Virial theorem for confined universal Fermi gases

TL;DR

This paper proves a universal virial theorem for confined Fermi gases near a Feshbach resonance, applicable to any trapping potential and spin mixture, enabling model-independent energy measurements and consistency checks.

Contribution

It provides a general proof of the virial theorem for universal Fermi gases without assuming harmonic traps or local density approximation.

Findings

The total energy relates to the trap potential via a scale-invariant form.

The virial theorem holds for any trapping potential and spin mixture.

Enables model-independent energy measurements in anharmonic traps.

Abstract

Optically-trapped two-component Fermi gases near a broad Feshbach resonance exhibit universal thermodynamics, where the properties of the gas are independent of the details of the two-body scattering interactions. We present a global proof that such a universal gas obeys the virial theorem for {\it any} trapping potential $U$ and any spin mixture, without assuming either the local density approximation or harmonic confinement. The total energy of the gas is given in scale invariant form by $E=<\epsilon\partial U/\partial\epsilon>$, where $\epsilon$ is an {\it arbitrary} energy scale in terms of which all length and energy scales that appear in the confining potential are written. This result enables model-independent energy measurement in traps that are anharmonic as well as anisotropic by observing only the cloud profile, and provides a consistency check for many-body calculations in the universal regime.