Equation of state and collective frequencies of a trapped Fermi gas along the BEC-unitarity crossover

TL;DR

This paper investigates how collective oscillations in a trapped Fermi gas can serve as precise probes of its equation of state across the BEC-unitarity crossover, using a scaling approach validated against hydrodynamic solutions.

Contribution

It introduces a high-accuracy scaling method to compute collective mode frequencies based on the equation of state, comparing mean field BCS and Monte-Carlo results.

Findings

Predicted collective frequencies vary with the equation of state.

Scaling approach matches exact hydrodynamic solutions.

Results provide sensitive tests for theoretical models.

Abstract

We show that the study of the collective oscillations in a harmonic trap provides a very sensitive test of the equation of state of a Fermi gas near a Feshbach resonance. Using a scaling approach, whose high accuracy is proven by comparison with exact hydrodynamic solutions, the frequencies of the lowest compressional modes are calculated at T=0 in terms of a dimensionless parameter characterizing the equation of state. The predictions for the collective frequencies, obtained from the equations of state of mean field BCS theory and of recent Monte-Carlo calculations, are discussed in detail.