Bound states of dark solitons and vortices in trapped multidimensional Bose-Einstein condensates

Abstract

We report on the existence and stability of multidimensional bound solitonic states in harmonically trapped scalar Bose-Einstein condensates. Their equilibrium separation, as a measure of the strength of the solitonsoliton or the solitonic vortex-vortex interaction, is provided for varying chemical potential μ. Static bound dark solitons are shown to be dynamically stable in elongated condensates within a range of intermediate (repulsive) interparticle-interaction strength. Beyond this range the snaking instability manifests during the time evolution of the planar solitons and produces the decay into nonstationary vortex states. A subsequent dynamical recurrence of solitons and vortices can be observed at low μ. At equilibrium, the bifurcations of bound dark solitons are bound solitonic vortices. Among them, both two-open and two-ring vortex lines are demonstrated to exist with both counter-and co-rotating steady velocity fields. The latter flow configurations evolve, for high chemical potential, into a stationary three-dimensional (3D)-chain-shaped vortex and a three vortex-antivortex-vortex ring sequence that arrest the otherwise increasing angular or linear momentum respectively. As a feature common to the bifurcated families of vortex states, their excitation spectra present unstable modes with associated oscillatory dynamics. In spite of this, the family of two-open counter-rotating vortices support dynamically stable 3D states.

Quantum Dark Solitons in the 1D Bose Gas: From Single to Double Dark-Solitons

“…Finally, we menton some potentially relevant results in the following. Bound states of dark solitons are numerically studied by solving the GP equation [21], dynamics of a bright soliton in BEC with time-dependent atomic scattering length in an repulsive parabolic potential [22], quantized quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity [23], matter rogue wave in Bose-Einstein condensates with attractive atomic interaction [24], exact soliton solutions, and nonlinear modulation instability in spinor Bose-Einstein condensates [25].…”

Engineering phase and density of Bose–Einstein condensates in curved waveguides with toroidal topology

“…, with (x 0 , y 0 ) determined using equation (14). The parameter λ is obtained by solving equation (15).…”

“…The influence of curvature on condensate properties has been extensively investigated in both experimental studies of quasi-2D manifolds [4,5] and theoretical investigations [6][7][8][9][10][11]. Quasi-1D BECs have attracted significant interest due to their ability to exhibit diverse nonlinear excitations, including dark solitons [12][13][14][15][16] and solitonic vortices [17][18][19][20][21][22][23]. Curved waveguides can be realized by using magnetic or optical fields to create trapping potentials with different shapes, such as rings, ellipses, or spirals.…”

Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose–Einstein condensation

“…Thus, condensate fraction n 0 is constant as particle number N becomes very large if interaction parameter γ is given by the power of particle number N as in equation (30).…”

“…For strong and intermediate interaction strengths, the Lieb-Liniger Gross-Pitaevski equation is introduced, which is an extension of the GP equation [29]. Associated with the quantum states of dark solitons, bound states of dark solitons are numerically studied by solving the GP equation [30], dynamics of a bright soliton in the quasi-BEC with time-dependent atomic scattering length in a repulsive parabolic potential [31], quantized quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity [32], matter rogue wave in Bose-Einstein condensates with attractive atomic interaction [33], exact soliton solutions, and nonlinear modulation instability in spinor Bose-Einstein condensates [34].…”