Transmission of matter-wave solitons through nonlinear traps and barriers

The transmission of matter wave packets through inhomogeneities of different types of Bose-Einstein condensates BECs has recently attracted a lot of attention, because this phenomenon is important for the design of control methods of the soliton parameters and atomic soliton lasers 1. The transmission and reflection of bright and dark matter wave solitons has been studied in the case of linear inhomogeneities, induced by the variations in space of the potential field 2‐8. In particular, the effect of a potential step or impurity, including the soliton train evolution, has been analyzed in Ref. 6. The adiabatic dynamics of a dark soliton, as well as the radiative wave emission leading to the dark soliton degradation, has been studied in Ref. 7. Finally, the continuous wave emission by a bright soliton in an optical lattice has been addressed in Ref. 8. The case of inhomogeneities produced by spatial variations of the scattering length has been less investigated. In Refs. 9‐11 the variational approach has been applied and numerical simulations have been performed. When the linear and nonlinear inhomogeneities compete with each other, direct numerical simulations of the soliton propagation have been carried out. The enhanced soliton transmission through a linear barrier is observed for well-chosen parameters of the nonlinear potential 12. The explanation of this phenomenon, as shown in this paper, requires to take into account the radiative effects when the soliton interacts with the nonlinear potential. The purpose of this work is to develop the theory describing the transmission of matter wave solitons through nonlinear barriers and traps. Such barriers can be produced by using the Feshbach resonance method, namely by the local variation of the external magnetic field Bz in space near the resonant value Bc 13. By the small variation of the field near the resonant value we can induce the large variations of the scattering length in space according to the formula

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