Description of Bose-Einstein Condensates in \(\mathcal {PT}\)-Symmetric Double Wells

  • Dennis Dast
  • Daniel Haag
  • Holger Cartarius
  • Günter Wunner
  • Rüdiger Eichler
  • Jörg Main
Conference paper
Part of the Understanding Complex Systems book series (UCS)

Abstract

The Gross-Pitaevskii equation for a Bose-Einstein condensate in a \(\mathcal {PT}\)-symmetric double-well potential is investigated theoretically. An in- and outcoupling of atoms is modelled by an antisymmetric imaginary potential rendering the Hamiltonian non-Hermitian. Stationary states with real energies and \(\mathcal {PT}\)-symmetric wave functions are found, which proves that Bose-Einstein condensates are a good candidate for a first experimental verification of a \(\mathcal {PT}\)-symmetric quantum system. Time-resolved calculations demonstrate typical effects only observable in \(\mathcal {PT}\)-symmetric potentials, viz. an oscillation of the condensate’s probability density between these wells with an oscillation frequency critically depending on the strength of the in- and outcoupling. \(\mathcal {PT}\)-broken eigenstates with complex energy eigenvalues are also solutions of the time-independent Gross-Pitaevskii equation but are not true stationary states of its time-dependent counterpart. The comparison of a one-dimensional and a three-dimensional calculation shows that it is possible to extract highly precise quantitative results for a fully three-dimensional physical setup from a simple one-dimensional description.

Keywords

Bose-einstein condensates \(\mathcal {PT}\) symmetry Gross-pitaevskii equation Stationary states Dynamics 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Dennis Dast
    • 1
  • Daniel Haag
    • 1
  • Holger Cartarius
    • 1
  • Günter Wunner
    • 1
  • Rüdiger Eichler
    • 1
  • Jörg Main
    • 1
  1. 1.Institut Für Theoretische Physik 1Universität StuttgartStuttgartGermany

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