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

The dynamics of a Bose-Einstein condensate are examined numerically in the presence of a one-dimensional bichromatic optical lattice with external harmonic confinement. The condensate is excited by a focusing red laser. For this purpose, the time-dependent Gross Pitaevskii equation is solved using the Crank Nicolson method in real time. Two realizations of the optical lattice are considered, one with a rational and the other with an irrational ratio of the two constituting wave lengths. For a weak bichromatic optical lattice, the long-time averaged physical observables of the condensate respond only very weakly (or not at all) to changes in the secondary optical lattice depth. However, for a much larger strength of the latter optical lattice, the response is stronger. It is found that qualitatively there is no difference between the dynamics of the condensate resulting from the use of a rational or irrational ratio of the optical lattice wavelengths since the external harmonic trap washes it out. It is further found that in the presence of an external harmonic trap, the bichromatic optical lattice acts in favor of superflow.