Description of Bose-Einstein Condensates in PT-Symmetric Double Wells

摘要

The Gross-Pitaevskii equation for a Bose-Einstein condensate in a 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 PT-symmetric wave functions are found, which proves that Bose-Einstein condensates are a good candidate for a first experimental verification of a PT-symmetric quantum system. Time-resolved calculations demonstrate typical effects only observable in 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. PT-broken eigen-states 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.