Interaction of dark solitons with localized impurities in Bose-Einstein condensates

Abstract

We study the interaction of dark solitons with a localized impurity in Bose-Einstein condensates. We apply the soliton perturbation theory developed earlier in optics for describing the soliton dynamics and solitonimpurity interaction analytically, and then verify the results by direct numerical simulations of the Gross-Pitaevskii equation. We find that a dark soliton can be reflected from or transmitted through a repulsive impurity in a controllable manner, while near the critical point the soliton can be quasitrapped by the impurity. Additionally, we demonstrate that an immobile soliton may be captured and dragged by an adiabatically moving attractive impurity.

Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates

“…Apparently, this issue is important for applications, since it would demonstrate a possibility of driving the dark solitons (and other coherent structures, more generally) in the BEC by means of OL potentials. Note that it has been recently shown that an attractive steadily moving localized impurity may drag a stationary DS [10], but here we aim to consider the more general problem of the targeted transfer of a dark soliton by an OL.…”

“…Then, we follow the procedure described in Ref. [10] (see also Ref. [13]) to derive the following effective perturbed NLS equation from Eq.…”

“…(8) recovers the result predicted in Refs. [9,13,10], i.e., the DS oscillates in the harmonic trap with the frequency ω = Ω/ √ 2. The combination of the MT and OL gives rise to the additional periodic term in the effective potential (9).…”

“…As BECs are confined in magnetic traps, many theoretical studies have been devoted to the dynamics of DSs in the presence of external potentials [9,10]. In particular, it has been found that in elongated harmonic traps a DS oscillates with frequency Ω/ √ 2, where Ω is the axial trap frequency.…”

“…In this case the full potential (including the MT and OL terms) varies slowly on the DS scale and the soliton dynamics can be treated analytically by means of the adiabatic perturbation theory for DSs [33] (see also Refs. [10,13] for applications of the perturbation theory in the BEC context). This way, we will demonstrate analytically (and confirm by direct numerical simulations) that the DS oscillates on top of the TF cloud with a frequency and amplitude modified by the presence of the OL.…”