Mean field thermodynamics of a spin-polarized spherically trapped Fermi gas at unitarity

TL;DR

This paper investigates the thermodynamics of a spin-imbalanced Fermi gas in a trap at unitarity, comparing theoretical approaches and matching experimental observations of density profiles and transition temperatures.

Contribution

It introduces an efficient method for solving Bogoliubov-de Gennes equations and demonstrates the agreement with local density approximation results, clarifying the nature of order parameter oscillations.

Findings

Agreement between Bogoliubov-de Gennes and local density approximation results.

Observation of bimodal density profiles at finite temperature.

Superfluid transition temperature aligns with experimental data.

Abstract

We calculate the mean-field thermodynamics of a spherically trapped Fermi gas with unequal spin populations in the unitarity limit, comparing results from the Bogoliubov-de Gennes equations and the local density approximation. We follow the usual mean-field decoupling in deriving the Bogoliubov-de Gennes equations and set up an efficient and accurate method for solving these equations. In the local density approximation we consider locally homogeneous solutions, with a slowly varying order parameter. With a large particle number these two approximation schemes give rise to essentially the same results for various thermodynamic quantities, including the density profiles. This excellent agreement strongly indicates that the small oscillation of order parameters near the edge of trap, sometimes interpreted as spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov states in previous studies of Bogoliubov-de Gennes equations, is a finite size effect. We find that a bimodal structure emerges in the density profile of the minority spin state at finite temperature, as observed in experiments. The superfluid transition temperature as a function of the population imbalance is determined, and is shown to be consistent with recent experimental measurements. The temperature dependence of the equation of state is discussed.