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arXiv:1202.6453 · Physical Review Letters

Role Reversal in a Bose-Condensed Optomechanical System

Keye Zhang, Pierre Meystre, Weiping Zhang

Published Jun 14, 2012• 24 citations
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Abstract

We analyze the optomechanicslike properties of a Bose-Einstein condensate (BEC) trapped inside an optical resonator and driven by both a classical and a quantized light field. We find that this system exhibits the nature of role reversal between the matter-wave field and the quantized light field. As a result, the matter-wave field now plays the role of the quantized light field, and the quantized light field behaves like a movable mirror, in contrast to the familiar situation in BEC-based cavity optomechanics [Brennecke et al., Science 322, 235 (2008); Murch et al., Nature Phys. 4, 561 (2008)]. We demonstrate that this system can lead to the creation of a variety of nonclassical matter-wave fields, in particular, cat states, and discuss several possible protocols to measure their Wigner function.

DOI
10.1103/physrevlett.108.240405

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We analyze the optomechanicslike properties of a Bose-Einstein condensate (BEC) trapped inside an optical resonator and driven by both a classical and a quantized light field. We find that this system exhibits the nature of role reversal between the matter-wave field and the quantized light field. As a result, the matter-wave field now plays the role of the quantized light field, and the quantized light field behaves like a movable mirror, in contrast to the familiar situation in BEC-based cavity optomechanics [Brennecke et al., Science 322, 235 (2008); Murch et al., Nature Phys. 4, 561 (2008)]. We demonstrate that this system can lead to the creation of a variety of nonclassical matter-wave fields, in particular, cat states, and discuss several possible protocols to measure their Wigner function.
We analyze an atomic Bose-Einstein condensate trapped in a high-Q optical cavity driven by a feeble optical field, a situation formally analogous to the central paradigm of cavity optomechanics [Brennecke et al., Science, 322, 235 (2008)]. We account for two-body interactions via a two-fluid model that retains the intuitive appeal of the optomechanical two-mode description. The Bogoliubov excitation spectrum of this system comprises a gapped upper branch and a lower branch that can include an unstable excitation mode.
Various lower- and higher-order nonclassical properties have been studied for two physical systems- (i) an optomechanical system composed of a Fabry-Perot cavity with one nonlinearly oscillating mirror and (ii) an optomechanical-like system formed using a Bose-Einstein condensate (BEC) trapped inside an optical cavity. The investigation is performed using a perturbation method that leads to closed form analytic expressions for the time evolution of the relevant bosonic operators. In the first system, it is observed that the radiation pressure coupling leads to the emergence of lower- and higher-order squeezing, antibunching, entanglement and intermodal squeezing. The effects of the coherent interaction of a nonlinear oscillating mirror with the cavity mode are studied, and it is observed that the optomechanical system studied here becomes more nonclassical (entangled) when the coupling strength is increased. It is also observed that the possibility of observing entanglement depends on the phase of the movable mirror. The Hamiltonian of the trapped BEC system is obtained as a special case of the Hamiltonian of the first system, and the existence of various nonclassicality in the trapped BEC system has been established, and variations of those with various physical parameters have been reported with an aim to understand the underlying physical process that leads to and controls the nonclassicality.
We analyze a detailed model of a Bose-Einstein condensate (BEC) trapped in a ring optical resonator and contrast its classical and quantum properties to those of a Fabry-P\'erot geometry. The inclusion of two counterpropagating light fields and three matter field modes leads to important differences between the two situations. Specifically, we identify an experimentally realizable region where the system's behavior differs strongly from that of a BEC in a Fabry-P\'erot cavity, and also where quantum corrections become significant. The classical dynamics are rich, and near bifurcation points in the mean-field classical system, the quantum fluctuations have a major impact on the system's dynamics.
The dispersive interaction of a Bose-Einstein condensate with a single mode of a high-finesse optical cavity realizes the radiation pressure coupling Hamiltonian. In this system the role of the mechanical oscillator is played by a single condensate excitation mode that is selected by the cavity mode function. We study the effect of atomic s-wave collisions and show that it merely renormalizes parameters of the usual optomechanical interaction. Moreover, we show that even in the case of strong harmonic confinement – which invalidates the use of Bloch states – a single excitation mode of the Bose-Einstein condensate couples significantly to the light field, that is the simplified picture of a single "mechanical" oscillator mode remains valid.
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 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.