Endpoint thermodynamics of an atomic Fermi gas subject to a Feshbach resonance

TL;DR

This paper analyzes the thermodynamics of an atomic Fermi gas near a Feshbach resonance, showing how to produce extremely cold degenerate gases and proposing a method to measure temperature and molecular condensation.

Contribution

It introduces a theoretical framework for the thermodynamics of Fermi gases with Feshbach resonances, including energy calculations and a protocol for achieving ultra-cold temperatures without additional cooling.

Findings

Degenerate Fermi gas can reach temperatures below 0.01 T_F^0

Adiabatic resonance passage can produce ultra-cold gases

Interaction to kinetic energy ratio can indicate molecular condensation

Abstract

The entropy and kinetic, potential, and interaction energies of an atomic Fermi gas in a trap are studied under the assumption of thermal equilibrium for finite temperature. A Feshbach resonance can cause the fermions to pair into diatomic molecules. The entropy and energies of mixtures of such molecules with unpaired atoms are calculated, in relation to recent experiments on molecular Bose-Einstein condensates produced in this manner. It is shown that, starting with a Fermi gas of temperature $T= 0.1 T_F^0$, where $T_F^0$ is the non-interacting Fermi temperature, an extremely cold degenerate Fermi gas of temperature $T \lesssim 0.01 T_F^0$ may be produced without further evaporative cooling. This requires adiabatic passage of the resonance, subsequent sudden removal of unpaired atoms, and adiabatic return. We also calculate the ratio of the interaction energy to the kinetic energy, a straightforward experimental signal which may be used to determine the temperature of the atoms and indicate condensation of the molecules.