Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models

TL;DR

This paper investigates the non-equilibrium dynamics of bosonic atoms in optical lattices, focusing on superfluid behavior, phase coherence evolution, and the emergence of complex quantum states following parameter changes.

Contribution

It introduces a framework using the discrete Gross-Pitaevskii equation to describe dynamics in regimes with strong interactions but superfluid ground states, and analyzes specific initial conditions.

Findings

Phase coherence evolves after quench from Mott insulator to superfluid regime.

Density wave order and Schrödinger cat states can emerge from pi phase initial conditions.

The discrete Gross-Pitaevskii equation effectively models non-equilibrium dynamics in certain parameter regimes.

Abstract

Motivated by recent experiments on trapped ultra-cold bosonic atoms in an optical lattice potential, we consider the non-equilibrium dynamic properties of such bosonic systems for a number of experimentally relevant situations. When the number of bosons per lattice site is large, there is a wide parameter regime where the effective boson interactions are strong, but the ground state remains a superfluid (and not a Mott insulator): we describe the conditions under which the dynamics in this regime can be described by a discrete Gross-Pitaevskii equation. We describe the evolution of the phase coherence after the system is initially prepared in a Mott insulating state, and then allowed to evolve after a sudden change in parameters places it in a regime with a superfluid ground state. We also consider initial conditions with a "pi phase" imprint on a superfluid ground state (i.e. the initial phases of neighboring wells differ by pi), and discuss the subsequent appearance of density wave order and "Schrodinger cat" states.