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.

13 pages, 11 figures

References in corpus (19)

• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Experimental observation of oscillating and interacting matter wave dark solitons
• Stationary and non-stationary fluid flow of a Bose-Einstein condensate through a penetrable barrier
• Energy spectra of vortex distributions in two-dimensional quantum turbulence
• Emergence of order from turbulence in an isolated planar superfluid
• Controlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier
• Light meets water in nonlocal media: Surface tension analogue in optics
• Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach
• Gray spatial solitons in nonlocal nonlinear media
• Phase-controlled bistability of a dark soliton train in a polariton fluid
• Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics
• Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach
• Scattering and leapfrogging of vortex rings in a superfluid
• Quantum fluctuations in the image of a Bose gas
• Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates
• Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation
• Parametric instability of oscillations of a vortex ring in a $z$-periodic Bose-Einstein condensate and the recurrence to starting state
• Adiabatic invariant analysis of dark and dark-bright soliton stripes in two-dimensional Bose-Einstein condensates
• Bound solitonic states in trapped multidimensional Bose-Einstein condensates

Cited by in corpus (5)

• Reduced dynamics for one and two dark soliton stripes in the defocusing nonlinear Schrödinger equation: a variational approach
• Generation of high winding-number superfluid circulation in Bose-Einstein condensates
• Pairwise Interactions of Ring Dark Solitons with Vortices and other Rings: Stationary States, Stability Features and Nonlinear Dynamics
• Physical realization of complex dynamical pattern formation in magnetic active feedback rings
• Characterising arbitrary dark solitons in trapped one-dimensional Bose-Einstein condensates