Collective Oscillations of Strongly Correlated One-Dimensional Bosons on a Lattice

TL;DR

This paper investigates the dynamics of strongly correlated 1D bosons on a lattice, revealing how damping and Mott insulator formation influence collective oscillations and momentum distribution.

Contribution

It provides an exact numerical analysis of dipole oscillations in 1D bosons, highlighting the effects of correlations and Mott insulator transition on dynamics.

Findings

Damping increases with larger initial displacements.

Mott insulator formation suppresses center of mass movement.

Natural orbital occupations and revival phenomena are affected by damping.

Abstract

We study the dipole oscillations of strongly correlated 1D bosons, in the hard-core limit, on a lattice, by an exact numerical approach. We show that far from the regime where a Mott insulator appears in the system, damping is always present and increases for larger initial displacements of the trap, causing dramatic changes in the momentum distribution, $n_k$. When a Mott insulator sets in the middle of the trap, the center of mass barely moves after an initial displacement, and $n_k$ remains very similar to the one in the ground state. We also study changes introduced by the damping in the natural orbital occupations, and the revival of the center of mass oscillations after long times.