Localized states in an ultracold atomic gas trapped in a bichromatic potential: The effect of a time-varying phase

Localization phenomena observed in an ultracold atomic gas trapped in a bichromatic optical lattice were found to be sensitive to the degree of lattice disorder, and are affected by the extent of interatomic interaction. In this work, I shall discuss the dependence of localization on the phase difference between the two superimposed optical waves. The step and sinusoidal phase functions in region III identified in the work by Larcher et al. [1], are studied. A step varying phase mildly distorts localization, whereas a sinusoidally varying phase will take the system to a unique form of localization, which we call logarithmic localization.