Density waves in a quasi-one-dimensional atomic gas mixture of bosons and two-component fermions

Density-wave structures are studied in a quasi-one-dimensional atomic gas mixture of one-component bosons and two-component fermions using the mean-field approximation at zero temperature. Owing to the Peierls instability in the fermion system, the ground state of the system shows a fermion density wave and periodic Bose-Einstein condensation induced by the boson-fermion interatomic interaction. For the two-component fermions, two density waves appear in each component, and their phase difference distinguishes two types of ground states, the in-phase and the out-phase density waves. In this paper, a self-consistent method is presented to treat the density-wave states in a boson-fermion mixture with two-component fermions. The analysis of the effective potential and the interaction energies shows that the density waves appearing in the ground state are in phase or out of phase depending on the strength of the interfermion interaction. It is also shown that the periodic Bose-Einstein condensate coexists with the in-phase density wave of fermions, but, in the case of out of phase, only the uniform condensate appears. The phase diagram of the system is given for the effective coupling constants