Non-autonomous bright solitons and their stability in Rabi coupled binary Bose–Einstein condensates

The dynamics of non-autonomous bright matter-wave solitons in Rabi coupled binary Bose–Einstein condensates is explored. By performing a unitary and similarity/lens-type transformation, we reduce the non-autonomous Gross–Pitaevskii (GP) equation into the celebrated Manakov model. Then, we construct the exact bright solitons of the non-autonomous GP system in the presence of time dependent nonlinearities for two specific forms, namely hyperbolic nonlinearities, which are of physical interest. The experimental possibilities of realizing the forms of temporally modulated potentials corresponding to these time dependent nonlinearities and supporting such localized structures are explored. Our study on the propagation of one soliton shows that the amplitude, velocity and shape of the bright soliton are altered by the time-dependent scattering length. We also analyze the non-trivial energy sharing collision of Manakov solitons in the presence of Rabi coupling and aforementioned nonlinearities. We find that breathers arise in two-soliton collisions and the nature of energy sharing collisions is altered from that of Manakov system due to Rabi coupling only. Further in the presence of time-dependent nonlinearities the collision scenario is again altered significantly. Finally, the stability of these localized structures is examined using a recently developed powerful analytic method by Quintero et al (2015 Phys. Rev. E 91, 012905) and it is shown that the non-autonomous bright solitons are indeed stable. The evolution of position and velocity is also studied. (paper)