Dynamics of interacting dark soliton stripes

Abstract

In the present work we examine the statics and dynamics of multiple parallel dark soliton stripes in a two-dimensional Bose-Einstein condensate. Our principal goal is to study the effect of the interaction between the stripes on the transverse instability of the individual stripes. We use a recently developed adiabatic invariant formulation to derive a quasi-analytical prediction for the stripe equilibrium position and for the Bogoliubov-de Gennes spectrum of excitations of stationary stripes. The cases of two-, three-and four-stripe states are studied in detail. We subsequently test our predictions against numerical simulations of the full two-dimensional Gross-Pitaevskii equation. We find that the number of unstable eigenmodes increases as the number of stripes increases due to (unstable) relative motions between the stripes. Their corresponding growth rates do not significantly change, although for large chemical potentials, the larger the stripe number, the larger the maximal instability growth rate. The instability induced dynamics of multiple stripe states and their decay into vortices are also investigated.

Reduced dynamics for one and two dark soliton stripes in the defocusing nonlinear Schrödinger equation: A variational approach

“…However, we note that, despite having the correct trend, the dispersion curves fail to accurately capture quantitatively the actual growth rates and wavenumber cutoffs for stability (i.e., wavenumbers k c such that ω(k c ) = 0). This qualitative shape improves on the previous reduced description for the dynamics of DSSs based on the AI assumption [27][28][29]. The reduced AI PDE for DSSs yields, for η = 0, the following (linear) dispersion relation [29]:…”

“…This qualitative shape improves on the previous reduced description for the dynamics of DSSs based on the AI assumption [27][28][29]. The reduced AI PDE for DSSs yields, for η = 0, the following (linear) dispersion relation [29]:…”

“…Moreover, we compare the VA results with the AI methodology put forward in Refs. [27][28][29] and showcase where the two display similar results, as well as where the former represents a significant improvement over the latter. It is important to stress that, from now on, we use the improved VA model that includes the h(B) term introduced in Eq.…”

“…In addition to testing the VA reduced equations of motion, we also implement the AI methodology put forward in Refs. [27][28][29]. As it can be seen from the figure, both the improved VA [see the thick green (gray) curves] and the AI [see the dark blue (black) dotted curves] methodologies give a reliable description of the snaking dynamics up to the point where the DSS loses its transverse dark-soliton-like profile as it nucleates vortices of alternate signs at the nodes of the perturbation mode.…”

Generation of high winding-number superfluid circulation in Bose-Einstein condensates

“…The superflow velocity profile becomes less smooth as the speed of the merging fluid increases. In particular, for τ s = 3 s we start to see evidence of a dark soliton excitation forming [42,53], which then evolves into a single unpinned vortex. We note that for τ s = 3 s, vortices depin from the stirring potential towards the end of the spiral trajectory.…”