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

Evolution of rarefaction pulses into vortex rings

The two-dimensional solitary waves of the Gross-Pitaevskii equation in the Kadomtsev-Petviashvili limit are unstable with respect to three-dimensional perturbations. We elucidate the stages in the evolution of such solutions subject to perturbations perpendicular to the direction of motion. Depending on the energy (momentum) and the wavelength of the perturbation different types of three-dimensional solutions emerge. In particular, we present new periodic solutions having very small energy and momentum per period. These solutions also become unstable and this secondary instability leads to vortex ring nucleation.Comment: 5 pages, 5 figure

Pade approximations of solitary wave solutions of the Gross-Pitaevskii equation

Pade approximants are used to find approximate vortex solutions of any winding number in the context of Gross-Pitaevskii equation for a uniform condensate and condensates with axisymmetric trapping potentials. Rational function and generalised rational function approximations of axisymmetric solitary waves of the Gross-Pitaevskii equation are obtained in two and three dimensions. These approximations are used to establish a new mechanism of vortex nucleation as a result of solitary wave interactions.Comment: In press by Journal of Physics: Mathematics and Genera

Roton dipole moment

The roton excitation in the superfluid He-4 does not possess a stationary dipole moment. However, a roton has an instantaneous dipole moment, such that at any given moment one can find it in the state either with positive or with negative dipole moment projection on its momentum direction. The instantaneous value of electric dipole moment of roton excitation is evaluated. The result is in reasonable agreement with recent experimental observation of the splitting of microwave resonance absorption line at roton frequency under external electric field.Comment: 5 page

Kolmogorov Spectrum of Quantum Turbulence

There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of stable topological defects called quantized vortices, and thus quantum turbulence provides a simpler prototype of turbulence than classical turbulence. In this paper, we investigate the dynamics and statistics of quantized vortices in quantum turbulence by numerically solving a modified Gross-Pitaevskii equation. First, to make decaying turbulence, we introduce a dissipation term that works only at scales below the healing length. Second, to obtain steady turbulence through the balance between injection and decay, we add energy injection at large scales. The energy spectrum is quantitatively consistent with the Kolmogorov law in both decaying and steady turbulence. Consequently, this is the first study that confirms the inertial range of quantum turbulence.Comment: 14pages, 24 figures and 1 table. Appeared in Journal of the Physical Society of Japan, Vol.74, No.12, p.3248-325

Out-of-phase oscillation between superfluid and thermal components for a trapped Bose condensate under oscillatory excitation

The vortex nucleation and the emergence of quantum turbulence induced by oscillating magnetic fields, introduced by Henn E A L, et al. 2009 (Phys. Rev. A 79, 043619) and Henn E A L, et al. 2009 (Phys. Rev. Lett. 103, 045301), left a few open questions concerning the basic mechanisms causing those interesting phenomena. Here, we report the experimental observation of the slosh dynamics of a magnetically trapped $^{87}$Rb Bose-Einstein condensate (BEC) under the influence of a time-varying magnetic field. We observed a clear relative displacement in between the condensed and the thermal fraction center-of-mass. We have identified this relative counter move as an out-of-phase oscillation mode, which is able to produce ripples on the condensed/thermal fractions interface. The out-of-phase mode can be included as a possible mechanism involved in the vortex nucleation and further evolution when excited by time dependent magnetic fields.Comment: 5 pages, 5 figures, 25 reference