Coherent impurity transport in an attractive binary Bose–Einstein condensate

Abstract

We study the dynamics of a soliton-impurity system modeled in terms of a binary Bose-Einstein condensate. This is achieved by 'switching off' one of the two self-interaction scattering lengths, giving a two component system where the second component is trapped entirely by the presence of the first component. It is shown that this system possesses rich dynamics, including the identification of unusual 'weak' dimers that appear close to the zero inter-component scattering length. It is further found that this system supports quasi-stable trimers in regimes where the equivalent single-component gas does not, which is attributed to the presence of the impurity atoms which can dynamically tunnel between the solitons, and maintain the required phase differences that support the trimer state. that the single component focussing nonlinear Schrödinger equation can possess chaotic solutions in the presence of an axial harmonic potential [29,30], as well as the observed interaction induced frequency shift of pairs of trapped bright solitons [31] in the experiment of [13]. Complementary to this, theoretical work has focussed on solitary waves in higher spin systems, revealing the existance of integrable points in the full parameter space of the spin-1 condensate, in the form of so-called 'polar' bright solitons [32,33]. Although solitons are usually studied as the solutions to one-dimensional nonlinear models, there have also been predictions of stable two-dimensional solitary wave solutions in dipolar Bose-Einstein condensates [34,35], where the additional nonlocal nonlinearity provides the stabilizing mechanism for these solitons. Very recently the Jones-Roberts soliton was realized experimentally, a true two-dimensional solitary wave structure [36].The realization of artificial electromagnetism with cold gases, and in particular spin-orbit coupling for Bose-Einstein condensates opens a novel route towards studying nonlinear wave structures. Here, the coupling of the condensates momentum to a quasi-spin leads to stripe-like soliton phases, related to the underlying immiscible phase of these systems [37,38]. Spin-orbit coupling forms a key ingredient in simulating more exotic scenarios, such as Dirac-like equations, where confined solutions have been predicted [39] that resemble their bright soliton cousins in single component condensates.Atomic condensates benefit from being exceptionally pure systems-this in turn allows one to investigate the effects of disorder and defects with an unprecedented level of control. The presence of impurities in ensembles of ultracold matter has led to predictions of impurity-molecules and lattices at the mean-field level [40], as well as the role of many-body correlations for a single impurity out-of-equilibrium [41]. Experimental work has studied the role that spin impurities have in the strongly correlated Tonks-Girardeau limit [42] and also magnetic spin models [43], which have also been the focus of subsequent theoretical investigations [44][45][46]. Complementary to this, recent exper...

The dispersion relation of a dark soliton

“…This is somewhat similar to our previous work [36,37], but the atoms in the bright soliton component must be very few [48]. The dynamics of this soliton-impurity system we considered can be described by the following equations [49][50][51],…”

Spin Solitons in Spin-1 Bose-Einstein Condensates

“…Spin density redistribution happens during the collision between spin solitons, which depends on the relative phase and velocity. They have great potential applications to study the negative inertial mass of solitons [8,16,57], the dynamics of soliton-impurity systems [57][58][59][60], and the spin dynamics in BEC systems [61][62][63].…”

Controlling dark solitons on the healing length scale

“…Such a situation can be achieved by tightly confining a gas in two directions using a harmonic oscillator of frequency ω ⊥ , such that the dynamics in these directions is frozen out [17]. The BEC is coupled to a small number of impurity atoms and in the limit of weak interactions the set of equations describing the dynamics of the coupled system is given by [18][19][20] i…”