Abstract
We investigate the superfluid properties of a Bose–Einstein condensate (BEC) trapped in aone-dimensional periodic potential. We study, both analytically (in the tight binding limit)and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubovdispersion relation, and we introduce two different, density dependent, effective masses andgroup velocities. The Bogoliubov spectrum predicts the existence of sound waves, andthe arising of energetic and dynamical instabilities at critical values of the BECquasi-momentum which dramatically affect its coherence properties. We investigate thedependence of the dipole and Bloch oscillation frequencies in terms of an effective massaveraged over the density of the condensate. We illustrate our results with severalanimations obtained solving numerically the time-dependent Gross–Pitaevskiiequation.
Highlights
The study of the superfluid properties of Bose-Einstein condensates (BECs) trapped in periodic potentials are attracting a fast growing interest
We investigate the superfluid properties of a Bose-Einstein condensate (BEC) trapped in a one dimensional periodic potential
We will see that this coincidence between the arising of dynamical instabilities and the inversion of sign of the effective mass does not take place at lower optical potentials
Summary
The study of the superfluid properties of Bose-Einstein condensates (BECs) trapped in periodic potentials are attracting a fast growing interest. The dynamics of BECs in lattices is highly non-trivial, essentially because of the competition/interplay between the discrete translational invariance of the periodic potential and the nonlinearity arising from the interatomic interactions. In this work we will study the system in a region of parameters such that its ground state stands deeply in the superfluid phase, with the dynamics governed by the Gross-Pitaevskii equation (GPE). The coexistence of Bloch bands and nonlinearity allows, for instance, solitonic structures [12,13,14] and dynamical instabilities [15,16,17] which do not have an analog neither in metals, nor in Galilean invariant systems. We compare our analytical expressions with full numerical solutions, and we extend our analysis to investigate the behaviour of the system at low optical potential depths, where the nonlinear tight binding approximation breaks down. We show that the phenomena predicted by the DNL equation (5) can be generalized to the case of shallow potentials, bringing new insights on the dynamics of the system
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