A theoretical scheme for the realization of the sphere-coherent motional states in an optomechanical cavity in the presence of a two-level atom is proposed. To this end, the analogy between an atom-assisted optomechanical cavity and a laser-driven trapped-ion system is used. This analogy provides us with a theoretical tool to show how sphere-coherent states can be generated for the motional degree of freedom of the macroscopic mechanical oscillator from atom-field-mirror interactions in a multi-mode optomechanical cavity. Some nonclassical properties of the generated state of the mechanical oscillator, including the degree of quadrature squeezing and the negativity of the Wigner distribution are studied. We also examine the effects of the dissipation mechanisms involved in the system under consideration, including the atomic spontaneous emission and the damping of the motion of the mechanical oscillator, on the generated motional sphere-coherent states.
We propose a spectrometric method to reconstruct the motional states of mechanical modes in optomechanics. This is achieved by detecting the single-photon emission and scattering spectra of the optomechanical cavity. Owing to an optomechanical coupling, the \emph{a priori} phonon-state distributions contribute to the spectral magnitude, and hence we can infer information on the phonon states from the measured spectral data. When the single-photon optomechanical-coupling strength is moderately larger than the mechanical frequency, then our method works well for a wide range of cavity-field deca…
We propose to synthesize arbitrary nonclassical motional states in optomechanical systems by using sideband excitations and photon blockade. We first demonstrate that the Hamiltonian of the optomechanical systems can be reduced, in the strong single-photon optomechanical coupling regime when the photon blockade occurs, to one describing the interaction between a driven two-level trapped ion and the vibrating modes, and then show a method to generate target states by using a series of classical pulses with desired frequencies, phases, and durations. We further analyze the effect of the photon l…
We theoretically propose a scheme for the generation of a non-classical single-mode motional state of a mechanical resonator (MR) in the three-mode optomechanical systems, in which two optical modes of the cavities are linearly coupled to each other and one mechanical mode of the MR is optomechanically coupled to the two optical modes with the same coupling strength simultaneously. One cavity is driven by a coherent laser light. By properly tuning the frequency of the weak driving field, we obtain engineered Liouvillian superoperator via engineering the selective interaction Hamiltonian confin…
We theoretically study the radiation-induced interaction between the mechanical motion of an oscillating mirror and a remotely trapped atomic cloud. When illuminated by continuous-wave radiation, the mirror motion will induce red and blue sideband radiation, which respectively increases and reduces motional excitation. We find that by suitably driving $Λ$-level atoms, the mirror correlation with a specific radiation sideband could be converted from the outgoing to the incoming radiation. Such process allows us to manipulate the heating and cooling effects. Particularly, we develop an optomecha…
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 …
We theoretically analyze the light scattering of an optomechanical cavity which strongly interacts with a single two-level system and couples simultaneously to a mechanical oscillator by radiation forces. The analysis is based on the assumptions that the system is driven at low intensity, and that the mechanical interaction is sufficiently weak, permitting a perturbative treatment. We find quantum interference in the scattering paths, which allows to suppress the Stokes-component of the scattered light. This effect can be exploited to reduce the motional energy of the mechanical oscillator.
