Hybrid Optomechanical System Research Articles

Precision measurement of electrical charge in a hybrid optomechanical system with Michelson interferometer

In this work, we present a scheme to measure electrical charge by combining a cavity optomechanical system with Michelson interferometer. The optomechanical cavity with a charged movable mirror is placed in one arm of a Michelson interferometer, in which the cavity length is modified due to the Coulomb force between the charged moveable mirror with the unknown charge and the charged body with the known charge, leading to a change in the output of the cavity mode. In addition, a perfectly reflecting mirror is rigidly fixed in the other arm. The unknown electrical charge can be measured by the difference of output intensities in both arms of the Michelson interferometer. The theoretical derivation and the numerical simulation indicate our scheme is more sensitive to the external Coulomb force and the precision of the scheme can reach unity charge, due to resorting to the Michelson interferometer. Besides, the effect of temperature on the sensitivity of electrical charge detector is also discussed.

Phase-controlled amplification and slow light in a hybrid optomechanical system.

We theoretically investigate the transmission and group delay of a probe field incident on a hybrid optomechanical system, which consists of a mechanical resonator simultaneously coupled to an optical cavity and a two-level system (qubit). The cavity field is driven by a strong red-detuned control field, and a weak coherent mechanical driving field is applied to the mechanical resonator. With the assistance of additional mechanical driving field, it is shown that double optomechanically induced transparency can be switched into absorption due to destructive interference or amplification because of constructive interference, which depends on the phase difference of the applied fields. We study in detail how to control the probe transmission by tuning the parameters of the optical and mechanical driving fields. Furthermore, we find that the group delay of the transmitted probe field can be prolonged by the tuning the amplitude and phase of the mechanical driving field.

Tunable transparency and amplification in a hybrid optomechanical system with quadratic coupling

We theoretically study the optical response of a hybrid optomechanical system with quadratic coupling, where an optomechanical cavity with a movable membrane in the middle is coupled to an auxiliary cavity with a tunable gain rate. We show that the optical transmission of the system can be controlled by a variety of parameters, including power of the control field, coupling strength between the two cavities, the gain rate of the auxiliary cavity, reflectivity of the membrane, and the temperature of the environment. In particular, tunable transparency and amplification can be realized by modifying the gain rate of the auxiliary cavity. Under the condition of two-phonon resonance, we find that (i) for the no-loss-gain cavity, a broad transparency window appears in the probe transmission due to the coupling between the two cavities; (ii) for the passive cavity, an extremely narrow transparency window occurs within a broad transmission window due to quadratic optomechanical coupling; (iii) for the active cavity, the probe field can be amplified in a wide frequency regime. Our proposal provides a new platform to control the propagation of light.

Tunable slow and fast light in an atom-assisted optomechanical system with a mechanical pump

We theoretically investigate the optical response of an atom-assisted optomechanical system to a weak probe field at the presence of a strong coupling field and a time-dependent mechanical pump. We show that the phenomenon of optomechanically induced transparency can be converted to that of perfect absorption due to Jaynes-Cummings (J-C) coupling between a single-mode cavity field and a two-level atom, and the probe transmission strength can be further enhanced or suppressed by tuning amplitude and phase of the mechanical pump. Furthermore, phase dispersion of the transmission optical field is modified by controlling the J-C coupling strength and the applied pump, which provides an approach to tune group delay of the output probe field. Based on this hybrid optomechanical system, we can realize a conversion between slow and fast light effect by adjusting the J-C coupling strength. Moreover, the amplitude and phase of the mechanical pump as well as the coupling field amplitude can also be used to control the group delay. These results provide us an approach to manipulate light propagation, which will be helpful for quantum information processing.

Controllable optical response properties in a hybrid optomechanical system

In this paper, we study theoretically the optical response properties of the output field in a hybrid optomechanical system, in which a degenerate optical parametric amplifier (OPA) and a $$\varLambda $$ -type three-level atomic ensemble are placed in a driven optical cavity with a moving end mirror. We show that due to the presence of the OPA and the atomic medium, our proposal has the ability to exhibit the optical tristability and multiple optomechanically induced transparency (OMIT)-like effects. Moreover, the combined effects of optical amplification and OMIT-like as well as the tunable switch from slow-to-fast light can be realized by tuning the gain coefficient of the OPA and the phase of the field driving the OPA. In addition, the role of the OPA on the higher-order sideband generation has also been investigated. We find that the presence of the OPA contributes to the enhancement of the second-order sideband generation. These results provide a new way to engineer the hybrid optomechanical devices for applications in optical communications and signal processing.

