Dynamical collapse in a degenerate binary fermion mixture using a hydrodynamic model

TL;DR

This paper investigates the conditions under which a degenerate fermion-fermion mixture collapses due to attractive interspecies interactions, using a hydrodynamic model and variational analysis, with implications for experimental observation.

Contribution

It introduces a hydrodynamic model to analyze collapse phenomena in a DFFM of different atoms, highlighting the role of interspecies attraction and Pauli-blocking effects.

Findings

Collapse occurs when interspecies attraction is sufficiently strong and negative.

Pauli-blocking prevents collapse among identical spin-polarized fermions.

Experimental suggestions are provided for observing collapse in DFFMs.

Abstract

We use a time-dependent dynamical hydrodynamic model to study a collapse in a degenerate fermion-fermion mixture (DFFM) of different atoms. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances there cannot be a collapse for repulsive interspecies fermion-fermion interaction. However, there can be a collapse for a sufficiently attractive interspecies fermion-fermion interaction in a DFFM of different atoms. Using a variational analysis and numerical solution of the hydrodynamic model we study different aspects of collapse in such a DFFM initiated by a jump in the interspecies fermion-fermion interaction (scattering length) to a large negative (attractive) value using a Feshbach resonance. Suggestion for experiments of collapse in a DFFM of distinct atoms is made.