# Oscillatory-like Expansion of a Fermionic Superfluid

## TL;DR

This study investigates the anisotropic oscillatory expansion of a fermionic superfluid across the BEC-BCS crossover, revealing non-monotonic behavior of the effective polytropic index and oscillation frequencies, enhancing understanding of strongly interacting Fermi gases.

## Contribution

It provides experimental measurements of expansion dynamics and polytropic index across the BEC-BCS crossover, connecting hydrodynamic behavior with theoretical models.

## Key findings

- Non-monotonic variation of polytropic index across the crossover
- Oscillatory expansion behavior with frequency minima near unitarity
- Agreement of experimental results with theoretical predictions

## Abstract

We study the expansion behaviours of a Fermionic superfluid in a cigar-shaped optical dipole trap for the whole BEC-BCS crossover and various temperatures. At low temperature ($0.06(1) T_F$), the atom cloud undergoes an anisotropic hydrodynamic expansion over 30~ms, which behaves like oscillation in the horizontal plane. By analyzing the expansion dynamics according to the superfluid hydrodynamic equation, the effective polytropic index $\bar{\gamma}$ of Equation-of-State of Fermionic superfluid is extracted. The $\bar{\gamma}$ values show a non-monotonic behavior over the BEC-BCS crossover, and have a good agreement with the theoretical results in the unitarity and BEC side. The normalized quasi-frequencies of the oscillatory expansion are measured, which drop significantly from the BEC side to the BCS side and reach a minimum value of 1.73 around $1/k_Fa=-0.25$. Our work improves the understanding of the dynamic properties of strongly interacting Fermi gas.