Stable and unstable regimes in Bose-Fermi mixture with attraction between components

TL;DR

This paper investigates the stability and collapse phenomena in a Bose-Fermi mixture with attractive interactions, analyzing the transition between stable and unstable regimes using numerical solutions of modified Gross-Pitaevskii equations.

Contribution

It provides a quantitative analysis of the collapse in a specific Bose-Fermi mixture and relates the onset of instability to macroscopic system properties.

Findings

Numerical solutions show a continuous transition from stable to unstable regimes.

Collapse onset correlates with specific macroscopic properties.

Comparison with $^7$Li condensate highlights differences in stability behavior.

Abstract

A collapse of the trapped boson- fermion mixture with the attraction between bosons and fermions is investigated in the framework of the effective Hamiltonian for the Bose system. The properties of the $^{87}$Rb and $^{40}$K mixture are analyzed quantitatively at $T= 0$. We find numerically solutions of modified Gross- Pitaevskii equation which continuously go from stable to unstable branch. We discuss the relation of the onset of collapse with macroscopic properties of the system. A comparison with the case of a Bose condensate of atomic $^7Li$ system is given.