Modulation‐Based Atom‐Mirror Entanglement and Mechanical Squeezing in an Unresolved‐Sideband Optomechanical System

A hybrid optomechanical system which is composed of an atomic ensemble and a standard optomechanical cavity driven by a periodically modulated external laser field is investigated. Based on the simple periodic modulation forms of the driving amplitude and effective optomechanical coupling, respectively, the atom‐mirror entanglement is discussed in detail. It is found that the maximum of the entanglement in the unresolved‐sideband regime can be further enhanced compared with the non‐modulation regime. On the other hand, we find that the introduction of the atomic ensemble permits the mechanical squeezing induced by the periodic amplitude modulation can be successfully generated even in the unresolved‐sideband regime. Due to the self‐cooling mechanism constructed by the atomic ensemble, the mechanical squeezing scheme no longer requires the extra precooling technologies.     

Generation of Optical and Mechanical Squeezing in the Linear‐and‐Quadratic Optomechanics

Generation of strong stationary optical and mechanical squeezing is proposed for the linear‐and‐quadratic optomechanical system, where two cavity modes induce linear and quadratic optomechanical couplings, respectively. Through the linearization treatment, linearized coupling between cavity mode and mechanical mode and the mechanical parametric amplification process are achievable and controllable by independent driving lasers. Optical and mechanical squeezing are generated following different mechanisms. Optical squeezing works in the strong coupling regime, and mechanical amplification would push the system close to instability threshold, which could deeply improve ponderomotive squeezing even significantly beyond the 3 dB squeezing limit. Mechanical squeezing is generated based on the reservoir engineering method, where parametric amplification induces the squeezing transformation of mechanical mode; and linearized coupling, which operates in the red‐sideband and weak coupling limits, induces the ground‐state cooling of transformed mechanical mode. Finally, the original mechanical mode would be squeezed, which could also exceed 3 dB limit.     

Qubit-assisted squeezing of mirror motion in a dissipative cavity optomechanical system

In this study, we investigate a hybrid system consisting of an atomic ensemble trapped inside a dissipative optomechanical cavity assisted with perturbative oscillator-qubit coupling. Such a system is generally very suitable for generating stationary squeezing of the mirror motion in the long-time limit under the unresolved sideband regime. Based on the master equation and covariance matrix approaches, we discuss in detail the respective squeezing effects. We also determine that in both approaches, simplifying the system dynamics with adiabatic elimination of the highly dissipative cavity mode is very effective. In the master equation approach, we find that the squeezing is a resulting effect of the cooling process and is robust against thermal fluctuations of the mechanical mode. In the covariance matrix approach, we can approximately obtain the analytical result of the steady-state mechanical position variance from the reduced dynamical equation. Finally, we compare the two approaches and observe that they are completely equivalent for the stationary dynamics. Moreover, the scheme may be useful for possible ultraprecise quantum measurement that involves mechanical squeezing.     

Squeezing of optomechanical modes in detuned Fabry–Perot interferometer

We carry out analysis of optomechanical system formed by movable mirror of Fabry–Perot cavity pumped by detuned laser. Optical spring arising from detuned pump creates in the system several eigen modes which could be treated as high-Q oscillators. Modulation of laser power results in parametric modulation of oscillators spring constants thus allowing to squeeze noise in quadratures of the modes. Evidence of the squeezing could be found in the light reflected from the cavity.     

Coherently Controlling Spin Squeezing in Optomechanical System

We investigate spin squeezing in optomechanical system. We first derive the mean spin direction, the optimally squeezed angle and then calculate the spin squeezing parameter, which is independent of the frequency of the cavity field. The lager coupling strength more rapidly generates spin squeezed state, but the corresponding spin squeezed state maintains shorter time interval.     

Tunable ponderomotive squeezing induced by Coulomb interaction in an optomechanical system

We investigate the properties of the ponderomotive squeezing in an optomechanical system coupled to a charged nanomechanical oscillator(NMO) nearby via Coulomb force. We find that the introduction of Coulomb interaction allows the generation of squeezed output light from this system. Our numerical results show that the degree of squeezing can be tuned by the Coulomb coupling strength, the power of laser, and the frequencies of NMOs. Furthermore, the squeezing generated in our approach can be used to measure the Coulomb coupling strength.     

Topological phase transition in cavity optomechanical system with periodical modulation

We investigate the topological phase transition and the enhanced topological effect in a cavity optomechanical system with periodical modulation. By calculating the steady-state equations of the system, the steady-state conditions of cavity fields and the restricted conditions of effective optomechanical couplings are demonstrated. It is found that the cavity optomechanical system can be modulated to different topological Su-Schrieffer-Heeger (SSH) phases via designing the optomechanical couplings legitimately. Meanwhile, combining the effective optomechanical couplings and the probability distributions of gap states, we reveal the topological phase transition between trivial SSH phase and nontrivial SSH phase via adjusting the decay rates of cavity fields. Moreover, we find that the enhanced topological effect of gap states can be achieved by enlarging the size of system and adjusting the decay rates of cavity fields.     

