Dimensionally Induced Phase Transition of the Weakly Interacting Ultracold Bose Gas

TL;DR

This paper studies how lowering the dimensionality induces a phase transition to Bose-Einstein condensation in a weakly interacting ultracold Bose gas, using an advanced theoretical approach that aligns well with experimental data.

Contribution

It introduces a Hartree-Fock-Bogoliubov-Popov theoretical framework including quantum fluctuations for analyzing the phase transition in lower dimensions.

Findings

Critical chemical potential matches experimental data better than previous models.

The critical temperature follows a universal power-law with an exponent of 1/2.

The critical exponent remains robust against finite interaction strengths.

Abstract

We investigate the dimensionally induced phase transition from the normal to the Bose-Einstein-condensed phase for a weakly interacting Bose gas in an optical lattice. To this end we make use of the Hartree-Fock-Bogoliubov-Popov theory, where we include numerically exact hopping energies and effective interaction strengths. At first we determine the critical chemical potential, where we find a much better agreement with recent experimental data than a pure Hartree-Fock treatment. This finding is in agreement with the dominant role of quantum fluctuations in lower dimensions, as they are explicitly included in our theory. Furthermore, we determine for the 1D-3D-transition the power-law exponent of the critical temperature for two different non-interacting Bose gas models yielding the same value of 1/2, which indicates that they belong to the same universality class. For the weakly interacting Bose gas we find for both models that this exponent is robust with respect to finite interaction strengths.