Scattering of a dark–bright soliton by an impurity

Abstract

We study the interaction of an atomic dark–bright soliton in a two-component Bose–Einstein condensate with an impurity modeled by a delta function. In order to capture both elastic and inelastic scattering, we allow for relative oscillations between the dark and bright soliton components as well as higher order internal modes. Using a modified perturbed dynamical variational Lagrangian approximation, we develop an analytical model to capture motion of the center of the mass (elastic scattering) and dominant relative motion (inelastic). Numerical integration further incorporates higher order inelastic effects when the kinetic energy of the dark–bright soliton approaches the impurity energy. We calculate the maximum velocity for a dark–bright soliton and find it is limited to a value below the sound speed, depending on the relative number of atoms present in the bright soliton component and excavated by the dark soliton component, respectively. Above a critical value of the maximum velocity, the two components are no longer described by one center of mass variable and spontaneously develop internal oscillations, eventually breaking apart when pushed to higher velocities. This effect limits the incident kinetic energy in scattering studies and presents a smoking gun experimental signal.