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Nonlinear effects of atomic collisions on the optomechanical properties of a Bose-Einstein condensate in an optical cavity

A. Dalafi, M. H. Naderi, M. Soltanolkotabi, and Sh. Barzanjeh
Phys. Rev. A 87, 013417 – Published 17 January 2013
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  • INTRODUCTION
  • THEORETICAL DESCRIPTION OF THE SYSTEM
  • DYANAMICS OF THE OPTOMECHANICAL SYSTEM
  • NUMERICAL SOLUTIONS TO THE MEAN FIELDS…
  • SUSCEPTIBILITY AND POWER SPECTRUM OF THE…
  • CONCLUSIONS
  • ACKNOWLEDGEMENTS
    • References

    Abstract

    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 s-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.

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    • Received 11 November 2012

    DOI:https://doi.org/10.1103/PhysRevA.87.013417

    ©2013 American Physical Society

    Authors & Affiliations

    A. Dalafi1,*, M. H. Naderi1,2, M. Soltanolkotabi1,2, and Sh. Barzanjeh1,3

    • 1Department of Physics, Faculty of Science, University of Isfahan, Hezar Jerib, 81746-73441, Isfahan, Iran
    • 2Quantum Optics Group, Department of Physics, Faculty of Science, University of Isfahan, Hezar Jerib, 81746-73441, Isfahan, Iran
    • 3School of Science and Technology, Physics Division, Universita di Camerino, I-62032 Camerino (MC), Italy

    • *adalafi@yahoo.co.uk

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    Vol. 87, Iss. 1 — January 2013

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    Images

    • Figure 1
      Figure 1
      N two-level atoms trapped in an optical cavity interacting dispersively with a single cavity mode. The cavity mode is driven by a laser at rate η and the decay rate is κ.Reuse & Permissions
    • Figure 2
      Figure 2
      (a) The mean cavity photon number and (b) the mean value fraction of atoms in the Bogoliubov side mode c10 versus the normalized cavity detuning Δc/ωR for two values of ωsw=ωR (thin line) and ωsw=10ωR (thick line). The parameters are N=6×104, U0=0.96ωR, κ=363.9ωR, γ=0.001κ, η=80.06ωR, and T=10−7K.Reuse & Permissions
    • Figure 3
      Figure 3
      (a) The normalized resonance frequency of the cavity Δc(Res)/ωR and (b) the normalized effective atom-photon coupling G/ωR (thick line) and the mean photon number magnified by 103 (thin line) versus the normalized s-wave scattering frequency ωsw/ωR. The parameters are the same as those of Fig. 2. The cavity detuning has been set at Δc=28966ωR.Reuse & Permissions
    • Figure 4
      Figure 4
      The incoherent excitation numbers of the photons (a), the incoherent excitation numbers of atoms in the Bogoliubov side mode c10 (b), and the entanglement between the Bogoliubov mode c10 and the optical field (c) versus normalized cavity detuning Δc/ωR for two different values of ωsw=ωR (thin line) and ωsw=10ωR (thick line). All parameters are the same as those of Fig. 2.Reuse & Permissions
    • Figure 5
      Figure 5
      The effects of temperature on the incoherent excitation numbers of photons (thin line) and atoms in the Bogoliubov side mode (dashed line) as well as the entanglement between photons and atoms (thick line). The cavity detuning has been set at Δc=28900ωR and the s-wave scattering frequency has been considered to be ωsw=ωR. The other parameters are the same as those of Fig. 2. For clarity, the values of δnph and EN have been multiplied by 100 and 1000, respectively.Reuse & Permissions
    • Figure 6
      Figure 6
      (a) Normalized effective Bogoliubov mechanical frequency Ωeff/ωm, (b) normalized effective Bogoliubov mechanical damping Γeff/ωm, and (c) normalized power spectrum of the displacement operator of the Bogoliubov mode versus the normalized frequency ω/ωm for two values of ωsw=80ωR (thin line) and ωsw=140ωR (thick line) and for Δc=28700ωR and κ=72.8ωR. The other parameters are the same as those of Fig. 2.Reuse & Permissions
    • Figure 7
      Figure 7
      (a) Normalized effective Bogoliubov mechanical frequency Ωeff/ωm, (b) normalized effective Bogoliubov mechanical damping Γeff/ωm, and (c) normalized power spectrum of the displacement operator of the Bogoliubov mode versus the normalized frequency ω/ωm for two values of ωsw=80ωR (thin line) and ωsw=140ωR (thick line) and for Δc=28700ωR and κ=24.3ωR. The other parameters are the same as those of Fig. 2.Reuse & Permissions
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