We explore the effect of all-optical feedback on the steady state dynamics of optomechanical arrays arising from various topologies. First we consider an array comprised of a pair of independent optomechanical cavities coupled reversibly via their optical modes. Next we consider an optomechanical network formed from coupling two optical modes with interactions mediated via a common mechanical mode. Finally we extend the analysis to a large network of N-coupled optomechanical systems. Our results show implementing an-all optical feedback loop in each arrangement can enhance the degree of steady…
Two close parallel mirrors attract due to a small force (Casimir effect) originating from the electromagnetic quantum vacuum uctuations of the electromagnetic field. These vacuum uctuations can also induce motional forces exerted upon one mirror when the other one moves. Here we consider an optomechanical system consisting of two vibrating mirrors coupled to an optical resonator. We find that motional forces can determine noticeable coupling rates between the two spatially separated vibrating mirrors. We show that, by tuning the two mechanical oscillators into resonance, energy is exchanged be…
Single atoms coupled to a cavity offer unique opportunities as quantum optomechanical devices because of their small mass and strong interaction with light. A particular regime of interest in optomechanics is that of "single-photon strong coupling," where motional displacements on the order of the zero-point uncertainty are sufficient to shift the cavity resonance frequency by more than its linewidth. In many cavity QED platforms, however, this is unfeasible due to the large cavity linewidth. Here, we propose an alternative route in such systems, which instead relies on the coupling of atomic …
A major trend within the field of cavity QED is to boost the interaction strength between the cavity field and the atomic internal degrees of freedom of the trapped atom by decreasing the mode volume of the cavity. In such systems, it is natural to achieve strong atom-cavity coupling, where the coherent interaction strength exceeds the cavity linewidth, while the linewidth exceeds the atomic trap frequency. While most work focuses on coupling of photons to the internal degrees of freedom, additional rich dynamics can occur by considering the atomic motional degree of freedom as well. In partic…
Mechanical oscillators which respond to radiation pressure are a promising means of transferring quantum information between light and matter. Optical--mechanical state swaps are a key operation in this setting. Existing proposals for optomechanical state swap interfaces are only effective in the resolved sideband limit. Here, we show that it is possible to fully and deterministically exchange mechanical and optical states outside of this limit, in the common case that the cavity linewidth is larger than the mechanical resonance frequency. This high-bandwidth interface opens up a significantly…
Photons of a laser beam driving the upper motional sideband of an optomechanical cavity can decay into photon-phonon pairs by means of an optomechanical parametric process. The phononic state can subsequently be mapped to a photonic state by exciting the lower sideband, hence creating photon-photon pairs out of an optomechanical system. We here demonstrate that these pairs can violate a Bell inequality when they are measured with photon counting techniques preceded by small displacement operations in the phase space. Our results show how to detect non-local light-mechanical correlations and op…
We propose how to achieve significantly enhanced quantum refrigeration and entanglement by coupling a pumped auxiliary cavity to an optomechanical cavity. We obtain both analytical and numerical results, and find optimal-refrigeration and -entanglement conditions under the auxiliary-cavity-assisted (ACA) mechanism. Our method leads to a giant amplification in the net refrigeration rate, and reveals that the ACA entanglement has a much stronger noise-tolerant ability in comparison with the unassisted case. By appropriately designing the ACA mechanism, an effective mechanical susceptibility can …
We investigate theoretically a hybrid system consisting of a Bose-Einstein condensate (BEC) trapped inside a laser driven membrane-in-the-middle optomechanical cavity assisted with squeezed vacuum injection whose moving membrane interacts both linearly and quadratically with the radiation pressure of the cavity. It is shown that such a hybrid system is very suitable for generating strong quadrature squeezing in the mechanical mode of the membrane and the Bogoliubov mode of the BEC in the unresolved sideband regime. More interestingly, by choosing a suitable sign for the quadratic optomechanica…
We demonstrate cavity sideband cooling of a single collective motional mode of an atomic ensemble down to a mean phonon occupation number of 2.0(-0.3/+0.9). Both this minimum occupation number and the observed cooling rate are in good agreement with an optomechanical model. The cooling rate constant is proportional to the total photon scattering rate by the ensemble, demonstrating the cooperative character of the light-emission-induced cooling process. We deduce fundamental limits to cavity-cooling either the collective mode or, sympathetically, the single-atom degrees of freedom.
Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to an ancillary cavity field via a quadratic optomechanical coupling. We find that their performances can be significantly modulated via the photon of the ancillary cavity, which comes from photon-dependent spin-oscillator coupling and detuning. Specifically, a fully switchable spin-oscillator entanglement…
In this paper we propose a scheme to model the phonon analog of optical elements, including a polarizing beam splitter, a half- wave plate, and a quarter- wave plate, as well as an implementation of CNOT and Pauli gates, by using two atoms confined in a 2D plane. The internal states of the atoms are taken to be Rydberg circular states. Using this model we can manipulate the motional state of the atom, with possible applications in optomechanical integrated circuits for quantum information processing and quantum simulation. Towards this aim, we study the interaction of two trapped atoms with tw…
We theoretically study a cavity filled with atoms, which provides the optical-mechanical interaction between the modified cavity photonic field and a movable mirror at one end. We show that the cavity field ``dresses'' these atoms, producing two types of polaritons, effectively enhancing the radiation pressure of the cavity field upon the end mirror, as well as establishing an additional squeezing mode of the end mirror. This squeezing produces an adiabatic entanglement, which is absent in usual vacuum cavities, between the oscillating mirror and the rest of the system. We analyze the entangle…
We propose a scheme to prepare a macroscopic mechanical oscillator in a catlike state, close to a coherent state superposition. The mechanical oscillator, coupled by radiation-pressure interaction to a field in an optical cavity, is first prepared close to a squeezed vacuum state using a reservoir engineering technique. The system is then probed using a short optical pulse tuned to the lower motional sideband of the cavity resonance, realizing a photon-phonon swap interaction. A photon number measurement of the photons emerging from the cavity then conditions a phonon-subtracted catlike state …
We study how an oscillating mirror affects the electromagnetically induced transparency (EIT) of an atomic ensemble, which is confined in a gas cell placed inside a micro-cavity with an oscillating mirror in one end. The oscillating mirror is modeled as a quantum mechanical harmonic oscillator. The cavity field acts as a probe light of the EIT system and also produces a light pressure on the oscillating mirror. The back-action from the mirror to the cavity field results in several (from one to five) steady-states for this atom-assisted optomechanical cavity, producing a complex structure in it…
Cooling to the motional ground state is an important first step in the preparation of nonclassical states of mesoscopic mechanical oscillators. Light-mediated coupling to a remote atomic ensemble has been proposed as a method to reach the ground state for low frequency oscillators. The ground state can also be reached using optical measurement followed by feedback control. Here we investigate the possibility of enhanced cooling by combining these two approaches. The combination, in general, outperforms either individual technique, though atomic ensemble-based cooling and feedback cooling each …
We investigate a hybrid system consisting of an atomic ensemble trapped inside a dissipative optomechanical cavity assisted with the perturbative oscillator-qubit coupling. It is shown that such a hybrid system is very suitable for generating stationary squeezing of the mirror motion in the long-time limit under the unresolved sideband regime. Based on the approaches of master equation and covariance matrix, we discuss the respective squeezing effects in detail and find that in both approaches, simplifying the system dynamics with adiabatic elimination of the highly dissipative cavity mode is …
We propose a dynamically-dark-mode (DDM) scheme to realize the reversible quantum conversion between microwave and optical photons in an electro-optomechanical (EOM) model. It is shown that two DDMs appear at certain times during the dynamical evolution of the EOM model. It is demonstrated that the DDMs can induce two kinds of reversible and highly efficient quantum conversion between the microwave and optical fields, the conditional quantum conversion (CQC) and the entanglement-assisted quantum conversion (EAQC). The CQC happens at the condition of vanishing of the initial-state mean value of…
We review and study the roles of quantum and classical fluctuations in recent cavity-optomechanical experiments which have now reached the quantum regime (mechanical phonon occupancy < 1) using resolved sideband laser cooling. In particular, both the laser noise heating of the mechanical resonator and the form of the optically transduced mechanical spectra, modified by quantum and classical laser noise squashing, are derived under various measurement conditions. Using this theory, we analyze our recent ground-state laser cooling and motional sideband asymmetry experiments with nanoscale optome…
In this paper, we study theoretically the bipartite and tripartite continuous variable entanglement as well as the normal-mode splitting in a single-atom cavity optomechanical system with intensity-dependent coupling. The system under consideration is formed by a Fabry-Perot cavity with a thin vibrating end mirror and a two-level atom in the Gaussian standing-wave of the cavity mode. We first derive the general form of Hamiltonian describing the tripartite intensity-dependent atom-field-mirror coupling due to the presence of cavity mode structure. We then restrict our treatment to the first vi…
