Mesoscopic Bose-Einstein condensates as quantum simulators

TL;DR

This paper demonstrates that mesoscopic Bose-Einstein condensates can serve as quantum simulators for condensed matter systems by analyzing their phase transitions and critical behavior beyond mean field theory.

Contribution

It introduces a mapping of mesoscopic BECs to spin models and defines correlations that reveal critical phenomena and universality, advancing their use as quantum simulators.

Findings

Critical behavior linked to correlation length divergence.

Gapless spectrum in the thermodynamic limit.

Critical exponents and universality demonstrated.

Abstract

Mesoscopic interacting Bose-Einstein condensates confined in a few traps display phase transitions that cannot be explained with a mean field theory. By describing each trap as an effective site of a Bose-Hubbard model and using the Schwinger representation of spin operators, these systems can be mapped to spin models. We show that it is possible to define correlations between bosons in such a way that critical behavior is associated to the divergence of a correlation length accompanied by a gapless spectrum in the thermodynamic limit. The latter is now defined as the limit in which the mean field analysis becomes valid. Such description provides critical exponents to the associated phase transitions and encompasses the notion of universality demonstrating thus the potential use of mesoscopic Bose-Einstein condensates as quantum simulators of condensed matter systems.