Dimensional crossover in ultracold Fermi gases from Functional Renormalisation

TL;DR

This paper studies the transition from three to two dimensions in ultracold Fermi gases across the BCS-BEC crossover using the functional renormalisation group, providing detailed phase diagrams and comparisons with experiments.

Contribution

It presents a first-principles analysis of dimensional crossover in ultracold Fermi gases, including finite temperature phase diagrams, using the FRG framework with periodic boundary conditions.

Findings

Calculated equation of state, gap parameter, and superfluid transition temperature.

Mapped the finite temperature phase diagram for various confinement lengths.

Compared theoretical results with recent experimental data.

Abstract

We investigate the dimensional crossover from three to two dimensions in an ultracold Fermi gas across the whole BCS-BEC crossover. Of particular interest is the strongly interacting regime as strong correlations are more pronounced in reduced dimensions. Our results are obtained from first principles within the framework of the functional renormalisation group (FRG). Here, the confinement of the transverse direction is imposed by means of periodic boundary conditions. We calculate the equation of state, the gap parameter at zero temperature and the superfluid transition temperature across a wide range of transversal confinement length scales. Particular emphasis is put on the determination of the finite temperature phase diagram for different confinement length scales. In the end, our results are compared with recent experimental observations and we discuss them in the context of other theoretical works.