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.
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Dast, D., Haag, D., Cartarius, H., Wunner, G., Eichler, R., Main, J. (2016). Description of Bose-Einstein Condensates in \(\mathcal {PT}\)-Symmetric Double Wells. In: Wunner, G., Pelster, A. (eds) Selforganization in Complex Systems: The Past, Present, and Future of Synergetics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-27635-9_9
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