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arXiv:1209.3354 · Journal of Modern Optics

Cavity optomechanics with a Bose–Einstein condensate: normal mode splitting

Muhammad Asjad

Published Apr 24, 2012• 16 citations
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Abstract

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.

DOI
10.1080/09500340.2012.679706

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We study an optomechanical system in which the collective density excitations (Bogoliubov modes) of a Bose Einstein condensate (BEC) is coupled to a cavity field. We show that the optical force changes the frequency and the damping constant of the collective density excitations of the BEC. We further analyze the occurrence of normal mode splitting (NMS) due to mixing of the fluctuations of the cavity field and the fluctuations of the condensate with finite atomic two-body interaction. The NMS is found to vanish for small values of the two-body interaction. We further show that the density excitations of the condensate can be used to squeeze the output quantum fluctuations of the light beam. This system may serve as an optomechanical control of quantum fluctuations using a Bose Einstein condensate.
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.
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.
We give a brief overview of the basic aspects of the optomechanical interaction between a light field and a mechanical mode of ultracold bosonic and fermionic atomic gases inside a Fabry–Pérot cavity, showing that these systems provide a ‘bottom up’ approach to cavity optomechanics. In contrast to the case of a Bose condensate, where the effective ‘moving mirror’ is a side mode whose occupation results simply from photon recoil, for fermionic atoms this ‘mirror’ is a collective density oscillation associated with particle–hole excitations. We also discuss the experimental consequences of the optomechanical coupling in optical bistability.
‎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.