Determination of the Equation of State of a Two-Component Fermi Gas at Unitarity

TL;DR

This paper measures the equation of state of a two-component Fermi gas at unitarity using in situ density profiles, providing insights into strongly interacting quantum gases at near-zero temperature.

Contribution

It introduces a method to determine the equation of state directly from density profiles, calibrated by the non-interacting outer region, at unitarity.

Findings

Determined the energy density as a function of component densities.

Estimated the zero-temperature equation of state.

Provided a new calibration method using the outer non-interacting region.

Abstract

We report on the measurement of the equation of state of a two-component Fermi gas of $^6$Li atoms with resonant interactions. By analyzing the \textit{in situ} density distributions of a population-imbalanced Fermi mixture reported in the recent experiment [Y. Shin \textit{et al.}, Nature \textbf{451}, 689 (2008)], we determine the energy density of a resonantly interacting Fermi gas as a function of the densities of the two components. We present a method to determine the equation of state directly from the shape of the trapped cloud, where the fully-polarized, non-interacting ideal Fermi gas in the outer region provides the absolute calibration of particle density. From the density profiles obtained at the lowest temperature, we estimate the zero-temperature equation of state.