Role of the Mean-field in Bloch Oscillations of a Bose-Einstein Condensate in an Optical Lattice and Harmonic Trap

TL;DR

This paper investigates how the mean field influences Bloch oscillations in a Bose-Einstein condensate within an optical lattice and harmonic trap, revealing suppression of dispersion and emergence of solitons and vortices at different mean field strengths.

Contribution

It demonstrates the significant role of the mean field in Bloch oscillations and the formation of nonlinear structures in the condensate.

Findings

Moderate mean field suppresses momentum dispersion.

Large mean field leads to soliton and vortex formation.

Mean field critically affects condensate dynamics.

Abstract

Using the Crank-Nicholson method, we study the evolution of a Bose-Einstein condensate in an optical lattice and harmonic trap. The condensate is excited by displacing it from the center of the harmonic trap. The mean field plays an important role in the Bloch-like oscillations that occur after sufficiently large initial displacement. We find that a moderate mean field significantly suppresses the dispersion of the condensate in momentum space. When the mean field becomes large, soliton and vortex structures appear in the condensate wavefunction.