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Physical Review A

Steady-state solutions of a hybrid system involving atom-light and optomechanical interactions: Beyond the weak-cavity-field approximation

Chang-Bao Fu, Xiao-Bo Yan, Kai-Hui Gu, Cui-Li Cui, Jin‐Hui Wu, Tai-Dong Fu

Published May 28, 2013• 28 citations
Publisher

Abstract

We investigate the steady-state properties of a hybrid system where many cold atoms are confined in an optical cavity with a movable end mirror. The confined cold atoms interact with an external pump field and an internal cavity field in the three-level $\ensuremath{\Lambda}$ configuration. The internal cavity field is excited by an external driving field and exerts a radiation pressure upon the movable end mirror. Then the coupled atom-light and optomechanical interactions offer an efficient nonlinear feedback mechanism permitting the observation of three steady-state solutions for relevant variables near one atomic resonance. We find, in particular, that the weak-cavity-field assumption may result in very large errors for the first and second solutions when the number of cavity photons is only about ${10}^{6}$. The main reason is that a typically weak light field can result in a sufficiently strong atom-light interaction in a very small cavity. Going beyond the weak-cavity-field assumption also allows us to observe an otherwise absent bistable behavior for the first solution in terms of mirror displacement and cavity photons, which is easy to control by modulating the pump and driving fields.

DOI
10.1103/physreva.87.053841

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We investigate the steady-state properties of a hybrid system where many cold atoms are confined in an optical cavity with a movable end mirror. The confined cold atoms interact with an external pump field and an internal cavity field in the three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration. The internal cavity field is excited by an external driving field and exerts a radiation pressure upon the movable end mirror. Then the coupled atom-light and optomechanical interactions offer an efficient nonlinear feedback mechanism permitting the observation of three steady-state solutions for relevant variables near one atomic resonance. We find, in particular, that the weak-cavity-field assumption may result in very large errors for the first and second solutions when the number of cavity photons is only about 106{10}^{6}106. The main reason is that a typically weak light field can result in a sufficiently strong atom-light interaction in a very small cavity. Going beyond the weak-cavity-field assumption also allows us to observe an otherwise absent bistable behavior for the first solution in terms of mirror displacement and cavity photons, which is easy to control by modulating the pump and driving fields.
We study the steady-state behaviors of a typical optomechanical cavity coupled to cold Rydberg atoms with dipole-dipole interactions. The interacting atoms are described as one superatom of three collective states in a ladder configuration in the limit of a strong dipole blockade and a weak cavity field. We find that this hybrid system exhibits phenomena of conditional duality and nonlinear bistability in terms of mirror displacement, number of cavity photons, and Rydberg population, depending on the detuning of the cavity field, the strength of the optical driving field, and the number of cold atoms. It is of particular interest that the two branches of relevant curves may intersect to yield a nontrivial duality and bistability. Such correlated optical, mechanical, and atomic responses arise from the efficient feedback between atom-light and optomechanical interactions and have realistic applications, e.g., in realizing accurate optomechanical detection or attaining deterministic single photons.
We study the optical bistability and dynamics in a hybrid optomechanical system, where the cavity mode is coupled to the mechanical resonator via radiation pressure and to a two-level atom via the Jaynes–Cummings coupling. The nonlinearity due to optomechanical coupling and the addition of an atom leads to bistable behaviors of the steady-state intracavity photon number and atomic population inversion. We show that the optical bistability can be effectively controlled by the Rabi frequency of the atomic driving field, the cavity–atom coupling strength, and the amplitude and frequency of the cavity pump field. Moreover, the effects of different initial conditions of the cavity field and the amplitude of the cavity pump field on the dynamics of the system also have been discussed.
Abstract We study the pump-probe response in an optomechanical cavity accommodating an ensemble of two-level atoms interacting with a cavity mode, which is pumped by a strong driving field and probed by a weak signal field. The atomic excitation is examined without taking any approximations and may be in any regimes ranging from the low limit to the high limit for a given collective coupling constant between the atomic ensemble and the cavity mode. This then results in different absorption and dispersion spectra (such as optomechanically induced transparency, Fano-resonance, normal-mode splitting) when the excitation transfer from cavity mode to atomic ensemble is controlled to change from ineffective to effective. This indicates that a hybrid optomechanical response is indeed determined by the excitation of the atomic ensemble embedded in the optomechanical cavity. It is also of interest that the output signal component and the inside atomic polarization show either synchronous or asynchronous behaviors depending on how the atom-field detuning is chosen, i.e. equal to the mechanical resonator frequency or its negative. Such features may open up an effective avenue in coherently manipulating the internal atomic polarization via the external signal field, and vice versa.
We have studied the steady-state properties of a hybrid optomechanical system, where a Y-type four-level atomic ensemble is confined in a microcavity with an oscillating mirror in one end. We find that the hybrid system will have multistability for the oscillating mirror and the confined atoms as the elastic coefficient of the spring decreases. When the elastic coefficient is very large, the oscillating mirror hardly affects the optomechanical system, therefore the system and the atomic ensemble have a single steady-state solution. However, when the elastic coefficient is small enough, the multiequilibrium positions of the oscillating mirror will be found, and the steady-state behaviors of the atomic ensemble confined in the microcavity may be affected. As a result, the susceptibility of the atomic ensemble will have multiple steady-state solutions and the probe absorption and dispersion will be changed as well. It has also been found that the number of steady-state solutions of the entire system could be controlled by changing the value of the elastic coefficient. These results may have potential applications in the area of high-precision quantum measurement and quantum information processing.
We investigate theoretically the effect of optical feedback from a cavity containing an ultracold two level atomic ensemble, on the bistable behavior shown by mean intracavity optical field in an optomechanical cavity resonator. It turns out that the optical bistability can be controlled by tuning the frequency and power of the single driving laser as well as by varying different system parameters provided by the hybrid interaction. Significantly, even though the atomic cavity is not driven by any laser pump and there is no coupling with the mechanical oscillator directly, the intracavity optical field in the atomic cavity also exhibits bistability due to the optical coupling with the optomechanical cavity. In essence, our work emphasizes the possibility of realization of a better controllable optical switch depending on the hybrid interaction.
‎We present a theoretical interacting one-dimensional Bose-Einstein condensate (BEC) inside an optical cavity which is driven through of the fixed end mirrors. Under the Bogoliubov approximation and when the number of photons inside the cavity is not too large, the atomic field operator can be considered as a single-mode quantum field which is coupled to the radiation pressure of the intracavity field. In this way, the system behaves like an optomechanical system with an extra nonlinear term corresponding to the atom-atom interaction.We show that one of the best ways of tracing the effect of atomic interaction is to study the noise power spectrum of the field of the cavity. For this purpose, we study the light intensity spectrum of the cavity as well as the entanglement between the optical cavity and the BEC. We show how the pattern of the power spectrum of the cavity changes due to the nonlinear effect of atomic collisions. Furthermore, it is shown that due to the s-wave scattering frequency of the atom-atom interaction, one can measure the strength of interatomic interaction. Besides, we show how the atomic collisions affect the entanglement between subsystems and cooling behavior of the BEC atoms.