非线性光学腔中的相位调制光机械动力学

研究了Fabry-Perot光学腔中包含一个光学参量放大器来增强腔场与机械振子之间的耦合的光机械动力学行为.在解析边带机制下用量子郞之万方程具体研究了振子的涨落光谱、光学多稳态行为、机械阻尼与修正共振频移和基态冷却.通过数值解讨论了辐射压力诱导机械振子和腔场的稳态振幅所展现的光学多稳态行为,同时也分析了辐射压力引起的修正共振频移和机械阻尼与参量增益、输入激光功率和参量相位这三个因素的关系.此外,随着调节泵浦场的参量相位,振子的涨落光谱呈现简正模式分裂.通过精确求解最终有效声子数论证了基态冷却.结果表明,机械振子的冷却由初始浴温度、机械品质因数和参量相位这个三个因素控制.参量相提供一个新的方法来操控非线性光机械动力学.     

Optomechanical coupling between two optical cavities: Cooling of a micro-mirror and parametric normal mode splitting

We propose a technique aimed at cooling a harmonically oscillating mirror mechanically coupled to another vibrating mirror to its quantum mechanical ground state. Our method involves optomechanical coupling between two optical cavities. We show that the cooling can be controlled by the mechanical coupling strength between the two movable mirrors, the phase difference between the mechanical modes of the two oscillating mirrors and the photon number in each cavity. We also show that both mechanical and optical cooling can be achieved by transferring energy from one cavity to the other. We also analyze the occurrence of normal-mode splitting (NMS). We find that a hybridization of the two oscillating mirrors with the fluctuations of the two driving optical fields occurs and leads to a splitting of the mechanical and optical fluctuation spectra.     

The occurrence of multistability and normal mode splitting in an optomechanical system

We provide a theoretical technique to study the occurrence of multistability and normal mode splitting in an optomechanical system driven by a single mode cavity field. For this purpose, we consider the position-dependent mass mechanical resonator (PDMR) which produces the nonlinearity in the system. This shifts the system from monostable to bistable regime and bistable to a multistable regime at different conditions of the nonlinearity. Further, we use the Fourier transform technique to find out the fluctuation in the position of the nano-mechanical resonator and their energy spectrum as well. Moreover, we used the input-output theory to analyze the transmitted field spectrum as well as x and y quadratures spectra of the output field. We explain the effect of the non-linearity on the normal mode splitting of the former and later spectra. In addition, we also explain the normal mode splitting as a function of cavity decay rate and laser power, respectively.     

非线性光学腔中的相位调制光机械动力学

研究了Fabry-Perot光学腔中包含一个光学参量放大器来增强腔场与机械振子之间的耦合的光机械动力学行为.在解析边带机制下用量子郎之万方程具体研究了振子的涨落光谱、光学多稳态行为、机械阻尼与修正共振频移和基态冷却,通过数值解讨论了辐射压力诱导机械振子和腔场的稳态振幅所展现的光学多稳态行为,同时也分析了辐射压力引起的修...     

Optomechanically dark state in hybrid BEC–optomechanical systems

We study theoretically the propagation of slow light in a hybrid BEC–optomechanical system comprising a Bose–Einstein condensate (BEC) trapped inside an optical cavity with a moving end mirror. We show that when the system is driven by a weak probe in the presence of a strong laser field, there exists an analog of the electromagnetically induced transparency (EIT) in coupled BEC–optomechanical systems. When the coupling of the cavity field with a mechanical mirror and the condensate mode is considered simultaneously, three absorption peaks appear in the output spectrum of the probe field. The central absorption peak appears in the reflection spectrum of the weak probe field when the pump-probe detuning occurs at half the sum of frequencies of the two oscillators, which corresponds to the long-live dark state. Furthermore, we also study the occurrence of normal mode splitting in the output spectrum of the probe and Stokes fields.     

Generation of Steady-State Entanglement in Quadratically Coupled Optomechanical System Assisted by Two-Level Atoms

We propose a scheme for the realization of a hybrid, strongly entangled system formed of an atomic ensemble surrounded by a quadratically coupled optomechanical cavity with a vibrating mirror. We firstly investigate the steady-state bipartite entanglement between the movable mirror and the cavity mode with the help of an atomic media. It shows that the introduction of the atomic medium can greatly improve the entanglement between the movable mirror and the cavity mode. Secondly, steady-state tripartite entanglement including the movable mirror, the cavity and atom media are investigated. We find the robust tripartite entanglement persists in the present system.     

