Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry breaking minimum energy solutions of the time dependent Gross-Pitaevskii equation, using the method of constrained optimization. In a non-rotating axially symmetric trap, the core of a single vortex precesses around the trap center and, at the same time, the phase of its wave function shifts at a constant rate. The precession velocity, the speed of phase shift, and the distance between the vortex core and the trap center, depend continuously on the value of the conserved angular momentum that is carried by the entire condensate. In the case of a symmetric pair of identical vortices, the precession engages an emergent gauge field in their relative coordinate, with a flux that is equal to the ratio between the precession and shift velocities.
The dynamics of a filled massive vortex is studied numerically and analytically using a two-dimensional model of a two-component Bose--Einstein condensate trapped in a harmonic trap. This condensate exhibits phase separation. In the framework of the coupled Gross--Pitaevskii equations, it is demonstrated that, in a certain range of parameters of the nonlinear interaction, the precession of a sufficiently massive vortex around the center is strongly slowed down and even reverses its direction with a further increase in the mass. An approximate ordinary differential equation is derived that make…
Dynamics of simplest vortex knots, unknots, and links of torus type inside an atomic Bose-Einstein condensate in anisotropic harmonic trap at zero temperature has been numerically simulated using three-dimensional Gross-Pitaevskii equation. The lifetime for such quasi-stationary rotating vortex structures has been found quite long in wide parametric domains of the system. This result is in qualitative agreement with a previous prediction based on a simplified one-dimensional model approximately describing dynamics of vortex filaments [V.P. Ruban, JETP 126, 397 (2018)].
Three coaxial quantized vortex rings in a Bose-Einstein condensate exhibit aperiodic leapfrogging dynamics. It is found that such circular vortex rings are dynamically unstable against deformation breaking axial rotational symmetry. The dynamics of the system are analyzed using the Gross-Pitaevskii and vortex-filament models. The dependence of the instability on the initial arrangement of the vortex rings is investigated. The system is found to be significantly unstable for a specific configuration of the three vortex rings.
The nonequilibrium dynamics of vortices in 2D quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a harmonically trapped fluid can be analyzed analytically to show that single vortices will move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself. This allows the vortex ellipticity to be estimated through observation of its trajectory. A combination of analysis and numerical simulation is then used to show that …
Vortex formation of a Bose-Einstein condensate in a rotating deep optical lattice
通过数值模拟Gros-Pitaevskii方程，研究了旋转正方形光晶格中玻色-爱因斯坦凝聚体中涡旋成核和晶格形成的动力学过程.不同的动力学制度的涡旋成核，这取决于光晶格的深度和周期。我们与Williams { \it et al.}的实验进行了广泛的比较。[Phys. Rev. Lett. { \bf 104}，050404（2010）]，特别关注第一涡流成核的临界旋转频率和作为旋转频率的函数的涡流数的问题。
We consider the mean-field vortex solutions and their stability within a two-component Bose Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains a single quantised vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation to the two-component vortex solution for a range of atom numbers of the in-filling component, by comparing the variational solutions to the full numerical solutions of the coupled Gross-Pitaevskii equations. We subseq…
We investigate spatiotemporal vortex rings with phase dislocation both in space and time. It is demonstrated that these structures naturally appear as a periodical in time edge phase dislocation at the low-density region of a perturbed atomic Bose-Einstein condensate. The condition of formation, dynamics and stability of the spatiotemporal vortex rings are investigated for repulsive and attractive interatomic interactions. These theoretical findings open up a perspective for experimental observation of novel type of topological coherent structures in ultracold gases.
The annihilation of vortex-antivortex pairs is a key event in two-dimensional Bose-Einstein condensates (BECs). It is known that dissipation or a catalyst vortex is required for the annihilation of the pairs in one-component BECs. We numerically confirmed in two-component BECs that the pairs can be annihilated even without any dissipation or catalyst vortices when the intercomponent interaction is strong. In addition, the pair is recreated alternately in two components under certain conditions, which we call the recurrence.
Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate
The physics of quantized vortex excitations in atomic Bose-Einstein condensates has been extensively studied in recent years.Although simple vortex lines are relatively easy to create, control, and measure in experiments, it is a lot more difficult to do the same for vortex ring structures.Here we suggest and explore a method for generating and controlling superfluid vortex rings, vortex ring lattices, and other three dimensional vortex structures in toroidally-trapped superfluid Bose--Einstein condensates by using the artificial magnetic field produced by an optical nanofiber.The presence of …
Generating a spin vortex in a $^{87}$Rb dipolar spinor Bose-Einstein condensate in a controllable way is still experimentally challenging. We propose an experimentally easy and tunable way to produce spin vortex by varying the potential barrier height and the width of an additionally applied optical plug. A topological phase transition occurs from the trivial single mode approximation phase to the optical-plug-assisted-vortex one, as the barrier height increases and the width lies in an appropriate range. The optical plug causes radial density variation thus the spin vortex is favored by signi…
We find a novel topological defect in a spin-nematic superfluid theoretically. A quantized vortex spontaneously breaks its axisymmetry, leading to an elliptic vortex in nematic-spin Bose-Einstein condensates with small positive quadratic Zeeman effect. The new vortex is considered the Joukowski transform of a conventional vortex. Its oblateness grows when the Zeeman length exceeds the spin healing length. This structure is sustained by balancing the hydrodynamic potential and the elasticity of a soliton connecting two spin spots, which are observable by in situ magnetization imaging. The theor…
