rich physics via strongly enhanced nonlinearities [5-8]. Addressing these issues, here we present a design of cavity optomechanics in the microwave frequency regime involving a Josephson junction qubit. We demonstrate boosting of the radiation pressure interaction energy by six orders of magnitude, allowing to approach the strong coupling regime, where a single quantum of vibrations shifts the cavity frequency by more than its linewidth. We observe nonlinear phenomena at single-photon energies, such as an enhanced damping due to the two-level system. This work opens up nonlinear cavity optomechanics as a plausible tool for the study of quantum properties of motion.

We revisit the problem of using a mechanical resonator to perform the transfer of a quantum state between two electromagnetic cavities (e.g. optical and microwave). We show that this system possesses an effective mechanical dark state which is immune to mechanical dissipation; utilizing this feature allows highly efficient transfer of intra-cavity states, as well as of itinerant photon states. We provide simple analytic expressions for the fidelity of transferring both Gaussian and non-Gaussian states.

We describe how to generate an Einstein-Podolsky-Rosen (EPR) paradox between a mesoscopic mechanical oscillator and an optical pulse. We find two types of paradox, defined by whether it is the oscillator or the pulse that shows the effect Schrodinger called "steering". Only the oscillator paradox addresses the question of mesoscopic local reality for a massive system. In that case, EPR's "elements of reality" are defined for the oscillator, and it is these elements of reality that are falsified (if quantum mechanics is complete). For this sort of paradox, we show that a thermal barrier exists, meaning that a threshold level of pulse-oscillator interaction is required for a given thermal occupation n_0 of the oscillator. We find there is no equivalent thermal barrier for the entanglement of the pulse with the oscillator, nor for the EPR paradox that addresses the local reality of the optical system. Finally, we examine the possibility of an EPR paradox between two entangled oscillators. Our work highlights the asymmetrical effect of thermal noise on quantum nonlocality.

Ultrastrong light-matter interaction in an optomechanical system can result in nonlinear optical effects such as photon blockade. The system-bath couplings in such systems play an essential role in observing these effects. Here we study the quantum coherence of an optomechanical system with a dressed-state master equation approach. Our master equation includes photon-number-dependent terms that induce dephasing in this system. Cavity dephasing, second-order photon correlation, and two-cavity entanglement are studied with the dressed-state master equation.

All quantum optomechanics experiments to date operate at cryogenic temperatures, imposing severe technical challenges and fundamental constraints. Here we present a novel design of on-chip mechanical resonators which exhibit fundamental modes with frequencies $f$ and mechanical quality factors $Q_\mathrm{m}$ sufficient to enter the optomechanical quantum regime at room temperature. We overcome previous limitations by designing ultrathin, high-stress silicon nitride (Si$_3$N$_4$) membranes, with tensile stress in the resonators' clamps close to the ultimate yield strength of the material. By patterning a photonic crystal on the SiN membranes, we observe reflectivities greater than 99%. These on-chip resonators have remarkably low mechanical dissipation, with $Q_\mathrm{m}$$\sim$$10^8$, while at the same time exhibiting large reflectivities. This makes them a unique platform for experiments towards the observation of massive quantum behavior at room temperature.

We propose a scheme to realize the phase-preserving amplification without the restriction of resolved sideband condition. As a result, our gain-bandwidth product is about one magnitude larger than the existing proposals. In our model, an additional cavity is coupled to the cavity-optomechanical system. Therefore our operating frequency is continuously tunable via adjusting the coupling coefficient of the two cavities.

We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment and when a two-level atom is introduced in the cavity. By using operator techniques we show how these problems may be either solved or how the Hamiltonians involved, via sets of unitary transformations, may be taken to known Hamiltonians for which there exist approximate solutions.