Mean-field model for Josephson oscillation in a Bose-Einstein condensate on an one-dimensional optical trap

TL;DR

This paper models phase coherence and Josephson oscillations in a Bose-Einstein condensate within a one-dimensional optical lattice using the Gross-Pitaevskii equation, aligning with experimental observations of superfluid-insulator transitions.

Contribution

It introduces a mean-field model that captures the dynamics of Josephson oscillations and phase coherence in BECs in optical lattices, matching experimental results.

Findings

Phase coherence persists after small displacements.

Interference patterns indicate superfluid behavior.

Large displacements lead to a transition to an insulator state.

Abstract

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the phase coherence in a repulsive Bose-Einstein condensate (BEC) trapped by a harmonic and an one-dimensional optical lattice potential to describe the experiment by Cataliotti {\it et al.} on atomic Josephson oscillation [Science {\bf 293}, 843 (2001)]. The phase coherence is maintained after the BEC is set into oscillation by a small displacement of the magnetic trap along the optical lattice. The phase coherence in the presence of oscillating neutral current across an array of Josephson junctions manifests in an interference pattern formed upon free expansion of the BEC. The numerical response of the system to a large displacement of the magnetic trap is a classical transition from a coherent superfluid to an insulator regime and a subsequent destruction of the interference pattern in agreement with the more recent experiment by Cataliotti {\it et al.} [e-print cond-mat/0207139].