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We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features…
The dynamics of two-component Bose-Einstein condensates in rotating traps is investigated. In the Thomas-Fermi limit, equations of motion are derived showing multiple static solutions for a vortex free condensate. Dynamic stability analysis…
The dynamics of a ring of vortices in two-dimensional Bose-Einstein condensates (with and without an additional vortex at the center) is studied for (1) a uniform condensate in a rigid cylinder and (2) a nonuniform trapped condensate in the…
The dynamics of vortices in trapped Bose-Einstein condensates are investigated both analytically and numerically. In axially symmetric traps, the critical rotation frequency for the metastability of an isolated vortex coincides with the…
The dynamics of deformations of a quantum vortex ring in a Bose-Einstein condensate with periodic equilibrium density $\rho(z)= 1-\epsilon\cos z$ has been considered within the local induction approximation. Parametric instabilities of the…
We perform numerical simulations of vortex motion in a trapped Bose-Einstein condensate by solving the two-dimensional Gross-Pitaevskii Equation in the presence of a simple phenomenological model of interaction between the condensate and…
We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii…
We study the precessing motion of a vortex in a Bose-Einstein condensate of atomic gases. In addition to the former zero-temperature studies, finite temperature systems are treated within the Popov and semiclassical approximations.…
The low temperature dynamics of a vortex in a trapped quasi-two-dimensional Bose-Einstein condensate are studied quantitatively. Precession of an off-centred vortex in a dimple trap, embedded in a weaker harmonic trap, leads to the emission…
We derive a general and exact equation of motion for a quantised vortex in an inhomogeneous two-dimensional Bose-Einstein condensate. This equation expresses the velocity of a vortex as a sum of local ambient density and phase gradients in…
We calculate the critical rotation frequency at which a vortex state becomes energetically favorable over the vortex-free ground state in a harmonically trapped Bose-Einstein condensate whose atoms have dipole-dipole interactions as well as…
Motivated by experiments in atomic Bose-Einstein condensates (BECs), we compare predictions of a system of ordinary differential equations (ODE) for dynamics of one and two individual vortices in the rotating BECs with those of the partial…
We consider a periodic vortex lattice in a rotating Bose-Einstein condensed gas, where the centrifugal potential is exactly compensated by the external harmonic trap. By introducing a gauge transformation which makes the Hamiltonian…
We study two-dimensional quantum turbulence in miscible binary Bose-Einstein condensates in either a harmonic trap or a steep-wall trap through the numerical simulations of the Gross-Pitaevskii equations. The turbulence is generated through…
We study the creation of vortices by triggering the rotating Bose-Einstein condensates in a toroidal trap with trap parameters such as laser beam waist and Gaussian potential depth. By numerically solving the time-dependent Gross-Pitaevskii…
The properties of vortex states in a Bose-Einstein condensed cloud of atoms are considered at zero temperature. Using both analytical and numerical methods we solve the time-dependent Gross-Pitaevskii equation for the case when a cloud of…
It is demonstrated that a two-component Bose-Einstein condensate (BEC) with all-repulsive inter-atomic interactions loaded into a radially symmetric harmonic trap supports robust non-coaxial vortices with approximately orthogonal vortex…
We study the quadrupole oscillation of a Bose-Einstein condensate of $^{87}$Rb atoms confined in an axisymmetric magnetic trap, after it has been stirred by an auxiliary laser beam. The stirring may lead to the nucleation of one or more…
We calculate the breathing mode frequency $\omega$ in a one-dimensional Bose gas confined to a harmonic trap of frequency $\omega_z$. We predict Exciting temporal oscillations of the density distribution is a high-precision method for…
We address the challenging proposition of using real experimental parameters in a three-dimensional numerical simulation of fast rotating Bose-Einstein condensates. We simulate recent experiments [V. Bretin, S. Stock, Y. Seurin and J.…