Exactly solvable models and ultracold Fermi gases

TL;DR

This paper reviews exactly solvable models of ultracold Fermi gases, providing analytical and numerical insights into their thermodynamics, ground states, and phase diagrams, with implications for cold atom experiments.

Contribution

It offers new analytical results for finite temperature corrections and confirms the accuracy of phase diagrams in the strong coupling regime for three-component models.

Findings

Universal finite temperature corrections for two-component model.

Numerical confirmation of analytical critical fields.

Accurate phase diagrams at zero temperature in strong coupling.

Abstract

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.