Atomic Boson – Fermion mixtures in box potentials

We study the density profiles of binary atomic boson-fermion mixtures confined in one dimensional box potentials by modelling the system with many-body density-density interactions. The bosons can interact with themselves and with the fermions, but identical fermions do not interact with each other through two-body s-wave scattering. The effects of mass ratio and boson-boson and boson-fermion interactions were considered. Using the Gross-Pitaevskii equation for bosons and Hartree-Fock approximation for fermions, we find a variety of different density profiles in the ground state. All the final configurations are verified to be the minima of the energy functional. We found that the atomic mixtures can remain mixed or phase separate in different parameter regime. Due to the hard-wall boundary condition, the structures may differ from boson-fermion mixtures in a harmonic trap.