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arXiv:1411.3865 · Journal of Physics B Atomic Molecular and Optical Physics

The effect of atomic collisions on the quantum phase transition of a Bose–Einstein condensate inside an optical cavity

A Dalafi, M. H. Naderi, M Soltanolkotabi

Published Apr 17, 2015• 18 citations
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Abstract

Abstract In this paper, we investigate the effect of atomic collisions on the phase transition form the normal to the superradiant phase in a one-dimensional Bose–Einstein condensate (BEC) trapped inside an optical cavity. Specifically, we show that driving the atoms from the side of the cavity leads to the excitation of modes in the edges of the first Brillouin zone of every energy band, which results in the two-mode approximation of the BEC matter field in the limit of weak coupling regime. The nonlinear effect of atom–atom interaction shifts the threshold of the quantum phase transition of the BEC and also affect the power low behavior of quantum fluctuations in the total particle number. Besides, we show the possibility of controlling the quantum phase transition of the system through the s -wave scattering frequency when the strength of the transverse pumping has been fixed.

DOI
10.1088/0953-4075/48/11/115507

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Abstract In this paper, we investigate the effect of atomic collisions on the phase transition form the normal to the superradiant phase in a one-dimensional Bose–Einstein condensate (BEC) trapped inside an optical cavity. Specifically, we show that driving the atoms from the side of the cavity leads to the excitation of modes in the edges of the first Brillouin zone of every energy band, which results in the two-mode approximation of the BEC matter field in the limit of weak coupling regime. The nonlinear effect of atom–atom interaction shifts the threshold of the quantum phase transition of the BEC and also affect the power low behavior of quantum fluctuations in the total particle number. Besides, we show the possibility of controlling the quantum phase transition of the system through the s -wave scattering frequency when the strength of the transverse pumping has been fixed.
In this paper, we have investigated theoretically the influence of atomic collisions on the behavior of a one-dimensional Bose-Einstein condensate inside a driven optical cavity. We develop the discrete-mode approximation for the condensate taking into account the interband transitions due to the sss-wave scattering interaction. We show that in the Bogoliubov approximation the atom-atom interaction shifts the energies of the excited modes and also plays the role of an optical parametric amplifier for the Bogoliubov side mode which can affect its normal-mode splitting behavior. On the other hand due to the atomic collisions the resonance frequency of the cavity is shifted which leads to the decrease of the number of cavity photons and the depletion of the Bogoliubov mode. Besides, it reduces the effective atom-photon coupling parameter which consequently leads to the decrease of the entanglement between the Bogoliubov mode and the optical field.
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.
‎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.
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.
Abstract We present a theoretical study of the phase noise, intensity and quadrature squeezing power spectra of the transmitted field of a driven optical cavity containing an interacting one-dimensional Bose–Einstein condensate. We show how the pattern of the output power spectrum of the cavity changes due to the nonlinear effect of atomic collisions. Furthermore, it is shown that due to a one-to-one correspondence between the splitting of the peaks in the phase noise power spectrum of the cavity output field and the s -wave scattering frequency of the atom–atom interaction, one can measure the strength of interatomic interaction. In addition, we show how the atomic collisions affect the squeezing behavior of the output field.