Classical and quantum features of the superfluid to Mott insulator transition

TL;DR

This paper presents a classical simulation approach for the superfluid to Mott insulator transition in Bose-Einstein condensates, bridging quantum and mean-field dynamics and enabling analysis of quantum features.

Contribution

It introduces a classical phase space ensemble method combined with a modified Gross-Pitaevskii equation to simulate quantum phase transitions.

Findings

Classical simulations can replicate superfluid to Mott insulator transition.

The approach extends to higher particle numbers and multidimensional lattices.

It effectively distinguishes quantum features from mean-field behavior.

Abstract

We analyze the correspondence of many-particle and mean-field dynamics for a Bose-Einstein condensate in an optical lattice. Representing many-particle quantum states by a classical phase space ensemble instead of one single mean-field trajectory and taking into account the quantization of the density by a modified integer Gross-Pitaevskii equation, it is possible to simulate the superfluid to Mott insulator transition and other phenomena purely classically. This approach can be easily extended to higher particle numbers and multidimensional lattices. Moreover it provides an excellent tool to classify true quantum features and to analyze the mean-field -- many particle correspondence.