Interactions of vortices with rarefaction solitary waves in a Bose-Einstein condensate and their role in the decay of superfluid turbulence

There are several ways to create the vorticity-free solitary waves -- rarefaction pulses -- in condensates: by the process of strongly nonequilibrium condensate formation in a weakly interacting Bose gas, by creating local depletion of the condensate density by a laser beam, and by moving a small object with supercritical velocities. Perturbations created by such waves colliding with vortices are studied in the context of the Gross-Pitaevskii model. We find that the effect of the interactions consists of two competing mechanisms: the creation of vortex line as rarefaction waves acquire circulation in a vicinity of a vortex core and the loss of the vortex line to sound due to Kelvin waves that are generated on vortex lines by rarefaction pulses. When a vortex ring collides with a rarefaction wave, the ring either stabilises to a smaller ring after emitting sound through Kelvin wave radiation or the entire energy of the vortex ring is lost to sound if the radius of the ring is of the order of the healing length. We show that during the time evolution of a tangle of vortices, the interactions with rarefaction pulses provide an important dissipation mechanism enhancing the decay of superfluid turbulence.Comment: Revised paper accepted by Phys. Rev.

Vortex Splitting in Subcritical Nonlinear Schrodinger Equation

Vortices and axisymmetric vortex rings are considered in the framework of the subcritical nonlinear Schrodinger equations. The higher order nonlinearity present in such systems models many-body interactions in superfluid systems and allows one to study the effects of negative pressure on vortex dynamics. We find the critical pressure for which the straight-line vortex becomes unstable to radial expansion of the core. The energy of the straight-line vortices and energy, impulse and velocity of vortex rings are calculated. The effect of a varying pressure on the vortex core is studied. It is shown that under the action of the periodically varying pressure field a vortex ring may split into many vortex rings and the conditions for which this happens are elucidated. These processes are also relevant to experiments in Bose-Einstein condensates where the strength and the sign of two-body interactions can be changed via Feshbach resonance.Comment: Invited submission to the special issue on Vortex Rings, Journal of Fluid Dynamics Researc

Universality in modelling non-equilibrium pattern formation in polariton condensates

The key to understanding the universal behaviour of systems driven away from equilibrium lies in the common description obtained when particular microscopic models are reduced to order parameter equations. Universal order parameter equations written for complex matter fields are widely used to describe systems as different as Bose-Einstein condensates of ultra cold atomic gases, thermal convection, nematic liquid crystals, lasers and other nonlinear systems. Exciton-polariton condensates recently realised in semiconductor microcavities are pattern forming systems that lie somewhere between equilibrium Bose-Einstein condensates and lasers. Because of the imperfect confinement of the photon component, exciton-polaritons have a finite lifetime, and have to be continuously re-populated. As photon confinement improves, the system more closely approximates an equilibrium system. In this chapter we review a number of universal equations which describe various regimes of the dynamics of exciton-polariton condensates: the Gross-Pitaevskii equation, which models weakly interacting equilibrium condensates, the complex Ginsburg-Landau equation---the universal equation that describes the behaviour of systems in the vicinity of a symmetry--breaking instability, and the complex Swift-Hohenberg equation that in comparison with the complex Ginsburg-Landau equation contains additional nonlocal terms responsible for spacial mode selection. All these equations can be derived asymptotically from a generic laser model given by Maxwell-Bloch equations. Such an universal framework allows the unified treatment of various systems and continuously cross from one system to another. We discuss the relevance of these equations, and their consequences for pattern formation.Comment: 19 pages; Chapter to appear in Springer&Verlag book on "Quantum Fluids: hot-topics and new trends" eds. A. Bramati and M. Modugn

Motion in a Bose condensate: IX. Crow instability of antiparallel vortex pairs

The Gross-Pitaevskii (GP) equation admits a two-dimensional solitary wave solution representing two mutually self-propelled, anti-parallel straight line vortices. The complete sequence of such solitary wave solutions has been computed by Jones and Roberts (J. Phys. A, 15, 2599, 1982). These solutions are unstable with respect to three-dimensional perturbations (the Crow instability). The most unstable mode has a wavelength along the direction of the vortices of the same order as their separation. The growth rate associated with this mode is evaluated here, and it is found to increase very rapidly with decreasing separation. It is shown, through numerical integrations of the GP equation that, as the perturbations grow to finite amplitude, the lines reconnect to produce a sequence of almost circular vortex rings.Comment: Submitted to J. Phys. A: Math. Gen.; Corrected reference