The radiation-pressure interaction between one or more laser fields and a mechanical oscillator gives rise to a wide range of phenomena: from sideband cooling and backaction-evading measurements to pondermotive and mechanical squeezing to entanglement and motional sideband asymmetry. In many protocols, such as dissipative mechanical squeezing, multiple lasers are utilized, giving rise to periodically driven optomechanical systems. Here we show that in this case, Floquet dynamics can arise due to presence of Kerr-type nonlinearities, which are ubiqitious in optomechanical systems. Specifically,…
The search for experimental demonstrations of the quantum behavior of macroscopic mechanical resonators is a fastly growing field of investigation and recent results suggest that the generation of quantum states of resonators with a mass at the microgram scale is within reach. In this chapter we give an overview of two important topics within this research field: cooling to the motional ground state, and the generation of entanglement involving mechanical, optical and atomic degrees of freedom. We focus on optomechanical systems where the resonator is coupled to one or more driven cavity modes…
We theoretically analyze the optical and optomechanical nonlinearity present in a hybrid system consisting of a quantum dot(QD) coupled to an optomechanical cavity in the presence of a nonlinear Kerr medium, and show that this hybrid system can be used as an all optical switch. A high degree of control and tunability via the QD-cavity coupling strength, the Kerr and the optomechanical nonlinearity over the bistable behavior shown by the mean intracavity optical field and the power transmission of the weak probe field can be achieved.The results obtained in this investigation has the potential …
$\mathcal{PT}$-symmetry-breaking enhanced cavity optomechanical magnetometer is proposed, which is achieved by monitoring the change of intensity of a nonlinear four-wave mixing (FWM) process in a gain-cavity-assisted cavity optomechanical system (COMS). Compared with the traditional single loss COMS, the FWM intensity can be enhanced by two orders of magnitude when the gain-cavity-assisted COMS operates at the $\mathcal{PT}$-symmetry-breaking phase. Meanwhile, the sensitivity of magnetic field sensing can be increased from $10^{-9}$T to $10^{-11}$T. This originally comes from the fact that th…
Preparing mechanical systems in their lowest possible entropy state, the quantum ground state, starting from a room temperature environment is a key challenge in quantum optomechanics. This would not only enable creating quantum states of truly macroscopic systems, but at the same time also lay the groundwork for a new generation of quantum-limited mechanical sensors in ambient environments. Laser cooling of optomechanical devices using the radiation pressure force combined with cryogenic precooling has been successful at demonstrating ground state preparation of various devices, while a simil…
We investigate periodic optomechanical arrays as reconfigurable platforms for engineering the coupling between multiple mechanical and electromagnetic modes and for exploring many-body phonon dynamics. Exploiting structural resonances in the coupling between light fields and collective motional modes of the array, we show that tunable effective long-range interactions between mechanical modes can be achieved. This paves the way towards the implementation of controlled phononic walks and heat transfer on densely-connected graphs as well as the coherent transfer of excitations between distant el…
Optical measurements of a nanoscale silicon optomechanical crystal cavity with a mechanical resonance frequency of 3.6GHz are performed at sub-kelvin temperatures. We infer optical-absorption-induced heating and damping of the mechanical resonator from measurements of phonon occupancy and motional sideband asymmetry. At the lowest probe power and lowest fridge temperature (10mK), the localized mechanical resonance is found to couple at a rate of 400Hz (Q=9x10^6) to a thermal bath of temperature 270mK. These measurements indicate that silicon optomechanical crystals cooled to millikelvin temper…
Preparing macroscopic mechanical resonators close to their motional quantum groundstate and generating entanglement with light offers great opportunities in studying fundamental physics and in developing a new generation of quantum applications. Here we propose an experimentally interesting scheme, which is particularly well suited for systems in the sideband-unresolved regime, based on coherent feedback with linear, passive optical components to achieve groundstate cooling and photon-phonon entanglement generation with optomechanical devices. We find that, by introducing an additional passive…
Standard optomechanical cooling methods ideally require weak coupling and cavity damping rates which enable the motional sidebands to be well resolved. If the coupling is too large then sideband-resolved cooling is unstable or the rotating wave approximation can become invalid. In this work we describe a protocol to cool a mechanical resonator coupled to a driven optical mode in an optomechanical cavity, which is also coupled to an optical mode in another auxiliary optical cavity, and both the cavities are frequency-modulated. We show that by modulating the amplitude of the drive as well, one …
We experimentally demonstrate microwave control of the motional state of a trapped ion placed in a state-dependent potential generated by a running optical lattice. Both the optical lattice depth and the running lattice frequency provide tunability of the spin-motion coupling strength. The spin-motional coupling is exploited to demonstrate sideband cooling of a Yb171 ion to the ground state of motion.