Mechanical squeezing of the tripod-type four-level atom-assisted optomechanical system

Quadrature squeezing of a mesoscopic mechanical oscillator is investigated in a driven hybrid optomechanical system with a membrane-in-middle configuration containing a tripod-type four-level atom on either side of the membrane. We analyze in detail the influence of the coupling constant between cavity field and atom, amplitude of pump field, cavity pump detuning and Rabi frequency of classical field on the squeezing of the position quadrature of the vibrating membrane. The results show that the mechanical squeezing can be controlled by choosing the evolved parameters and initial state of atom, appropriately. Also, it is shown that a noticeable amount of squeezing can be obtained by increasing the amplitude of the classical pump field and therefore effective coupling constant. More over, we investigate that such a system can lead to a larger squeezing than the case with Λ-type three-level atom.

Auxiliary cavity enhanced mode splitting and ground-state cooling of mechanical resonator in hybrid optomechanical system

We theoretically demonstrate the mode splitting and the ground-state cooling of optomechanical resonator in a hybrid optomechanical system, where one optomechanical cavity with high cavity dissipation is coupled to an auxiliary optical cavity with high quality factor. The fluctuation spectrum of the resonator presents the behavior of mode splitting with controlling the parameters, such as the cavity-pump-field detuning, the cavity-cavity coupling strength J, the pump power P, and the decay rate ratio δ of the two cavities. In addition, the resonator can also reach the ground-state cooling under different parametric regimes. Our study may provide a further insight into cooling macroscopic objects in a hybrid optomechanical systems.

Controllable and tunable multiple optomechanically induced transparency and Fano resonance mediated by different mechanical resonators

We demonstrate the multiple optomechanically induced transparency (OMIT) and Fano resonance in a hybrid optomechanical system, in which an optical cavity is coupled to two mechanical resonators with interaction (such as Coulomb interaction) via radiation pressure. The probe transmission spectra experience the transition from single-mode OMIT to multiple OMIT with controlling the interaction of the two resonators, and we discuss the robustness of the system against the cavity decay rate. Compared with the situation of without considering the interaction of the two resonators, the transmission spectra present asymmetric Fano line shapes via manipulating the optomechanical coupling strengths between the optical cavity and the two resonators with taking into account the resonator interaction. Furthermore, we compare the results of identical mechanical resonators with the same mass and frequencies to different mechanical resonators with different mass and frequencies. The results indicate that the probe transmission spectra undergo a series of transition from Fano resonances to OMIT by controlling the different mechanical resonators as well as the interaction between the two mechanical resonators, and we can present a scheme to determine the resonator interaction via measuring the peaks splitting. Finally, the transparency windows in the probe transmission spectrum are accompanied by the rapid normal phase dispersion under different mechanical resonators, which may indicate the slow and fast light effect.

Phase-dependent double optomechanically induced transparency in a hybrid optomechanical cavity system with coherently mechanical driving**Project supported by the Strategic Priority Research Program of China (Grant No. XDB01010200), the National Natural Science Foundation of China (Grant Nos. 61605225, 11674337, and 11547035), and Natural Science Foundation of Shanghai, China (Grant No. 16ZR1448400).

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.

Heisenberg-Langevin Formalism for Squeezing Dynamics of Linear Hybrid Optomechanical System

A hybrid quantum optomechanical system is an interface made from coupling between photons, excitons and mechanical oscillations. We use the quantum Langevin approach to study a hybrid optomechanical system which contains a single undoped semiconductor quantum well placed inside a cavity as well as one mirror of the optical resonator linear coupled to the cavity fields. A decorrelation method is employed to get a closed set of coupled equations. Furthermore, we have used these solutions to discuss squeezing dynamics for the coupled mode quadratures of the cavity field and the semiconductor quantum well exciton. We have illustrated that squeezing dynamics can be controlled by appropriate choice of physical parameters present in our hybrid optomechanical system.

