The equation of state of ultracold Bose and Fermi gases: a few examples

TL;DR

This paper introduces a versatile in situ imaging method to determine the equation of state of ultracold Bose and Fermi gases, enabling detailed thermodynamic analysis across different phases and regimes.

Contribution

The authors develop a novel in situ imaging technique to measure local pressure and equation of state in ultracold gases, applicable to various quantum phases and regimes.

Findings

Measured the grand-canonical equation of state for a resonant Fermi gas across temperatures.

Identified a thermodynamic signature of the superfluid transition.

Revealed Mott insulator behavior in a Bose gas within an optical lattice.

Abstract

We describe a powerful method for determining the equation of state of an ultracold gas from in situ images. The method provides a measurement of the local pressure of an harmonically trapped gas and we give several applications to Bose and Fermi gases. We obtain the grand-canonical equation of state of a spin-balanced Fermi gas with resonant interactions as a function of temperature. We compare our equation of state with an equation of state measured by the Tokyo group, that reveals a significant difference in the high-temperature regime. The normal phase, at low temperature, is well described by a Landau Fermi liquid model, and we observe a clear thermodynamic signature of the superfluid transition. In a second part we apply the same procedure to Bose gases. From a single image of a quasi ideal Bose gas we determine the equation of state from the classical to the condensed regime. Finally the method is applied to a Bose gas in a 3D optical lattice in the Mott insulator regime. Our equation of state directly reveals the Mott insulator behavior and is suited to investigate finite-temperature effects.