63 research outputs found
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 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
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