Optimal control of hybrid optomechanical systems for generating non-classical states of mechanical motion

Cavity optomechanical systems are one of the leading experimental platforms for controlling mechanical motion in the quantum regime. We exemplify that the control over cavity optomechanical systems greatly increases by coupling the cavity also to a two-level system, thereby creating a hybrid optomechanical system. If the two-level system can be driven largely independently of the cavity, we show that the nonlinearity thus introduced enables us to steer the extended system to non-classical target states of the mechanical oscillator with Wigner functions exhibiting significant negative regions. We illustrate how to use optimal control techniques beyond the linear regime to drive the hybrid system from the near ground state into a Fock target state of the mechanical oscillator. We base our numerical optimization on realistic experimental parameters for exemplifying how optimal control enables the preparation of decidedly non-classical target states, where naive control schemes fail. Our results thus pave the way for applying the toolbox of optimal control in hybrid optomechanical systems for generating non-classical mechanical states.

Generation of entangled Schrödinger cat state of two macroscopic mirrors.

We propose a scheme to generate the macroscopic entangled Schrödinger cat state of two mechanical resonators in a hybrid optomechanical system by introducing modulated photon-hopping interaction between two cavities. We show that the obtained entangled cat state possesses large average phonon number and the two base vectors of which are nearly orthogonal, thus causing the high degree of entanglement. To justify the robust of the scheme, the dissipation of the system and the noise from the environment are considered. It shows that the high fidelity between the obtained state and the target state can be achieved in the presence of dissipation and thermal noise within our parameter regions, which suggests that our state-generation proposal is feasible.

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

AbstractA 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.

Manipulation of multi-transparency windows and fast-slow light transitions in a hybrid cavity optomechanical system

We study the generation of quadruple-transparency windows and the implementation of a conversion between slow and fast light in a hybrid optomechanical system. By demonstrating the generation of these transparency windows one by one, we analyze the physical mechanism through which each transparency window forms in detail. Additionally, we discuss how the system parameters affect the formation of transparency windows and conclude that the location, width, and absorption of each transparency window can be arbitrarily manipulated by varying the appropriate parameters. Moreover, when the pump field is changed from red to blue detuning, conversions between slow and fast light occur in the output field. These interesting properties of the output field can be applied to achieve the coherent control and manipulation of light pulses using cavity optomechanical system.

Novel transparency, absorption and amplification in a driven optomechanical system with a two-level defect

A study on optomechanically induced transparency (OMIT), optomechanically induced amplification (OMIAm) and optomechanically induced absorption (OMIAb) in a hybrid optomechanical system (OMS) with an intrinsic two-level defect was conducted. The OMS consists of a cavity, a mechanical resonator and a two-level defect. The coupling interaction between the two-level defect (the cavity field) and the mechanical resonator is described by the Jaynes–Cummings (radiation-pressure) Hamiltonian, while there is no direct coupling between the two-level defect and the cavity filed. In the resolved sideband regime, when only a probe light is applied on the left side of the cavity, double OMIT is obtained due to the additional interference pathway where spacing between the two transparency window dips is determined by the coupling strength between the two-level defect and the mechanical resonator. When an auxiliary driving field is applied on the mechanical resonator it induces OMIAm due to its negative impact on the cavity field. Further, with the increasing amplitude of the auxiliary driving field, amplitudes of the two transparency window dips symmetrically become much deeper. Moreover, when the two probe fields are applied to the right and left sides of the cavity, the destructive interference of the probe fields generates three channels of OMIAb, where summation of the excitations of resonator and two-level defect is always two times of the normalized intracavity probe photon number for different values of the effective radiation pressure coupling.

Steady-state phase diagram of quantum gases in a lattice coupled to a membrane

In a recent experiment [Vochezer {\it et al.,} Phys. Rev. Lett. \textbf{120}, 073602 (2018)], a novel kind of hybrid atom-opto-mechanical system has been realized by coupling atoms in a lattice to a membrane. While such system promises a viable contender in the competitive field of simulating non-equilibrium many-body physics, its complete steady-state phase diagram is still lacking. Here we study the phase diagram of this hybrid system based on an atomic Bose-Hubbard model coupled to a quantum harmonic oscillator. We take both the expectation value of the bosonic operator and the mechanical motion of the membrane as order parameters, and thereby identify four different quantum phases. Importantly, we find the atomic gas in the steady state of such non-equilibrium setting undergoes a superfluid-Mott-insulator transition when the atom-membrane coupling is tuned to increase. Such steady-state phase transition can be seen as the non-equilibrium counterpart of the conventional superfluid-Mott-insulator transition in the ground state of Bose-Hubbard model. Further, no matter which phase the quantum gas is in, the mechanic motion of the membrane exhibits a transition from an incoherent vibration to a coherent one when the atom-membrane coupling increases, agreeing with the experimental observations. Our present study provides a simple way to study non-equilibrium many-body physics that is complementary to ongoing experiments on the hybrid atomic and opto-mechanical systems.

