Mean-field description of a dynamical collapse of a fermionic condensate in a trapped boson-fermion mixture

Abstract

We suggest a time-dependent dynamical mean-field-hydrodynamic model for the collapse of a trapped boson-fermion condensate and perform numerical simulation based on it to understand some aspects of the experiment by Modugno et al. [Science 297, 2240] on the collapse of the fermionic condensate in the 40 K-87 Rb mixture. We show that the mean-field model explains the formation of a stationary boson-fermion condensate at zero temperature with relative sizes compatible with experiment. This model is also found to yield a faithful representation of the collapse dynamics in qualitative agreement with experiment. In particular we consider the collapse of the fermionic condensate associated with (a) an increase of the number of bosonic atoms as in the experiment and (b) an increase of the attractive boson-fermion interaction using a Feshbach resonance. Suggestion for experiments of fermionic collapse using a Feshbach resonance is made.

Free expansion of fermionic dark solitons in a boson–fermion mixture

“…Also, there have been studies of a degenerate mixture of two components of fermionic 40 K [1] and 6 Li [2] atoms. The collapse of the DFG in a boson-fermion mixture 87 Rb-40 K has been observed and studied by Modugno et al [5,10,13]. In these studies of a mixed Bose-Einstein condensate (BEC) and a DFG the initial states were the stationary ground states of the systems.…”

“…We developed a set of practical time-dependent mean-field-hydrodynamic equations for the interacting boson-fermion mixture starting from the following Lagrangian density [13] …”

“…This time-dependent mean-field-hydrodynamic model was suggested recently by the present author [13] to study the collapse dynamics of a DFG and is a time-dependent extension of a time-independent model suggested for the stationary states by Capuzzi et al [11,12] based essentially on a Thomas-Fermi-Weizsäcker approximation.…”

“…Trapped DFG has been achieved only by sympathetic cooling in the presence of a second boson or fermion component. Recently, there have been successful observation [1][2][3][4] and associated experimental [5][6][7] and theoretical [8][9][10][11][12][13] studies of degenerate boson-fermion mixtures by different experimental groups [1][2][3][4] in the following systems: 6,7 Li [3], 23 Na- 6 Li [4] and 87 Rb-40 K [5,6]. Also, there have been studies of a degenerate mixture of two components of fermionic 40 K [1] and 6 Li [2] atoms.…”

Dipolar Bose-Einstein condensates with large scattering length

“…(1) and (4) are the Euler-Lagrange equations for the Lagrangian density (9) [36], which should be used in the variational formulation [37]. To develop the variational approximation, we consider the following Gaussian ansatz for the wave function [28]…”