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Register a new userDevelopment of instability of dark solitons generated by a flow of Bose-Einstein condensate past a concave corner
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The stability of dark solitons generated by a supersonic flow of a Bose-Einstein condensate past a concave corner (or a wedge) is studied. It is shown that solitons in the dispersive shock wave generated at the initial moment of time demonstrate a snake instability during their evolution to stationary curved solitons. Time of decay of soliton to vortices agrees very well with analytical estimates of the instability growth rate.
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Stability of dark solitons generated by a supersonic flow of Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow velocity from absolute instability of dark solitons to their convective instability. This leads to decay of disturbances of solitons at fixed distance from the obstacle and formation of effectively stable dark solitons. This phenomenon explains surprising stability of the flow picture that has been observed in numerical simulations.
We study the flow of a spinor (F=1) Bose-Einstein condensate in the presence of an obstacle. We consider the cases of ferromagnetic and polar spin-dependent interactions and find that the system demonstrates two speeds of sound that are identified analytically. Numerical simulations reveal the nucleation of macroscopic nonlinear structures, such as dark solitons and vortex-antivortex pairs, as well as vortex rings in one- and higher-dimensional settings respectively, when a localized defect (e.g., a blue-detuned laser beam) is dragged through the spinor condensate at a speed larger than the second critical speed.
We investigate the dynamical instability of Bose-Einstein condensates (BECs) with higher-order interactions immersed in an optical lattice with weak driving harmonic potential. For this, we compute both analytically and numerically a modified Gross-Pitaevskii equation with higher-order nonlinearity and external potentials generated by magnetic and optical fields. Using the time-dependent variational approach, we derive the ordinary differential equations for the time evolution of the amplitude and phase of modulational perturbation. Through an effective potential, we obtain the modulational instability condition of BECs and discuss the effect of the higher-order interaction in the dynamics of the condensates in presence of optical potential. We perform direct numerical simulations to support our analytical results, and good agreement is found.
Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schroedinger or Gross-Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.
We numerically study the breathing dynamics induced by collision between bright solitons in the one-dimensional Bose-Einstein condensates with strong dipole-dipole interaction. This breathing phenomenon is closely related to the after-collision short-lived attraction of solitons induced by the dipolar effect. The initial phase difference of solitons leads to the asymmetric dynamics after collision, which is manifested on their different breathing amplitude, breathing frequency, and atom number. We clarify that the asymmetry of breathing frequency is directly induced by the asymmetric atom number, rather than initial phase difference. Moreover, the collision between breathing solitons can produce new after-two-collision breathing solitons, whose breathing amplitude can be adjusted and reach the maximum (or minimum) when the peak-peak (or dip-dip) collision happens.
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