Spacetime analog of Bose-Einstein condensates: Bogoliubov–de Gennes formulation

Yasunari Kurita, Michikazu Kobayashi, Takao Morinari, Makoto Tsubota, and Hideki Ishihara
Phys. Rev. A 79, 043616 – Published 15 April 2009

Abstract

We construct quantum field theory in an analog curved spacetime in Bose-Einstein condensates based on the Bogoliubov–de Gennes equations by exactly relating quantum particles in curved spacetime with Bogoliubov quasiparticle excitations in Bose-Einstein condensates. Here, we derive a simple formula relating the two, which can be used to calculate the particle creation spectrum by solving the time-dependent Bogoliubov–de Gennes equations. Using our formulation, we numerically investigate particle creation in an analog expanding universe which can be expressed as Bogoliubov quasiparticles in an expanding Bose-Einstein condensate. We obtain its spectrum, which follows the thermal Maxwell-Boltzmann distribution, the temperature of which is experimentally attainable. Our derivation of the analogy is useful for general Bose-Einstein condensates and not limited to homogeneous ones, and our simulation is an example of particle creations by solving the Bogoliubov–de Gennes equation in an inhomogeneous condensate.

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  • Received 19 October 2008

DOI:https://doi.org/10.1103/PhysRevA.79.043616

©2009 American Physical Society

Authors & Affiliations

Yasunari Kurita1, Michikazu Kobayashi2, Takao Morinari3, Makoto Tsubota4, and Hideki Ishihara4

  • 1Department of Physics, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan
  • 2Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
  • 3Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
  • 4Department of Mathematics and Physics, Osaka City University, Osaka 558-8585, Japan

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Issue

Vol. 79, Iss. 4 — April 2009

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