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arXiv:0909.5465 · Physical Review A

Hamiltonian chaos in a coupled BEC–optomechanical-cavity system

K. Zhang, W. Chen, Mishkatul Bhattacharya, Pierre Meystre

Published Jan 5, 2010• 106 citations
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Abstract

We present a theoretical study of a hybrid optomechanical system consisting of a Bose-Einstein condensate (BEC) trapped inside a single-mode optical cavity with a moving end mirror. The intracavity light field has a dual role: it excites a momentum side mode of the condensate, and acts as a nonlinear spring that couples the vibrating mirror to that collective density excitation. We present the dynamics in a regime where the intracavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the dynamics of the system exhibits Hamiltonian chaos for appropriate initial conditions.

DOI
10.1103/physreva.81.013802

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We present a theoretical study of a hybrid optomechanical system consisting of a Bose-Einstein condensate (BEC) trapped inside a single-mode optical cavity with a moving end mirror. The intracavity light field has a dual role: it excites a momentum side mode of the condensate, and acts as a nonlinear spring that couples the vibrating mirror to that collective density excitation. We present the dynamics in a regime where the intracavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the dynamics of the system exhibits Hamiltonian chaos for appropriate initial conditions.
Cavity-optomechanics, a rapidly developing area of research, has made a remarkable progress. A stunning manifestation of optomechanical phenomena is in exploiting the mechanical effects of light to couple the optical degree of freedom with mechanical degree of freedom. In this report, we investigate the controlled bistable dynamics of such hybrid optomechanical system composed of cigar-shaped Bose-Einstein condensate (BEC) trapped inside high-finesse optical cavity with one moving-end mirror and is driven by a single mode optical field. The numerical results provide evidence for controlled optical bistability in optomechanics using transverse optical field which directly interacts with atoms causing the coupling of transverse field with momentum side modes, exited by intra-cavity field. This technique of transverse field coupling is also used to control bistable dynamics of both moving-end mirror and BEC. The report provides an understanding of temporal dynamics of moving-end mirror and BEC with respect to transverse field. Moreover, dependence of effective potential of the system on transverse field has also been discussed. To observe this phenomena in laboratory, we have suggested a certain set of experimental parameters. These findings provide a platform to investigate the tunable behavior of novel phenomenon like electromagnetically induced transparency and entanglement in hybrid systems.
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 cavity). 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 system 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.
We study the normal mode splitting in a system consisting of a Bose–Einstein condensates (BECs) trapped inside a Fabry–Pérot cavity driven by a single mode laser field. We analyze the variations in frequency and damping rate of the collective density excitation of a BEC imparted by the optical field. We study the occurrence of normal mode splitting which appears as consequences of the hybridization of the fluctuations of the intracavity field and the condensate mode. It is shown that normal mode splitting vanishes for weak coupling between the condensate mode and the intracavity field. Moreover, we investigate the normal mode splitting in the transmission spectrum of the cavity field.
We investigate the effects of atomic collisions as well as optomechanical mirror–field coupling on the optical bistability in a hybrid system consisting of a Bose–Einstein condensate inside a driven optical cavity with a moving end mirror. It is shown that the bistability of the system can be controlled by the s-wave scattering frequency which can provide the possibility of realizing a controllable optical switch. On the other hand, by studying the effect of the Bogoliubov mode, as a secondary mechanical mode relative to the mirror vibrations, on the cooling process as well as the bipartite mirror–field and atom–field entanglements we find an interpretation for the cooling of the Bogoliubov mode. The advantage of this hybrid system in comparison to the bare optomecanical cavity with a two-mode moving mirror is the controllability of the frequency of the secondary mode through the s-wave scattering interaction.
We investigate the effects of atomic collisions as well as optomechanical mirror–field coupling on the optical bistability in a hybrid system consisting of a Bose–Einstein condensate inside a driven optical cavity with a moving end mirror. It is shown that the bistability of the system can be controlled by the s-wave scattering frequency which can provide the possibility of realizing a controllable optical switch. On the other hand, by studying the effect of the Bogoliubov mode, as a secondary mechanical mode relative to the mirror vibrations, on the cooling process as well as the bipartite mirror–field and atom–field entanglements we find an interpretation for the cooling of the Bogoliubov mode. The advantage of this hybrid system in comparison to the bare optomecanical cavity with a two-mode moving mirror is the controllability of the frequency of the secondary mode through the s-wave scattering interaction.
We consider a cavity optomechanical system consisting of a Bose-Einstein condensate (BEC) interacting with two counterpropagating traveling-wave modes in an optical ring cavity. In contrast to the more familiar case where the condensate is driven by the standing-wave field of a high-QQQ Fabry-P\'erot cavity we find that both symmetric and antisymmetric collective density side modes of the BEC are mechanically excited by the light field. In the semiclassical, mean-field limit where the light field and the zero-momentum mode of the condensate are treated classically the system is found to exhibit a rich multistable behavior, including the appearance of isolated branches of solutions (isolas). We also present examples of the dynamics of the system as input parameters such as the frequency of the driving lasers are varied.