The Unitary Gas and its Symmetry Properties

TL;DR

This paper explores the symmetry properties of the unitary Fermi gas, highlighting its scaling and dynamical symmetries, and connects various measurable quantities across the BEC-BCS crossover.

Contribution

It provides a detailed analysis of the symmetry properties of the unitary gas and links experimental measurements to theoretical models across the BEC-BCS crossover.

Findings

The unitary gas exhibits scale invariance and dynamical symmetry in harmonic traps.

Analytical relations connect momentum distribution tails, pair correlations, and molecule numbers.

Symmetry properties facilitate understanding of strongly interacting quantum gases.

Abstract

The physics of atomic quantum gases is currently taking advantage of a powerful tool, the possibility to fully adjust the interaction strength between atoms using a magnetically controlled Feshbach resonance. For fermions with two internal states, formally two opposite spin states, this allows to prepare long lived strongly interacting three-dimensional gases and to study the BEC-BCS crossover. Of particular interest along the BEC-BCS crossover is the so-called unitary gas, where the atomic interaction potential between the opposite spin states has virtually an infinite scattering length and a zero range. This unitary gas is the main subject of the present chapter: It has fascinating symmetry properties, from a simple scaling invariance, to a more subtle dynamical symmetry in an isotropic harmonic trap, which is linked to a separability of the N-body problem in hyperspherical coordinates. Other analytical results, valid over the whole BEC-BCS crossover, are presented, establishing a connection between three recently measured quantities, the tail of the momentum distribution, the short range part of the pair distribution function and the mean number of closed channel molecules.