Correlation functions of cold bosons in an optical lattice

TL;DR

This paper analyzes the correlation functions of cold bosons in an optical lattice, comparing different quantum states and proposing methods to observe interference patterns in specific quantum phases.

Contribution

It provides detailed calculations of correlation functions for Bose fields and compares Fock and coherent state predictions, offering insights into experimental observations.

Findings

Correlation functions differ significantly between Fock and coherent states.

Interference patterns can be observed in the Mott insulator state.

Theoretical predictions align with potential experimental measurements.

Abstract

We investigate the experiment of collapses and revivals of matter wave field in more detail. To this end we calculate the lowest-order correlation functions of the Bose field. We compare predictions of the total Fock state with the commonly used coherent state approximation. We also show how to observe an interference pattern for the celebrated Mott state.