Dimensional crossover for the beyond-mean-field correction in Bose gases

TL;DR

This paper analyzes the transition of a weakly interacting Bose gas from three to low dimensions, providing analytical solutions and exploring beyond-mean-field effects in various confinement potentials.

Contribution

It offers an analytical approach to the energy in the dimensional crossover and examines the limitations of local-density approximation in inhomogeneous systems.

Findings

Leading beyond-mean-field contribution of confinement-induced resonance identified

Analytical solutions for energy in box potential with periodic boundary conditions

Characterization of crossover in harmonic potentials with specific interactions

Abstract

We present a detailed beyond-mean-field analysis of a weakly interacting Bose gas in the crossover from three to low dimensions. We find an analytical solution for the energy and provide a clear qualitative picture of the crossover in the case of a box potential with periodic boundary conditions. We show that the leading contribution of the confinement-induced resonance is of beyond-mean-field order and calculate the leading corrections in the three- and low-dimensional limits. We also characterize the crossover for harmonic potentials in a model system with particularly chosen short- and long-range interactions and show the limitations of the local-density approximation. Our analysis is applicable to Bose-Bose mixtures and gives a starting point for developing the beyond-mean-field theory in inhomogeneous systems with long-range interactions such as dipolar particles or Rydberg-dressed atoms.