Solitons and soliton interactions in repulsive spinor Bose-Einstein condensates with non-zero background

Abstract

We characterize the soliton solutions and their interactions for a system of coupled evolution equations of nonlinear Schrödinger (NLS) type that models the dynamics in one-dimensional repulsive Bose-Einstein condensates with spin one, taking advantage of the representation of such model as a special reduction of a 2 × 2 matrix NLS system. Specifically, we study in detail the case in which solutions tend to a non-zero background at space infinities. First we derive a compact representation for the multisoliton solutions in the system using the Inverse Scattering Transform (IST). We introduce the notion of canonical form of a solution, corresponding to the case when the background as x → ∞ is proportional to the identity. We show that solutions for which the asymptotic behavior at infinity is not proportional to the identity, referred to as being in non-canonical form, can be reduced to canonical form by unitary transformations that preserve the symmetric nature of the solution (physically corresponding to complex rotations of the quantization axes). Then we give a complete characterization of the two families of onesoliton solutions arising in this problem, corresponding to ferromagnetic and to polar states of the system, and we discuss how the physical parameters of the solitons for each family are related to the spectral data in the IST. We also show that any ferromagnetic one-soliton solution in canonical form can be reduced to a single dark soliton of the scalar NLS equation, and any polar one-soliton solution in canonical form is unitarily equivalent to a pair of oppositely polarized displaced scalar dark solitons up to a rotation of the quantization axes. Finally, we discuss two-soliton interactions and we present a complete classification of the possible scenarios that can arise depending on whether either soliton is of ferromagnetic or polar type.

On-demand generation of dark soliton trains in Bose-Einstein condensates

“…An immediate extension of this work points towards richer systems, e.g., spinor BECs [73][74][75]. These systems are already experimentally realizable [76][77][78], and several works have already exposed the existence of stable solitonic structures both experimentally [32] and theoretically [70,[79][80][81][82]]. Yet, another possibility for future study is the construction of more complex initial configurations, consisting, for example, of multiple boxes in order to mimic phase structures such as the dark antidark solitons realized in the experiments of Refs.…”