Quantum dynamics in splitting a harmonically trapped Bose-Einstein condensate by an optical lattice: Truncated Wigner approximation

TL;DR

This paper explores the quantum dynamics of splitting a harmonically trapped Bose-Einstein condensate using an optical lattice, highlighting the effects of quantum fluctuations, temperature, and lattice height on coherence and atom number squeezing.

Contribution

It applies the truncated Wigner approximation to analyze nonequilibrium dynamics and demonstrates the limitations in achieving strongly number squeezed states in deep lattices.

Findings

Atom number squeezing saturates in deep lattices due to nonadiabaticity.

Quantum fluctuations increase with lattice height and temperature.

The truncated Wigner approximation provides insights into condensate fragmentation.

Abstract

We study the splitting of a harmonically trapped atomic Bose-Einstein condensate when we continuously turn up an optical lattice (or a double-well) potential. As the lattice height is increased, quantum fluctuations of atoms are enhanced. The resulting nonequilibrium dynamics of the fragmentation process of the condensate, the loss of the phase coherence of atoms along the lattice, and the reduced atom number fluctuations in individual lattice sites are stochastically studied within the truncated Wigner approximation. We perform a detailed study of the effects of temperature and lattice height on atom dynamics, and investigate the validity of the classical Gross-Pitaevskii equation in optical lattices. We find the atom number squeezing to saturate in deep lattices due to nonadiabaticity in turning up of the lattice potential that is challenging to avoid in experiments when the occupation number of the lattice sites is large, making it difficult to produce strongly number squeezed (or the Mott insulator) states with large filling factors. We also investigate some general numerical properties of the truncated Wigner approximation.