Atomic matter-wave revivals with definite atom number in an optical lattice

TL;DR

This paper investigates the collapse and revival phenomena in the momentum distribution of atoms in optical lattices, employing a projection technique to accurately account for fixed atom numbers and analyzing effects of tunneling and interactions.

Contribution

It introduces a projection method for exact treatment of inhomogeneous systems with fixed atom numbers and compares it with standard approaches, revealing measurable discrepancies.

Findings

Good agreement with naive models for small systems

Discrepancies appear in larger systems (~10 sites)

Method accurately accounts for fixed atom number in inhomogeneous systems

Abstract

We study the collapse and revival of interference patterns in the momentum distribution of atoms in optical lattices, using a projection technique to properly account for the fixed total number of atoms in the system. We consider the common experimental situation in which weakly interacting bosons are loaded into a shallow lattice, which is suddenly made deep. The collapse and revival of peaks in the momentum distribution is then driven by interactions in a lattice with essentially no tunnelling. The projection technique allows to us to treat inhomogeneous (trapped) systems exactly in the case that non-interacting bosons are loaded into the system initially, and we use time-dependent density matrix renormalization group techniques to study the system in the case of finite tunnelling in the lattice and finite initial interactions. For systems of more than a few sites and particles, we find good agreement with results calculated via a naive approach, in which the state at each lattice site is described by a coherent state in the particle occupation number. However, for systems on the order of 10 lattice sites, we find experimentally measurable discrepancies to the results predicted by this standard approach.