Collapse in boson-fermion mixtures with all-repulsive interactions

Abstract

We describe the collapse of the bosonic component in a boson-fermion mixture due to the pressure exerted on them by a large fermionic component, leading to collapse in a system with all-repulsive interactions. We describe the phenomena early collapse and of super-slow collapse of the mixture. Several interesting nonlinear phenomena have been studied in the context of boson-fermion mixtures. First, the fact that interspecies interactions may result in attraction among bosons [3], implies that solitons could also in quasi-one dimensional boson-fermion mixtures [4,5,6]. Also, collapse of the atomic cloud induced by the interspecies attraction in boson-fermion mixtures was observed experimentally [7] and studied theoretically [8].The usual scenario of collapse in single-species quantum gases corresponds to a BEC which collapses because of its attractive self-interaction [9]. This phenomenon had been long known in mathematical physics [10] but the theoretical description of its specificities for BECs has motivated a lot of theoretical research. In boson-fermion mixtures, it is the attractive interspecies interaction what drives the blow-up of the atomic cloud [7].In this paper we describe new blow-up scenarios in degenerate quantum gases, namely in boson-fermion mixtures, when all interatomic interactions are repulsive. More specifically we will describe the phenomena of early collapse and of super-slow collapse of the mixtures.The model.-We describe bosons in the mean field approximation and spin polarized fermions at zero temperature in the hydrodynamic approximation, when the number of fermions is much larger than the number of bosons. The respective dynamical system reads [3,11]

Analysis and Computation for Ground State Solutions of Bose--Fermi Mixtures at Zero Temperature

“…Later Nygaard and Molmer extended their numerical studies on the component separation of Bose-Fermi mixtures [24], where the wavefunction for bosons is governed by a GP equation, while the wavefunction for fermions is still approximated with TF approximations. Based on the mean-field model with fermions approximated by TF approximations, many aspects of the ground state structure of Bose-Fermi mixtures have been intensively studied, including its stability [20,24,28], its collapse [9,21,26], its separation [19], its collective excitations [10,18], and its vortex states [35]. In detail, when N F 1, we have the TF approximation for the fermions.…”