Long-time averaged dynamics of a Bose–Einstein condensate in a bichromatic optical lattice with external harmonic confinement

Abstract

The dynamics of a Bose–Einstein condensate are examined numerically in the presence of a one-dimensional bichromatic optical lattice (BCOL) with external harmonic confinement in the strongly interacting regime. The condensate is excited by a focusing stirring red laser. Two realizations of the BCOL are considered, one with a rational and the other with an irrational ratio of the two constituting wave lengths. The system is simulated by the time-dependent Gross Pitaevskii equation that is solved using the Crank Nicolson method in real time. It is found that for a weak BCOL, the long-time averaged physical observables of the condensate respond only very weakly (or not at all) to changes in the secondary OL depth V1 showing that under these conditions the harmonic trap plays a dominant role in governing the dynamics. However, for a much larger strength of the BCOL, the response is stronger as it begins to compete with the external harmonic trap, such that the frequency of Bloch oscillations of the bosons rises with V1 yielding higher time-averages. Qualitatively there is no difference between the dynamics of the condensate resulting from the use of a rational or irrational ratio of the wavelengths since the external harmonic trap washes it out. It is further found that in the presence of an external harmonic trap, the BCOL acts in favor of superflow.