Quantum Coherence and Spin Squeezing in Optomechanical System

We investigate quantum coherence and spin squeezing in optomechanical system. We first determine the mean spin direction, the optimally squeezed angle and then calculate the first-order temporal correlation function, the squeezing parameter, which are independent of the frequency of the cavity field. The lager coupling strength more rapidly generates spin squeezed state, but the corresponding spin squeezed state maintains shorter time interval.     

Enhancing stationary optomechanical entanglement with the Kerr medium

We theoretically investigate the stationary entanglement of a optomechanical system with an additional Kerr medium in the cavity. There are two kinds of interactions in the system, photon-mirror interaction and photon-photon interaction. The optomechanical entanglement created by the former interaction can be effectively controlled by the latter one. We find that the optomechanical entanglement is suppressed by Kerr interaction due to photon blockage. We also find that the Kerr interaction can create the stationary entanglement and induce the resonance of entanglement in the small detuning regime. These results show that the Kerr interaction is an effective control for the optomechanical system.     

Using coherent feedback loop for high quantum state transfer in optomechanics

We investigate the coherent feedback loop scheme to improve the quantum correlations transfer from optical to mechanical degrees of freedom in a double cavity optomechanical system. We use the Duan criterion to determine the separability of the two-mode mechanical states. The logarithmic negativity is employed to quantify the amount of the entanglement between mechanical modes in steady and dynamical regimes. We show that the entanglement can be significantly enhanced by a coherent feedback using a suitable tuning of the reflectivity parameter of the beam splitter located in each cavity. We also show that this enhancement is influenced by the temperature, the light squeezing parameter and the gain of the parameter amplifier. The entanglement dynamics in presence of the coherent feedback loop is also analyzed.     

A short walk through quantum optomechanics

This paper gives a 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 covers 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.     

Entanglement of movable mirror and cavity field enhanced by an optical parametric amplifier

A scheme to generate entanglement in a cavity optomechanical system filled with an optical parametric amplifier is proposed. With the help of the optical parametric amplifier, the stationary macroscopic entanglement between the movable mirror and the cavity field can be notably enhanced, and the entanglement increases when the parametric gain increases.Moreover, for a given parametric gain, the degree of entanglement of the cavity optomechanical system increases with increasing input laser power.     

Generating a Squeezed‐Coherent‐Cat State in a Double‐Cavity Optomechanical System

A squeezed‐coherent‐cat state (SCCS) in a mechanical system not only plays an important role for macroscopic quantum coherence, but also can be a carrier for quantum information. A scheme to generate a SCCS in a two‐mode optomechanical system is proposed, in which the modulated hopping interaction of two cavities is introduced. The two cavity modes couple with the same mechanical mode with linear and quadratic interaction, respectively. The SCCS is analytically deduced under an appropriate initial state, and the average phonon number and the parameter of squeeze are numerically calculated. Wigner function shown the properties of superposition and squeezing is plotted. Including the dissipation of the environment, the results show that a high quality mechanical resonator and a low noise environment are required to obtain high fidelity.     

Generating large steady-state optomechanical entanglement by the action of Casimir force

In this paper,we study an optomechanical device consisting of a Fabry-P′erot cavity with two dielectric nanospheres trapped near the cavity mirrors by an external driving laser.In the condition where the distances between the nanospheres and cavity mirrors are small enough,the Casimir force helps the optomechanical coupling to induce a steady-state optomechanical entanglement of the mechanical and optical modes in a certain regime of parameters.We investigate in detail the dependence of the steadystate optomechanical entanglement on external control parameters of the system,i.e.,the effective detuning,the pump powers of the cavity,the cavity decay rate and the wavelength of the driving field.It is found that the large steady-state optomechanical entanglement,i.e.EN=5.76,can be generated with experimentally feasible parameters,i.e.the pump power P=18.2μW,the cavity decay rateκ=0.5 MHz and the wavelength of the laserλL=1064 nm,which should be checked by optical measurement.     

Bistability in a Hybrid Optomechanical System under the Effect of a Nonlinear Medium

We investigate a hybrid optomechanical system consisting of two coupled cavities, one of them is composed of two-end fixed mirrors(called the traditional cavity), and the other has a one-end oscillating mirror(named as the optomechanical eavity). A Kerr medium is inside the traditional cavity to enhance the nonlinearity due to the fact that it can cause observing of bistable behavior in intracavity intensity for the optomechanical cavity.The Hamiltonian of the system is written in a rotating frame and its dynamics is described by quantum Langevin equations of motion. Our proposed s.ystem exhibits unconventional plots for the mean photon number of the optomechanical cavity which are not observed in previous works. The present results show a deep effect of the Kerr medium on optical bistability of intracavity intensity for the optomechanical cavity. Also, coupling strength of the cavities can effectively change the stability of the system.     

