Theory of Critical Temperature Adiabatic Change for Ideal Gas Bose-Einstein Condensation in Optical Lattices

TL;DR

This paper analytically investigates how the critical temperature for Bose-Einstein condensation in ideal gases within optical lattices depends on the energy band width and tunneling effects, providing a simple proportionality relation.

Contribution

It introduces an analytical scheme to determine the critical temperature and condensed atom number considering the band structure in optical lattices, emphasizing the role of tunneling.

Findings

Critical temperature is mainly determined by the lowest energy band width.

A simple proportionality relation of 1/3 degree for the critical temperature dependence.

Tunneling plays a fundamental role in condensate formation.

Abstract

We present a scheme of analytical calculations determining the critical temperature and the number of condensed atoms of ideal gas Bose-Einstein condensation in external potentials with 1D, 2D or 3D periodicity. In particular we show that the width of the lowest energy band appears as the main parameter determining the critical temperature of condensation. Is obtained a very simple, proportional to 1/3 degree, regularity for this dependence. The fundamental role of tunneling in physics of condensate establishment is underscored.