Quantum state transfer is crucial for quantum information processing and quantum computation. Here, we propose a hybrid optomechanical system capable of coupling a qubit, an optical mode and a mechanical oscillator. The displacement of the mechanical oscillator,due to radiation pressure, induces spatial variation in the cavity field, which in turn couples the qubit with phonon mode. This allows state transfer between the cavity mode and the qubit without an actual interaction between them. We present a scheme for the transitionless quantum state transfer based on the transitionless quantum dri…
We perform a theoretical study on quantum correlations in an optomechanical system where the mechanical mirror is perturbatively coupled to an auxiliary qubit. In our study, we consider logarithmic negativity to quantify the degree of stationary entanglement between the cavity field and mechanical mirror, and, Gaussian quantum discord as an witness of the quantumness of the correlation beyond entanglement. Utilizing experimentally feasible parameters, we show that both entanglement and quantum discord enhance significantly with increase in mirror-qubit coupling. Moreover, we find that in prese…
We consider an optomechanical system that is composed of a mechanical and an optical mode interacting through a linear and quadratic optomechanical dispersive couplings. The system is operated in an unresolved side band limit with a high quality factor mechanical resonator. Such a system then acts as parametrically driven oscillator, giving access to an intensity assisted tunability of the spring constant. This enables the operation of optomechanical system in its 'soft mode' wherein the mechanical spring softens and responds with a lower resonance frequency. We show that this soft mode can be…
We investigate the optomechanical properties of a periodic array of identical scatterers placed inside an optical cavity and extend the results of [A. Xuereb, C. Genes, and A. Dantan, Phys. Rev. Lett. 109, 223601 (2012)]. We show that operating at the points where the array is transmissive results in linear optomechanical coupling strengths between the cavity field and collective motional modes of the array that may be several orders of magnitude larger than is possible with an equivalent reflective ensemble. We describe and interpret these effects in detail and investigate the nature of the s…
The properties of open quantum system in quantum information science is now extensively investigated more generally by the research community as a fundamental issue for a variety of applications. Usually, the states of the open quantum system might be disturbed by the decoherence which will reduce the fidelity in the quantum information processing. So it is better to eliminate the influence of the environment. However, as part of the composite system, rational use of the environment system could be beneficial to quantum information processing. Here we theoretically studied the environment indu…
We investigate a hybrid quantum system consisting of a cavity optomechanical device optically coupled to an ultracold quantum gas. We show that the dispersive properties of the ultracold gas can be used to dramatically modify the optomechanical response of the mechanical resonator. We examine hybrid schemes wherein the mechanical resonator is coupled either to the motional or the spin degrees of freedom of the ultracold gas. In either case, we find an enhancement of more than two orders of magnitude in optomechanical cooling due to this hybrid interaction. Significantly, based on demonstrated …
We investigate a system consisting of a two-component Bose-Einstein condensate interacting dispersively with a Fabry-Perot optical cavity where the two components of the condensate are resonantly coupled to each other by another classical field. The key feature of this system is that the atomic motional degrees of freedom and the internal pseudo-spin degrees of freedom are coupled to the cavity field simultaneously, hence an effective spin-orbital coupling within the condensate is induced by the cavity. The interplay among the atomic center- of-mass motion, the atomic collective spin and the c…
We propose a protocol to realize fast high-fidelity quantum state transfer between distant optomechanical interfaces connected by a continuum waveguide. The scheme consists of three steps: two accelerating adiabatic processes joined by a population conversion process. In comparison to the traditional adiabatic technique, our method reaches a higher transfer fidelity with a shorter time. Numerical results show that the fidelity of this transfer scheme in the dissipative system mainly depends on the protocol speed and the coupling strength of the waveguide and cavities. Assisted by inverting the…