Normal mode splitting and ground state cooling in a Fabry-Perot optical cavity and transmission line resonator

Optomechanical dynamics in two systems which are a transmission line resonator and Fabrya-Perot optical cavity via radiation-pressure are investigated by linearized quantum Langevin equation. We work in the resolved sideband regime where the oscillator resonance frequency exceeds the cavity linewidth. Normal mode splittings of the mechanical resonator as a pure result of the coupling interaction in the two optomechanical systems is studied, and we make a comparison of normal mode splitting of mechanical resonator between the two systems. In the optical cavity, the normal mode splitting of the movable mirror approaches the latest experiment very well. In addition, an approximation scheme is introduced to demonstrate the ground state cooling, and we make a comparison of cooling between the two systems dominated by two key factors, which are the initial bath temperature and the mechanical quality factor. Since both the normal mode splitting and cooling require working in the resolved sideband regime, whether the normal mode splitting influences the cooling of the mirror is considered. Considering the size of the mechanical resonator and precooling the system, the mechanical resonator in the transmission line resonator system is easier to achieve the ground state cooling than in optical cavity.     

Optical multistability and cooling of a micromechanical mirror induced by radiation pressure in optomechanical cavity

The radiation-pressure induces the movable mirror and the steady-state amplitude of the cavity field displaying an optical multistable behavior is investigated in detail by numerical evaluation in Fabry–Perot optical cavity. We introduce an approximation scheme to derive and analyze the final effective mean phonon number using linearized quantum Langevin equation to describe optomechanical cooling. Our results show that the movable mirror can be cooled close to its ground state with low initial temperature and high mechanical quality factor.     

Optomechanical dynamics in detuned whispering-gallery modes cavity

The dynamics of a microresonator in detuned whispering-gallery modes (WGM) cavity opto-mechanical system are investigated by the quantum Langevin equation. A WGM cavity coupling to two parallel waveguides is devised to study the transmission and reflection of this system. In single mode WGM cavity, without optomechanical coupling, both the transmission and reflection of the cavity present a Lorentzian dip and peak. When the coupling between the cavity mode and mechanical mode is considered, the transmission and reflection of the optomechanical cavity show “W” and “M” shape mode splitting. Moreover, under the action of a controlling and a probe laser, the output field at the probe frequency presents electromagnetically induced transparency (EIT)-like spectrum in the system. We give the physical origin of EIT-like and the pump-probe response for the WGM shares all the features of the Λ system in atoms. Further, due to backscattering, the two traveling waves in WGM are coupled with a rate γ. The transmission and reflection of the optomechanical cavity display three modes splitting in the spectra with optomechanical coupling between the two cavity modes and the mechanical mode.     

Controllable Photon Transport in a Three-Mode Optomechanical System with the Non-Rotating Wave Approximation Effect

We propose a scheme for realizing controllable photon transport in a three-mode optomechanical system comprising one cavity and two mechanical modes. We found that the non-rotating wave approximation effect can cause the ideal optomechanically induced transparency of the output field. The effects of the cavity mode decay rate on the width of the optomechanically induced transparency window, the dispersion curve slope are discussed in the resolved sideband regime and the unresolved sideband regime.

     

Cavity-mediated stationary atom–mirror entanglement in the presence of photothermal effects

We study stationary entanglement properties of an optomechanical system containing an atomic ensemble. We focus onto the case of the movable mirror strongly coupled to the cavity field through both radiation pressure and photothermal force. Exploiting a quantum Langevin equation approach we investigate the bipartite entanglement properties of various bipartite subsystems as well as stationary tripartite entanglement of the system. We particularly study robustness of the atom–mirror entanglement against temperature. We show that, even though the photothermal force is a dissipative force, it can significantly improve the cavity mediated atom–mirror entanglement.     

Electromagnetically induced transparency and quadripartite macroscopic entanglement generated in a ring cavity

We propose a feasible scheme to generate electromagnetically induced transparency(EIT) and quadripartite macroscopic entanglement in an optomechanical system with one fixed mirror and three movable perfectly reflecting mirrors.We explore the EIT phenomena in this optomechanical system.Results show the appearance of EIT dips in the output field.Moreover,we demonstrate how steady-state quadripartite entanglement can be generated via radiation pressure.We also quantify the bipartite entanglement in each field-mirror subsystem and in the mirror-mirror subsystem.Findings show that a high intensity of entanglement between two subsystems can be achieved.     

