We numerically study dynamical creation of vortex excitations in Bose-Einstein condensates (BECs) within the framework of mean-field theory using dissipative Gross-pitaevskii equation. Vortex dipoles and
We study the formation and dynamics of vortices in quasi two-dimensional dipolar Bose-Einstein condensates (BECs). We solve the time dependent two-dimensional Gross-Pitaevskii equation by using a combined split-step Crank-Nicolson (SSCN) and Fast Fourier-Transform (FFT) based numerical scheme and investigate the vortex dynamics in dipolar BECs trapped with harmonic and optical lattice potentials. The consequence of dipole-dipole interaction on vortex nucleation and number of vortices has been analysed. We observe that the breaking of symmetry due to anisotropic dipolar interaction enormously increase the speed of creation of vortices.
In this paper, we investigate the collective excitations of an attractively interacting Bose–Einstein condensate confined in a two-channel potential. Using the Bogoliubov approximation, we derive the Bogoliubov–de Gennes equations and determine the excitation spectrum numerically. Two distinct modes are identified: the well-known Josephson mode, associated with periodic inter-channel tunneling, and a novel antisymmetric translational mode, describing out-of-phase oscillations of the condensate center of mass. Unlike conventional dipole oscillations, the latter arises from the interplay between inter-channel coupling and attractive nonlinearity and does not follow the Kohn theorem. We then employ the variational approximation to describe the condensate dynamics under these excitations and to extract the corresponding mode frequencies. The results are further validated by real-time simulations of the governing Gross–Pitaevskii equations, showing good agreement between analytical and numerical approaches.
For study of Continuous matter waves in Bose-Einstein condensates in nonlinear and quantum atom optics, the two-dimensional Gross-Pitaevskii equation (GPE) is chosen as the reliable model for studying the dynamics of vortices in the framework of mean-field theory. In related problems in several recent studies showing that higher-order interrelationships are an indispensable component of the GPE even at the mean-field level, by numerically estimating the vortex dynamics variables. In this paper, derive the vortex soliton solutions using the variational method and investigate the effect of higher-order nonlinear corrections on the behavior of the vortex dynamics, which are shown to have an important impact on the vortex dynamics behavior.
We study the influence of dipole–dipole interaction on the formation of vortices in a rotating dipolar Bose–Einstein condensate (BEC) of 52 Cr and 164 Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross–Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices, while a repulsive contact interaction increases the stability of the vortices. Furthermore, an ordered vortex lattice of a relatively large number of vortices is found in a strongly dipolar BEC.