In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric non…
Optomechanical cavities in the well-resolved-sideband regime are ideally suited for the study of a myriad of quantum phenomena with mechanical systems, including backaction-evading measurements, mechanical squeezing, and generation of non-classical states. For these experiments, the mechanical oscillator should be prepared in its ground state; residual motion beyond the zero-point motion must be negligible. The requisite cooling of the mechanical motion can be achieved using the radiation pressure of light in the cavity by selectively driving the anti-Stokes optomechanical transition. To date,…
We propose and analyze nonlinear optomechanical protocols that can be implemented by adding a single atom to an optomechanical cavity. In particular, we show how to engineer the environment in order to dissipatively prepare the mechanical oscillator in a superposition of Fock states with fidelity close to one. Furthermore, we discuss how a single atom in a cavity with several mechanical oscillators can be exploited to realize nonlinear many-body physics by stroboscopically driving the mechanical oscillators. We show how to prepare non-classical many-body states by either applying coherent prot…
Generation of non-Gaussian quantum states of macroscopic mechanical objects is key to a number of challenges in quantum information science, ranging from fundamental tests of decoherence to quantum communication and sensing. Heralded generation of single-phonon states of mechanical motion is an attractive way towards this goal, as it is, in principle, not limited by the object size. Here we demonstrate a technique which allows for generation and detection of a quantum state of motion by phonon counting measurements near the ground state of a 1.5 MHz micromechanical oscillator. We detect scatte…
We consider a hybrid quantum many-body system formed by both a vibrational mode of a nanomembrane, which interacts optomechanically with light in a cavity, and an ultracold atom gas in the optical lattice of the out-coupled light. After integrating over the light field, an effective Hamiltonian reveals a competition between the localizing potential force and the membrane displacement force. For increasing atom-membrane interaction we find a nonequilibrium quantum phase transition from a localized non-motional phase of the atom cloud to a phase of collective motion. Near the quantum critical po…
We introduce a scheme to perform dissipation-assisted quantum information processing in ion traps considering realistic decoherence rates, for example, due to motional heating. By means of continuous sympathetic cooling, we overcome the trap heating, and show that the damped vibrational excitations can still be exploited to mediate coherent interactions as well as collective dissipative effects. We describe how to control their relative strength experimentally, allowing for protocols of coherent or dissipative generation of entanglement. This scheme can be scaled to larger ion registers for co…
Quantum manipulation of macroscopic mechanical systems is of great interest in both fundamental physics and applications ranging from high-precision metrology to quantum information processing. A crucial goal is to cool the mechanical system to its quantum ground state. In this review, we focus on the cavity optomechanical cooling, which exploits the cavity enhanced interaction between optical field and mechanical motion to reduce the thermal noise. Recent remarkable theoretical and experimental efforts in this field have taken a major step forward in preparing the motional quantum ground stat…
We show that the vibrations of an ion Coulomb crystal can be cooled to the zero-point motion through the optomechanical coupling with a high-finesse cavity. Cooling results from the interplay between coherent scattering of cavity photons by the ions, which dynamically modifies the vibrational spectrum, and cavity losses, that dissipate motional energy. The cooling mechanism we propose requires that the length scales of the crystal and the cavity are mismatched so that the system is intrinsically frustrated, leading to the formation of defects (kinks). When the pump is strong enough, the anti-S…
Optomechanics is currently believed to provide a promising route towards the achievement of genuine quantum effects at the large, massive-system scale. By using a recently proposed figure of merit that is well suited to address continuous-variable systems, in this paper we analyze the requirements needed for the state of a mechanical mode (embodied by an end-cavity cantilever or a membrane placed within an optical cavity) to be qualified as macroscopic. We show that, according to the phase space-based criterion that we have chosen for our quantitative analysis, the state achieved through stron…
