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

TL;DR

This study numerically investigates the long-time averaged behavior of a Bose-Einstein condensate in a one-dimensional bichromatic optical lattice with harmonic confinement, revealing weak responses to lattice depth variations and the promotion of superflow.

Contribution

It provides a detailed numerical analysis of BEC dynamics in bichromatic lattices with harmonic traps, comparing rational and irrational wavelength ratios, and highlights the lattice's role in enhancing superflow.

Findings

Weak response of condensate observables to secondary lattice depth at low strengths

Stronger response observed at higher lattice strengths

No qualitative difference between rational and irrational wavelength ratios due to harmonic confinement

Abstract

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.