Collective modes of trapped gases at the BEC-BCS crossover

TL;DR

This paper calculates collective mode frequencies of trapped gases across the BEC-BCS crossover, using polytropic equations of state and models for different phases, providing insights into their dynamic properties.

Contribution

It introduces a general framework for calculating collective modes in trapped gases with polytropic equations of state across the BEC-BCS crossover, incorporating realistic effective power laws.

Findings

Mode frequencies depend on trap geometry and polytropic index γ.

Effective γ values are estimated for molecular BECs and Fermi gases near Feshbach resonances.

Results provide predictions for collective excitations in different quantum phases.

Abstract

The collective mode frequencies in isotropic and deformed traps are calculated for general polytropic equation of states, $P\propto n^{\gamma+1}$, and expressed in terms of $\gamma$ and the trap geometry. For molecular and standard Bose-Einstein condensates and Fermi gases near Feshbach resonances, the effective power $\gamma\simeq0.5-1.3$ is calculated from Jastrow type wave-function ans\"atze, and from the crossover model of Leggett. The resulting mode frequencies are calculated for these phases around the BCS-BEC crossover.