Reflection, transmission, and trapping of an ultracold atomic soliton at an attractive contact impurity

Reflection and transmission (tunneling) reveal the wave nature of ultracold matter when scattered from an impurity and are of great importance in atomtronics technology. Using the time-dependent Gross-Pitaevskii equation (GPE), we investigate the trapping, reflection, and transmission of a bright soliton in an ultracold-atom gas propagating through a one-dimensional waveguide with a contact defect. This allows us to analyze the dynamics of the scattering as a function of soliton velocity v , the strength of the contact impurity V 0 , and the intensity of the attractive nonlinear coupling g < 0 . We evolve the GPE numerically with the contact defect modeled as a δ sequence for the Dirac delta function. We find a universal behavior in terms of v / V 0 and | g | / V 0 , thus reducing the dimension of the parameter space. Our analysis identifies four distinct regions of nonlinear coupling | g | / V 0 that govern scattering dynamics, delimited by | g | / V 0 ≈ 2 , 4, and 6. Particularly, we observe distinct parameter dependent onsets between the soliton character and highly radiative-dispersive wave packets for the scattering products. To quantify the nature of the scattering products, we use the differential and Fisher information-theoretical measures to determine the degree of localization of the scattering products. The implications of these findings are discussed in the context of both fundamental quantum mechanics and potential experimental setups.