Directional amplifiers in a hybrid optomechanical system

The unidirectional amplification of signals is of great importance in signal processing and communication. We propose a hybrid optomechanical system to achieve directional amplification between light fields with different frequencies, where three cavities are coupled to a common mechanical resonator. Two cavities function as an input cavity and an output cavity, respectively, while the third cavity is introduced to facilitate the unidirectional transfer between the input and output cavities. In our scheme, three tones are required to realize the directional amplifier without requiring any gain medium or additional mechanical driving. We find that under certain conditions, the amplifier can reach a large photon number gain with the quantum-limited added noise, with no limitation on the gain–bandwidth product. Furthermore, the directional amplification behavior is controllable by modulating the phase differences between the effective optomechanical couplings.

Interference effects in hybrid cavity optomechanics

Radiation pressure forces in cavity optomechanics allow for efficient cooling of vibrational modes of macroscopic mechanical resonators, the manipulation of their quantum states, as well as generation of optomechanical entanglement. The standard mechanism relies on the cavity photons directly modifying the state of the mechanical resonator. Hybrid cavity optomechanics provides an alternative approach by coupling mechanical objects to quantum emitters, either directly or indirectly via the common interaction with a cavity field mode. While many approaches exist, they typically share a simple effective description in terms of a single force acting on the mechanical resonator. More generally, one can study the interplay between various forces acting on the mechanical resonator in such hybrid mechanical devices. This interplay can lead to interference effects that may, for instance, improve cooling of the mechanical motion or lead to generation of entanglement between various parts of the hybrid device. Here, we provide such an example of a hybrid optomechanical system where an ensemble of quantum emitters is embedded into the mechanical resonator formed by a vibrating membrane. The interference between the radiation pressure force and the mechanically modulated Tavis–Cummings interaction leads to enhanced cooling dynamics in regimes in which neither force is efficient by itself. Our results pave the way towards engineering novel optomechanical interactions in hybrid optomechanical systems.

Enhanced generation of charge-dependent second-order sideband and high-sensitivity charge sensors in a gain-cavity-assisted optomechanical system

We theoretically investigate the enhanced charge-dependent generation of the optical second-order sidebands (OSS) in a gain-cavity-assisted optomechanical (GCAOM) system coupled to a charged object. The hybrid optomechanical system is coherently driven by an external two-tone laser field which consists of a continuous-wave pump field and a pulsed probe field. Beyond the conventional linearized description of optomechanical interactions, the nonlinear optomechanical interactions are included in the Heisenberg-Langevin equations and are treated analytically by means of the perturbation method. It is shown that an assisted gain cavity can significantly enhance the OSS generation and can also lead to higher charge dependence of the output OSS spectrum than that achieved from a lossy cavity optomechanical system. Subsequently we discuss the application of such a GCAOM system as a family of high-sensitivity sensor for measuring the charges. Using experimentally achievable parameters, we identify the conditions under which the assisted gain cavity allows us to enhance the OSS generation and improve sensitivity of the sensor beyond what is achievable in a lossy cavity optomechanical system. The present investigation may provide a route toward modulating the nonlinear optical properties of the electro-optic hybrid system, as well as to guide the design of sensitive devices.

Effects of the Casimir force on the properties of a hybrid optomechanical system**Project supported by the National Natural Science Foundation of China (Grant Nos. 11574092, 61775062, 61378012, 91121023, and 60978009), the National Basic Research Program of China (Grant No. 2013CB921804), and the Innovation Project of Graduate School of South China Normal University (Grant No. 2017LKXM090).

We investigate the effects of the Casimir force on the output properties of a hybrid optomechanical system. In this system, a nanosphere is fixed on the movable-mirror side of the standard optomechanical system, and the nanosphere interacts with the movable-mirror via the Casimir force, which depends on the mirror–sphere separation. In the presence of the probe and control fields, we analyze the transmission coefficient and the group delay of the field-component with the frequency of the probe field. We also study the transmission intensity of the field-component with the frequency of a newly generated four-wave mixing (FWM) field. By manipulating the Casimir force, we find that a tunable slow light can be realized for the field-component with the frequency of the probe field, and the intensity spectrum of the FWM field can be enhanced and shifted effectively.