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Temperature Effects on the Quantum Coherence of Bosonic Josephson Junctions

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Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Part of the book series: Progress in Optical Science and Photonics ((POSP,volume 1))

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Abstract

We analyze the effects of temperature on the properties of a system of ultracold atoms confined by a double-well potential. We consider the case of repulsive interactions and review the different approximations to the exact many-body results.

Useful discussions with M. K. Oberthaler are gratefully acknowledged. This work has been supported by FIS2008-01661, and 2009-SGR1289. B. Juliá-Díaz is supported by the Ramón y Cajal program.

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Notes

  1. 1.

    Although the physics is of course different, the mathematical approach followed here is the familiar one in the theory of paramagnetism. See e.g. the textbooks of Ashcroft and Mermin [21] or Kittel [22]. In particular Eqs. (14), and (25) involve the same Brillouin function that plays a central role in the study of paramagnetic ions.

  2. 2.

    Note that in Refs. [23, 24] experimental data are measured for \(E_C = 0.016\,{\text{nK}},\, E_J =0.43\,{\text{nK}}\) and \(N=3000\) atoms. Thus \(E_J/(E_C N^2) =2.986 \cdot 10^{-4} \ll 1\). In our notations: \(E_J/(E_C N^2) = ( J N)/(2 UN^2) = 1/(4\gamma)\), and indeed this implies that \(\gamma \gg 1\) in their experiment.

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Authors and Affiliations

  1. ICFO-Institut de Ciències Fotòniques, Parc Mediterrani de la Tecnologia, 08860, Barcelona, Spain

    B. Juliá-Díaz

  2. Departament d’Estructura i Constituents de la Matèria, Facultat de Física, U. Barcelona, 08028, Barcelona, Spain

    J. Martorell & A. Polls

Authors
  1. B. Juliá-Díaz
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  2. J. Martorell
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  3. A. Polls
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Correspondence to B. Juliá-Díaz .

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Editors and Affiliations

  1. Faculty of Engineering The Iby and Aladar Fleischman, Tel Aviv University, Ramat Aviv, Israel

    Boris A. Malomed

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Juliá-Díaz, B., Martorell, J., Polls, A. (2012). Temperature Effects on the Quantum Coherence of Bosonic Josephson Junctions. In: Malomed, B. (eds) Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations. Progress in Optical Science and Photonics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10091_2012_17

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  • DOI: https://doi.org/10.1007/10091_2012_17

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  • Print ISBN: 978-3-642-21206-2

  • Online ISBN: 978-3-642-21207-9

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