Triple optomechanical induced transparency in a two-cavity system

We theoretically investigate the optomechanical induced transparency(OMIT) phenomenon in a two-cavity system which is composed of two optomechanical cavities. Both of the cavities consist of a fixed mirror and a high-Q mechanical resonator, and they couple to each other via a common waveguide. We show that in the presence of a strong pump field applied to one cavity and a weak probe field applied to the other, a triple-OMIT can be observed in the output field at the probe frequency. The two mechanical resonators in the two cavities are identical, but they lead to different quantum interference pathways. The transparency windows are induced by the coupling of the two cavities and the optical pressure radiated to the mechanical resonators, which can be controlled via the power of the pump field and the coupling strength of the two cavities.     

Double optomechanical transparency with direct mechanical interaction

We present a mechanism for double transparency in an optomechanical system. This mechanism is based on the coupling of a moving cavity mirror to a second mechanical oscillator. Due to the purely mechanical coupling and the radiation pressure, three pathways are established for excitations of the probe photons into the cavity photons. Destructive interference occurs at two different frequencies, leading to double transparency to the probe field. It is the coupling strength between the mechanical oscillators that determines the locations of the transparency windows. Moreover, the normal splitting appears for the generated Stokes field and the four-wave mixing process is inhibited on resonance.     

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.     

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.     

Opto-Mechanical Effects in Superradiant Light Scattering by Bose-Einstein Condensate in an Optical Cavity

We investigate the effects of a movable mirror (cantilever) of an optical cavity on the superradiant light scattering from a Bose-Einstein condensate (BEC) in an optical lattice. We show that the mirror motion has a dynamic dispersive effect on the cavity-pump detuning. Varying the intensity of the pump beam, one can switch between the pure superradiant regime and the Bragg scattering regime. The mechanical frequency of the mirror strongly influences the time interval between two Bragg peaks. We find that when the system is in the resolved side band regime for mirror cooling, the superradiant scattering is enhanced due to coherent energy transfer from the mechanical mirror mode to the cavity field mode.     

Opto-Mechanical Effects in Superradiant Light Scattering by Bose-Einstein Condensate in an Optical Cavity

We investigate the effects of a movable mirror (cantilever) of an optical cavity on the superradiant light scattering from a Bose-Einstein condensate (BEC) in an optical lattice. We show that the mirror motion has a dynamic dispersive effect on the cavity-pump detuning. Varying the intensity of the pump beam, one can switch between the pure superradiant regime and the Bragg scattering regime. The mechanical frequency of the mirror strongly influences the time interval between two Bragg peaks. We find that when the system is in the resolved side band regime for mirror cooling, the superradiant scattering is enhanced due to coherent energy transfer from the mechanical mirror mode to the cavity field mode.     

Tunable optomechanically induced transparency and fast–slow light in a loop-coupled optomechanical system

We theoretically explore the tunability of optomechanically induced transparency(OMIT) phenomenon and fast–slow light effect in a loop-coupled hybrid optomechanical system in which two optical modes are coupled to a common mechanical mode. In the probe output spectrum, we find that the interference phenomena OMIT caused by the optomechanical interactions and the normal mode splitting(NMS) induced by the strong tunnel coupling between the cavities can be observed. We further observe that the tunnel interaction will affect the distance and the heights of the sideband absorption peaks. The results also show that the switch from absorption to amplification can be realized by tuning the driving strength because of the existence of stability condition. Except from modulating the tunnel interaction, the conversion between slow light and fast light also can be achieved by adjusting the optomechanical interaction in the output field. This study may provide a potential application in the fields of high precision measurement and quantum information processing.     

Observation of electromagnetically induced transparency in a ring cavity

A scheme to observe Electromagnetically induced transparency (EIT) in an optomechanical system is proposed in the current paper. We treat a narrowband squeezed field as the weak probe field. We find that EIT dips exist in the output field. Moreover, the dependence of the EIT dips on the effective cavity detuning Δ and the input power ζ are explored. We show that the width of the EIT dips can be controlled by the parameters ξ and the detuning Δ.