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

Abstract

Abstract.We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic dark solitons in a trapped degenerate fermi gas mixed with a Bose-Einstein condensate in a harmonic as well as a periodic optical-lattice potential. The dark soliton with a "notch" in the probability density with a zero at the minimum is simulated numerically as a nonlinear continuation of the first vibrational excitation of the linear mean-field-hydrodynamic equations, as suggested recently for pure bosons. We study the free expansion of these dark solitons as well as the consequent increase in the size of their central notch and discuss the possibility of experimental observation of the notch after free expansion.

Josephson oscillation of a superfluid Fermi gas

“…Such models have provided results [19] for collapse in a boson-fermion mixture of 87 Rb-40 K in qualitative agreement with the observation by Modugno et al [15,22]. There have also been studies of fermionic bright [28], dark [29], and gap solitons [30] in a boson-fermion mixture where the bosonic component is treated by the mean-field GP equation [3] and the fermionic component by a hydrodynamic model [19,18].…”

“…A proper treatment of SFG should be performed using a fully antisymmetrized many-body Slater determinant wave function [20,33] as in the case of atomic and molecular scattering [48]. However, in view of the success of the hydrodynamic model in other contexts [19,28,29] we do not believe that the present study on Josephson oscillation of a DFG in an OL potential to be so peculiar as to have no general validity. I thank Dr. Paulsamy Muruganandam for help in preparing the figures.…”

Black soliton in a quasi-one-dimensional trapped fermion-fermion mixture

“…To develop a set of practical time-dependent mean-fieldhydrodynamic equations for a DFFM, we consider the following Lagrangian density [15,13] …”

On the bright soliton in the Bose–Einstein condensate (to the third order in the interaction radius)

“…The fermionic bright soliton in a boson-fermion mixture was considered in [7]. The process of forming the fermionic dark soliton in the trapped degenerated Fermi gas mixture with the Bose-Einstein condensate in a harmonic trap as well as the periodic potential of the optical lattice was considered in [8]. With the help of the system of equations for the order parameters of bosons and fermions, the families of band solitons in a quasi-one-dimensional boson-fermion mixture at periodic potential of an optical trap were constructed in [9]; moreover, the bosons and fermions were in the state of the BoseEinstein condensate and the Bardeen-Cooper-Schiffer superfluid, respectively.…”