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Register a new userSingle and Multiple Vortex Rings in Three-Dimensional Bose-Einstein Condensates: Existence, Stability and Dynamics
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In the present work, we explore the existence, stability and dynamics of single and multiple vortex ring states that can arise in Bose-Einstein condensates. Earlier works have illustrated the bifurcation of such states, in the vicinity of the linear limit, for isotropic or anisotropic three-dimensional harmonic traps. Here, we extend these states to the regime of large chemical potentials, the so-called Thomas-Fermi limit, and explore their properties such as equilibrium radii and inter-ring distance, for multi-ring states, as well as their vibrational spectra and possible instabilities. In this limit, both the existence and stability characteristics can be partially traced to a particle picture that considers the rings as individual particles oscillating within the trap and interacting pairwise with one another. Finally, we examine some representative instability scenarios of the multi-ring dynamics including breakup and reconnections, as well as the transient formation of vortex lines.
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We examine the spectral properties of single and multiple matter-wave dark solitons in Bose-Einstein condensates confined in parabolic traps, where the scattering length is periodically modulated. In addition to the large-density limit picture previously established for homogeneous nonlinearities, we explore a perturbative analysis in the vicinity of the linear limit, which provides good agreement with the observed spectral modes. Between these two analytically tractable limits, we use numerical computations to fill in the relevant intermediate regime. We find that the scattering length modulation can cause a variety of features absent for homogeneous nonlinearities. Among them, we note the potential oscillatory instability even of the single dark soliton, the potential absence of instabilities in the immediate vicinity of the linear limit for two dark solitons, and the existence of an exponential instability associated with the in-phase motion of three dark solitons.
We study stationary clusters of vortices and antivortices in dilute pancake-shaped Bose-Einstein condensates confined in nonrotating harmonic traps. Previous theoretical results on the stability properties of these topologically nontrivial excited states are seemingly contradicting. We clarify this situation by a systematic stability analysis. The energetic and dynamic stability of the clusters is determined from the corresponding elementary excitation spectra obtained by solving the Bogoliubov equations. Furthermore, we study the temporal evolution of the dynamically unstable clusters. The stability of the clusters and the characteristics of their destabilizing modes only depend on the effective strength of the interactions between particles and the trap anisotropy. For certain values of these parameters, there exist several dynamical instabilities, but we show that there are also regions in which some of the clusters are dynamically stable. Moreover, we observe that the dynamical instability of the clusters does not always imply their structural instability, and that for some dynamically unstable states annihilation of the vortices is followed by their regeneration, and revival of the cluster.
Quantum vortex reconnections can be considered as a fundamental unit of interaction in complex turbulent quantum gases. Understanding the dynamics of single vortex reconnections as elementary events is an essential precursor to the explanation of the emergent properties of turbulent quantum gases. It is thought that a lone pair of quantum vortex lines will inevitably interact given a sufficiently long time. This paper investigates aspects of reconnections of quantum vortex pairs imprinted in a Bose-Einstein condensate held in an anisotropic three dimensional trap using an exact many-body treatment. In particular the impact of the interaction strength and the trap anisotropy in the reconnection time is studied. It is found that interaction strength has no effect on reconnection time over short time scales and that the trap anisotropy can cause the edge of the condensate to interfere with the reconnection process. It is also found that the initially coherent system fragments very slowly, even for relatively large interaction strength, and therefore the system likes to stay condensed during the reconnections.
We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of the parabolic trap there is a logarithmic correction in the dependence of the precession frequency $omega$ on the chemical potential $mu$, this is no longer true for a general potential $V(r) propto r^p$. Our calculations suggest that for $p>2$, the precession frequency scales with $mu$ as $omega sim mu^{-2/p}$. This theoretical prediction is corroborated by numerical computations, both at the level of spectral (Bogolyubov-de Gennes) stability analysis by identifying the relevant precession mode dependence on $mu$, but also through direct numerical computations of the vortex evolution in the large $mu$, so-called Thomas-Fermi, limit. Additionally, the dependence of the precession frequency on the radius of an initially displaced from the center vortex is examined and the corresponding predictions are tested against numerical results.
Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schroedinger or Gross-Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.
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