Critical Behaviour in Trapped Strongly Interacting Fermi Gases

TL;DR

This paper examines the critical behavior near the superfluid transition in strongly interacting trapped Fermi gases, highlighting the suppression of observable critical phenomena due to inhomogeneity and discussing potential experimental signatures.

Contribution

It provides an analysis of the critical region's width and explores how inhomogeneity affects the detection of critical behavior in trapped Fermi gases near unitarity.

Findings

Critical region width is of order unity but difficult to observe experimentally.

Specific heat shows linear dependence on reduced temperature above T_c.

Inhomogeneity suppresses bulk critical signatures, complicating detection.

Abstract

We investigate the width of the Ginzburg critical region and experimental signatures of critical behavior in strongly interacting trapped Fermi gases close to unitarity, where the s-wave scattering length diverges. Despite the fact that the width of the critical region is of the order unity, evidence of critical behavior in the bulk thermodynamics of trapped gases is strongly suppressed by their inhomogeneity. The specific heat of a harmonically confined gas, for instance, is \textit{linear} in the reduced temperature $t = (T-T_{\mathrm{c}})/T_{\mathrm{c}}$ above $T_{\mathrm{c}}$. We also discuss the prospects of observing critical behavior in the local compressibility from measurements of the density profile.