Topological Excitation Of Bose-Einstein Condensates In Different Dimensions

The Bose-Einstein condensation is an ancient and deeply studied quantum phe-nomenon in which the multibody Bose subsystem undergoes a phase change in which a single particle state becomes a macroscopic occupation.BEC is a very ideal experi-mental platform,which has ultra-high precision,controllability and easy operation.Since the experimental implementation of dipole BEC,a lot of attention has been drawn.The characteristics of dipole interaction are non-local long-range and anisotropic interaction,which have caused many new effects.One aspect is the generation of solitary waves.Sim-ilar to nonlinear optics,the effects of dispersion and nonlinearity may cancel each other out.This causes the shape of the agglomerates to be maintained longer.Considering the dipole⁵²Cr atomic BEC bound to the harmonic potential well,it can be described by the GP equation under the average field approximation.The virtual state evolution method is used to solve the ground state,that is,the soliton state.It is found that the amplitude of the soliton generally increases with the increase of contact interaction,but the ratio of dipole interaction and contact interaction is?_ddWhen small-er,the amplitude decreases with the increase of contact interaction,which is caused by competition between dipole interaction and contact interaction.The perturbation of the solitons was dynamically evolved,and it was found that when the 0<?_dd<2,the solitons showed strong stability.Collision studies of solitons in a dipole BEC show that there are totally elastic and inelastic collisions for solitons under external potential constraints.The type of collision depends on the strength of the dipole and contact interactions.When the dipole or con-tact interaction is small,a completely elastic collision occurs,otherwise it is an inelastic collision.The initial phase difference before the collision will affect the symmetry of the collision point.When the phase difference is an odd multiple of pi/2,the interference pattern generated by the collision is asymmetric about the origin.When the phase differ-ence is an even number of pi/2 At times,the interference pattern is symmetrical about the origin.And the elastic collision interferes at the collision point.The soliton collision without external potential bond has only found inelastic collisions.Interestingly,after the collision,the type of solitons has changed to become breathing-like.The frequency of the breather is related to the dipole and contact interactions of the solitons before the collision.The effect of the previous phase difference on the collision point is similar here.The dynamics of pseudo-spin-1/2 Bose-Einstein condensates with weak spin-orbit coupling?SOC?cause by a moving obstacle are investigated numerically.The Bénard-von Kármán vortex street can be observed when the physical parameters lie in an appropriate range.Other patterns of vortex shedding,such as V-shaped vortex pairs and irregular turbulence,can be also formed.When Bénard-von Kármán vortex street forms,the two point vortices rotate around their center,and the angular velocity and their distance changes periodically as time goes.For a given obstacle potential diameter,higher velocities are required to generate vortex street when the spin-orbit coupling strength increases.Because of the SOC effect,the stability condition of the vortex street ranges from 0.14to 0.25 in the present simulations while 0.28 in the classical fluid.The types of wake dynamics are described by the Reynolds number,Re_s,and it shows the transition to turbulence occurs at Re_s>0.23,regardless of the obstacle diameters.Finally,we provide an experimental protocol for the above realization and observation.