Bose-Einstein condensates in PT-symmetric double wells |
|
| Günter Wunner | |
| Universität Stuttgart | |
|
The existence of PT-symmetric wave functions describing Bose-Einstein condensates in realistic one-dimensional and fully three-dimensional double-well setups is investigated theoretically. When particles are removed from one well and coherently injected into the other the external potential is PT-symmetric. We solve the nonlinear Gross-Pitaevskii equation using the time-dependent variational principle (TDVP). We show that the PT-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. We find that indeed two branches of real eigenvalues exist up to a critical strength of the nonlinearity, at which the two solutions merge in a branch point. This behaviour is analogous to that found in studies of optical wave guides with loss and gain [1].
A surprising result, however, is that although there also appears a branch of two complex conjugate eigenvalues, which correspond to PT-broken solutions, the latter are not born at the branch point but at a lesser value of the strength of the nonlinearity where they bifurcate from the real eigenvalue branch of the ground state. This implies that there is a range of values of the nonlinearity where two real and two complex eigenvalues coexist. Obviously this is a consequence of the nonlinearity in this PT-symmetric system. It agrees with previous findings in studies of a Bose-Einstein condensate in a PT-symmetric delta-functions double well [2] and of a PT symmetric Bose-Hubbard dimer with loss and gain [3]. The applicability of the TDVP is confirmed by comparing its results with numerically exact solutions in the one-dimensional case. The linear stability analysis and the temporal evolution of condensate wave functions reveal [4] that the PT-symmetric condensates are stable and should be observable in an experiment. [1] S. Klaiman, U. G¸nther, and N. Moiseyev, Phys. Rev. Lett. 101, 080402 (2008). |