Nonreciprocal Mechanical Squeezing in a Spinning Optomechanical System

A scheme for nonreciprocal mechanical squeezing (NMS) based on the three‐mode optomechanical interaction is proposed. In this scheme, a mechanical mode couples to a spinning whispering‐gallery‐cavity (WGC) mode and to an optical mode. An external laser is coupled into and thus drives the WGC via a waveguide. Mechanical squeezing results from the joint effect of the mechanical intrinsic nonlinearity and the quadratic optomechanical coupling, which, in the presence of strong thermal noise, is still considerable, while the nonreciprocity originates from the optical Sagnac effect. There are two NMS areas in the parametric space, one works for the laser driving from the left of the waveguide and another, from the right. For a given spinning speed of the WGC, the squeezing values in these two areas are equal if the corresponding detunings of the WGC differ from each other by two‐times of the Sagnac–Fizeau shift. At the red‐detuning resonance, the analytical results for the mechanical squeezing and cooling are obtained. The NMS scheme is robust to the thermal noise of the mechanical environment.     

Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice

We propose a scheme to investigate the topological phase transition and the topological state transfer based on the small optomechanical lattice under the realistic parameters regime.We find that the optomechanical lattice can be equivalent to a topologically nontrivial Su-Schrieffer Heeger(SSH)model via designing the effective optomechanical coupling.Especially,the optomechanical lattice experiences the phase transition between topologically nontrivial SSH phase and topologically trivial SSH phase by controlling the decay of the cavity field and the opto mechanical coupling.We stress that the to pological phase transition is mainly induced by the decay of the cavity field,which is counter-intuitive since the dissipation is usually detrimental to the system.Also,we investigate the photonic state transfer between the two cavity fields via the topologically protected edge channel based on the small optomechanical lattice.We find that the quantum st ate transfer assisted by the topological zero energy mode can be achieved via implying the external lasers with the periodical driving amplitudes into the cavity fields.Our scheme provides the fundamental and the insightful explanations towards the mapping of the photonic topological insulator based on the micro-nano optomechanical quantum optical platform.     

Phase-dependent double optomechanically induced transparency in a hybrid optomechanical cavity system with coherently mechanical driving

We propose a scheme that can generate tunable double optomechanically induced transparency in a hybrid optomechanical cavity system.In this system, the mechanical resonator of the optomechanical cavity is coupled with an additional mechanical resonator and the additional mechanical resonator can be driven by a weak external coherently mechanical driving field.We show that both the intensity and the phase of the external mechanical driving field can control the propagation of the probe field, including changing the transmission spectrum from double windows to a single-window.Our study also provides an effective way to generate intensity-controllable, narrow-bandwidth transmission spectra, with the probe field modulated from excessive opacity to remarkable amplification.     

Nonreciprocal coupling induced entanglement enhancement in a double-cavity optomechanical system

We investigate the quantum entanglement in a double-cavity optomechanical system consisting of an optomechanical cavity and an auxiliary cavity, where the optomechanical cavity mode couples with the mechanical mode via radiation-pressure interaction, and simultaneously couples with the auxiliary cavity mode via nonreciprocal coupling. We study the entanglement between the mechanical oscillator and the cavity modes when the two cavities are reciprocally or nonreciprocally coupled. The logarithmic negativity $E_{n}^{(1)}$ ($E_{n}^{(2)}$) is adopted to describe the entanglement degree between the mechanical mode and the optomechanical cavity mode (the auxiliary cavity mode). We find that both $E_{n}^{(1)}$ and $E_{n}^{(2)}$ have maximum values in the case of reciprocal coupling. By using nonreciprocal coupling, $E_{n}^{(1)}$ and $E_{n}^{(2)}$ can exceed those maximum values, and a wider detuning region where the entanglement exists can be obtained. Moreover, the entanglement robustness with respect to the environment temperature is also effectively enhanced.     

Controllable four-wave mixing response in a dual-cavity hybrid optomechanical system

We systematically investigate the four-wave mixing(FWM) spectrum in a dual-cavity hybrid optomechanical system,which is made up of one optical cavity with an ensemble of two-level atoms and another with a mechanical oscillator. In this work, we propose that the hybrid dual-cavity optomechanical system can be employed as a highly sensitive mass sensor due to the fact that the FWM spectrum generated in this system has a narrow spectral width and the intensity of the FWM can be easily tuned by controlling the coupling strength(cavity–cavity, atom–cavity). More fascinatingly, the dual-cavity hybrid optomechanical system can also be used as an all-optical switch in view of the easy on/off control of FWM signals by adjusting the atom-pump detuning to be positive or negative. The proposed schemes have great potential applications in quantum information processing and highly sensitive detection.