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Register a new userVortex solutions in atomic Bose-Einstein condensates via the Adomian Decomposition Method
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We study the dynamics of vortices with arbitrary topological charges in weakly interacting Bose-Einstein condensates using the Adomian Decomposition Method to solve the nonlinear Gross-Pitaevskii equation in polar coordinates. The solutions of the vortex equation are expressed in the form of infinite power series. The power series representations are compared with the exact numerical solutions of the Gross-Pitaevskii equation for the uniform and the harmonic potential, respectively. We find that there is a good agreement between the analytical and the numerical results.
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Reconnections and interactions of filamentary coherent structures play a fundamental role in the dynamics of fluids, plasmas and nematic liquid crystals. In fluids, vortex reconnections redistribute energy and helicity among the length scales and induce fine-scale turbulent mixing. Unlike ordinary fluids where vorticity is a continuous field, in quantum fluids vorticity is concentrated into discrete (quantized) vortex lines turning vortex reconnections into isolated events, making it conceptually easier to study. Here we report experimental and numerical observations of three-dimensional quantum vortex interactions in a cigar-shaped atomic Bose-Einstein Condensate (BEC). In addition to standard reconnections, already numerically and experimentally observed in homogeneous systems away from boundaries, we show that double reconnections, rebounds and ejections can also occur as a consequence of the non-homogeneous, confined nature of the system.
Quantum vortices naturally emerge in rotating Bose-Einstein condensates (BECs) and, similarly to their classical counterparts, allow the study of a range of interesting out-of-equilibrium phenomena like turbulence and chaos. However, the study of such phenomena requires to determine the precise location of each vortex within a BEC, which becomes challenging when either only the condensate density is available or sources of noise are present, as is typically the case in experimental settings. Here, we introduce a machine learning based vortex detector motivated by state-of-the-art object detection methods that can accurately locate vortices in simulated BEC density images. Our model allows for robust and real-time detection in noisy and non-equilibrium configurations. Furthermore, the network can distinguish between vortices and anti-vortices if the condensate phase profile is also available. We anticipate that our vortex detector will be advantageous both for experimental and theoretical studies of the static and dynamical properties of vortex configurations in BECs.
The Lowest Landau Level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of Bose-Einstein Condensates (BEC) in two-dimensional isotropic harmonic traps in the limit of weak interactions. Building on recent developments in the field of spatially confined extended Hamiltonian systems, we find a fully nonlinear solution of this equation representing periodically modulated precession of a single vortex. Motions of this type have been previously seen in numerical simulations and experiments at moderately weak coupling. Our work provides the first controlled analytic prediction for trajectories of a single vortex, suggests new targets for experiments, and opens up the prospect of finding analytic multi-vortex solutions.
The behaviour of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilise linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.
We investigate the effects of vortex interaction on the formation of interference patterns in a coherent pair of two-dimensional Bose condensed clouds of ultra-cold atoms traveling in opposite directions subject to a harmonic trapping potential. We identify linear and nonlinear regimes in the dipole oscillations of the condensates according to the balance of internal and centre-of-mass energies of the clouds. Simulations of the collision of two clouds each containing a vortex with different winding number (charge) were carried out in these regimes in order to investigate the creation of varying interference patterns. The interaction between different vortex type can be clearly distinguished by those patterns.
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