A Bose-Einstein condensate in a ���� symmetric double well



The existence of ���� symmetric wave functions describing Bose-Einstein condensates in a one-dimensional and a fully three-dimensional double-well setup is investigated theoretically. When particles are removed from one well and coherently injected into the other the external potential is ���� symmetric. We solve the underlying Gross-Pitaevskii equation by way of the time-dependent variational principle (TDVP) and show that the ���� symmetry of the external potential is preserved by both the wave functions and the nonlinear Hamiltonian as long as eigenstates with real eigenvalues are obtained. ���� broken solutions of the time-independent Gross-Pitaevskii equation are also found but have no physical relevance. To prove the applicability of the TDVP we compare its results with numerically exact solutions in the one-dimensional case. The linear stability analysis and the temporal evolution of condensate wave functions demonstrate that the ���� symmetric condensates are stable and should be observable in an experiment.