Gap solitons in spin–orbit-coupled Bose–Einstein condensates in bichromatic optical lattices

Abstract

We investigate gap solitons in spin–orbit-coupled Bose–Einstein condensates in bichromatic optical lattices and mainly focus the effect of the secondary periodic potential trap on the gap solitons. The gap solitons and linear Bloch waves are obtained by solving coupled Gross–Pitaevskii equations in bichromatic optical lattice. The results show that parity symmetry plays an important role when the detuning between the Raman beam and energy levels of the atoms is zero. It is shown that the soliton amplitude increases with the increasing secondary periodic potential well depth. The gap solitons become spin polarization for the case of nonzero detuning. Linear stability analysis method has been employed to investigate the stability of gap solitons located in the first and second band gaps. The results prove that the periodic secondary potential trap depths have important effects on the stability of gap solitons.