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Generation of atomic-squeezed states via dynamical Casimir effect

Neha Aggarwal, Aranya B. Bhattacherjee, Arup Banerjee

Published Aug 18, 2013• 1 citation
OpenAlex

Abstract

We investigate the generation of atomic-squeezed states due to the dynamical Casimir effect in a lossless optomechanical cavity containing a Bose-Einstein Condensate. In particular, we study the combined effect of dynamical Casimir effect and nonlinear atomic interaction on spin-squeezing for the three special cases- initial cavity field in coherent state, squeezed vaccum state and squeezed state. We show that the dynamical Casimir effect plays a significant role in producing the squeezed-spin states by producing squeezed states of the optical field which is then transferred to the condensate atoms. We further show that the maximum spin-squeezing is obtained in the case of initial cavity field prepared in the squeezed state.

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We investigate the generation of atomic-squeezed states due to the dynamical Casimir effect in a lossless optomechanical cavity containing a Bose-Einstein Condensate. In particular, we study the combined effect of dynamical Casimir effect and nonlinear atomic interaction on spin-squeezing for the three special cases- initial cavity field in coherent state, squeezed vaccum state and squeezed state. We show that the dynamical Casimir effect plays a significant role in producing the squeezed-spin states by producing squeezed states of the optical field which is then transferred to the condensate atoms. We further show that the maximum spin-squeezing is obtained in the case of initial cavity field prepared in the squeezed state.
We investigate the effect of optomechanical coupling on the squeezed-spin states for a Bose-Einstein Condensate embedded within the lossless optomechanical cavity for the three special cases of initial states of cavity field, namely, a coherent state, a squeezed vacuum state and a squeezed state. We show that the radiation pressure or pondermotive force acting on the cavity end mirror plays a significant role in producing the atomic-squeezed states by producing squeezed states of the cavity field which is then transferred to the condensate. We further show that the maximum spin-squeezing along the x-direction is obtained in the presence of optomechanical coupling for the initial cavity field prepared in the amplitude squeezed state, whereas, squeezing along the y-direction reaches a maximum value in the absence of optomechanical coupling for the initial coherent cavity field. We also study the additional effect of nonlinear atomic interaction on spin-squeezing.
We study the generation of atomic-squeezed states for a Bose-Einstein Condensate confined within the lossless optomechanical cavity using pondermotively squeezed light. We show that the radiation pressure coupling between the optical cavity field and mechanical motion of the cavity end mirror generates squeezing of light. This radiation pressure induced light squeezing gets transferred to the condensate atoms via Tavis-Cummings type interaction and results in squeezed-spin states. We further discuss the effect of optomechanical coupling on squeezed atomic states.
It is well known that squeezed states can be produced by nonlinear optical processes, such as parametric amplification and four wave mixing, in which two photons are created or annihilated simultaneously. Since the Hamiltonian of the dynamic Casimir effect contains a 2 and a +2, photons in such a process are also generated or annihilated in pairs. Here we propose to get squeezed light through the dynamic Casimir effect. Specifically, we demonstrate it from the full quantum perspective and the semiclassical perspective successively. Different from previous work, we focus on generating squeezed states with the lowest average photon number, because such squeezed states have better quantum properties. For the full quantum picture, that is, phonons also have quantum properties, when the system is initially in the excited state of phonons, squeezed light cannot be generated during the evolution, but the light field can collapse to the squeezed state by measuring the state of phonons. When the phonon is treated as a classical quantity, that is, the cavity wall is continuously driven, squeezed light with the minimum average photon number will be generated in the case of off-resonance. This will play a positive role in better regulating the photon state generated by the dynamic Casimir system in the future.
In this paper, we investigate theoretically a system consisting of a one dimensional Bose-Einstein condensate trapped inside the optical lattice of an optical cavity. In the weak-interaction regime and under the Bogoliubov approximation, the wave function of the Bose-Einstein condensate can be described by a classical field (condensate mode) having some quantum fluctuations (the Bogoliubov mode) about the mean value. Such a system behaves as a so-called atomic parametric amplifier, similar to an optical parametric amplifier, where the condensate and the Bogoliubov modes play respectively, the roles of the pump field and the signal mode in the degenerate parametric amplifier and the s-wave scattering frequency of atom-atom interaction plays the role of the nonlinear gain parameter. We show that using the nonlinear effect of atomic collisions, how one can manipulate and control the state of the Bogoliubov mode and produce squeezed states.
In this paper, we investigate theoretically a system consisting of a one-dimensional Bose–Einstein condensate trapped inside the optical lattice of an optical cavity. In the weak-interaction regime and under the Bogoliubov approximation, the wave function of the Bose–Einstein condensate can be described by a classical field (condensate mode) having some quantum fluctuations (the Bogoliubov mode) about the mean value. Such a system behaves as a so-called atomic parametric amplifier, similar to an optical parametric amplifier, where the condensate and the Bogoliubov modes play, respectively, the roles of the pump field and the signal mode in the degenerate parametric amplifier and the s-wave scattering frequency of atom–atom interaction plays the role of the nonlinear gain parameter. We show that using the nonlinear effect of atomic collisions, how one can manipulate and control the state of the Bogoliubov mode and produce squeezed states.