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Optics Express

A scheme for detecting the atom-field coupling constant in the Dicke superradiation regime using hybrid cavity optomechanical system

Yueming Wang, Bin Liu, Jinling Lian, Jiuqing Liang

Published Apr 18, 2012• 7 citations
Publisher

Abstract

We proposed a scheme for detecting the atom-field coupling constant in the Dicke superradiation regime based on a hybrid cavity optomechanical system assisted by an atomic gas. The critical behavior of the Dicke model was obtained analytically using the spin-coherent-state representation. Without regard to the dynamics of cavity field an analytical formula of one-to-one correspondence between movable mirror's steady position and atom-field coupling constant for a given number of atoms is obtained. Thus the atom-field coupling constant can be probed by measuring the movable mirror's steady position, which is another effect of the cavity optomechanics.

DOI
10.1364/oe.20.010106

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We proposed a scheme for detecting the atom-field coupling constant in the Dicke superradiation regime based on a hybrid cavity optomechanical system assisted by an atomic gas. The critical behavior of the Dicke model was obtained analytically using the spin-coherent-state representation. Without regard to the dynamics of cavity field an analytical formula of one-to-one correspondence between movable mirror's steady position and atom-field coupling constant for a given number of atoms is obtained. Thus the atom-field coupling constant can be probed by measuring the movable mirror's steady position, which is another effect of the cavity optomechanics.
We propose a scheme for entangling a movable mirror and two atomic ensembles in a coupled hybrid optomechanical system. Using the logarithmic negativity for the entanglement measure, we analyze the effect of the coupling strength between the two cavities on the entanglement of the movable mirror and the atomic ensembles, and we analyze the effect of the atom-cavity coupling constant on the entanglement of the movable mirror and the atomic ensembles. It is found that the entanglements of the movable mirror with one atomic ensemble transfer to the movable mirror with another atomic ensemble, and the robustness of the entanglement is enhanced by the coupling between the two cavities. The entanglements between the movable mirror and atomic ensembles are enhanced together with atom-cavity coupling increasing, and the entanglements have maxima in the accessibly parameters regime of the atom-cavity coupling constant.
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 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.
In this work, we explore the superradiant behavior of two Dicke models mechanically coupled through a shared vibrating membrane. Using a variational mean-field approach, we analyze the system's critical behavior and derive analytical expressions that reveal a threshold for the mechanical coupling. Below this threshold, the system allows for higher atomic-radiation couplings before resonant damping occurs, thereby extending the superradiant region compared to a single-cavity optomechanical Dicke model. Additionally, we examine the behavior of relevant observables across all regions of the phase diagram. Our findings suggest that these observables provide a more accurate characterization of the system's critical behavior than the traditionally used coupling parameters.
Abstract Motivated by the experimental realization of Dicke model in optical cavities, we model an optomechanical system consisting of two-level BEC atoms with transverse pumping. We investigate the transition from normal and inverted state to the superradiant phase through a detailed study of the phase portraits of the system. The rich phase portraits generated by analytical arguments display two types of superradiant phases, regions of coexistence and some portion determining the persistent oscillations. We study the time evolution of the system from any phase and discuss the role of mirror frequency in reaching their attractors. Further, we add an external mechanical pump to the mirror which is capable of changing the mirror frequency through radiation pressure and study the impact of the pump on the phase portraits and the dynamics of the system. We find the external mirror frequency changing the phase portraits and even shifting the critical transition point, thereby predicting a system with controllable phase transition.
We theoretically investigate optical bistability for a hybrid optomechanical system, where two cavities (an optomechanical cavity and a traditional one) are coupled together. A Kerr medium is inserted in the optomechanical cavity and there is an ultra-cold atomic gas inside the other. Dynamics of the system is described by Heisenberg-Langevin equations of motion in the steady-state regime. Bistability is observed in intracavity intensity for the optomechanical cavity, and the response of this phenomenon to optical parameters of the system is investigated. It is observed that the atomic medium has a deep effect on bistable behavior of intracavity intensity for the optomechanical cavity. Also, we determine a critical value for the Kerr coefficient of the Kerr medium to observe bistability in intracavity intensity for the optomechanical cavity.