20 research outputs found
Experiments on Multidimensional Solitons
This article presents an overview of experimental efforts in recent years
related to multidimensional solitons in Bose-Einstein condensates. We discuss
the techniques used to generate and observe multidimensional nonlinear waves in
Bose-Einstein condensates with repulsive interactions. We further summarize
observations of planar soliton fronts undergoing the snake instability, the
formation of vortex rings, and the emergence of hybrid structures.Comment: review paper, to appear as Chapter 5b in "Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P.
G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez
(Springer-Verlag
Radiating dispersive shock waves in nonlocal optical media
We consider the step Riemann problem for the system of equations describing
the propagation of a coherent light beam in nematic liquid crystals, which is a
general system describing nonlinear wave propagation in a number of different
physical applications. While the equation governing the light beam is of
defocusing nonlinear Schr\"odinger equation type, the dispersive shock wave
(DSW) generated from this initial condition has major differences from the
standard DSW solution of the defocusing nonlinear Schr\"odinger equation. In
particular, it is found that the DSW has positive polarity and generates
resonant radiation which propagates ahead of it. Remarkably, the velocity of
the lead soliton of the DSW is determined by the classical shock velocity. The
solution for the radiative wavetrain is obtained using the WKB approximation.
It is shown that for sufficiently small initial jumps the nematic DSW is
asymptotically governed by a Korteweg-de Vries equation with fifth order
dispersion, which explicitly shows the resonance generating the radiation ahead
of the DSW. The constructed asymptotic theory is shown to be in good agreement
with the results of direct numerical simulations.Comment: 22 pages, 6 figures; accepted for publication in Proc. Roy.Soc.
London A (2016
Disorder Effects on Exciton-Polariton Condensates
The impact of a random disorder potential on the dynamical properties of Bose
Einstein condensates is a very wide research field. In microcavities, these
studies are even more crucial than in the condensates of cold atoms, since
random disorder is naturally present in the semiconductor structures. In this
chapter, we consider a stable condensate, defined by a chemical potential,
propagating in a random disorder potential, like a liquid flowing through a
capillary. We analyze the interplay between the kinetic energy, the
localization energy, and the interaction between particles in 1D and 2D
polariton condensates. The finite life time of polaritons is taken into account
as well. In the first part, we remind the results of [G. Malpuech et al. Phys.
Rev. Lett. 98, 206402 (2007).] where we considered the case of a static
condensate. In that case, the condensate forms either a glassy insulating phase
at low polariton density (strong localization), or a superfluid phase above the
percolation threshold. We also show the calculation of the first order spatial
coherence of the condensate versus the condensate density. In the second part,
we consider the case of a propagating non-interacting condensate which is
always localized because of Anderson localization. The localization length is
calculated in the Born approximation. The impact of the finite polariton life
time is taken into account as well. In the last section we consider the case of
a propagating interacting condensate where the three regimes of strong
localization, Anderson localization, and superfluid behavior are accessible.
The localization length is calculated versus the system parameters. The
localization length is strongly modified with respect to the non-interacting
case. It is infinite in the superfluid regime whereas it is strongly reduced if
the fluid flows with a supersonic velocity.Comment: chapter for a book "Exciton Polaritons in Microcavities: New
Frontiers" by Springer (2012), the original publication is available at
http://www.springerlink.co
Dispersive, superfluid-like shock waves in nonlinear optics
In most classical fluids, shock waves are strongly dissipative, their energy
being quickly lost through viscous damping. But in systems such as cold
plasmas, superfluids, and Bose-Einstein condensates, where viscosity is
negligible or non-existent, a fundamentally different type of shock wave can
emerge whose behaviour is dominated by dispersion rather than dissipation.
Dispersive shock waves are difficult to study experimentally, and analytical
solutions to the equations that govern them have only been found in one
dimension (1D). By exploiting a well-known, but little appreciated,
correspondence between the behaviour of superfluids and nonlinear optical
materials, we demonstrate an all-optical experimental platform for studying the
dynamics of dispersive shock waves. This enables us to observe the propagation
and nonlinear response of dispersive shock waves, including the interaction of
colliding shock waves, in 1D and 2D. Our system offers a versatile and more
accessible means for exploring superfluid-like and related dispersive
phenomena.Comment: 21 pages, 6 figures Revised abstrac
Wave instabilities in the presence of non vanishing background in nonlinear Schrodinger systems
We investigate wave collapse ruled by the generalized nonlinear Schroedinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign
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Wave patterns generated by a supersonic moving body in a binary Bose-Einstein condensate
Generation of wave structures by a two-dimensional (2D) object (laser beam) moving in a 2D two-component Bose-Einstein condensate with a velocity greater than the two sound velocities of the mixture is studied by means of analytical methods and systematic simulations of the coupled Gross-Pitaevskii equations. The wave pattern features three regions separated by two Mach cones. Two branches of linear patterns similar to the so-called âship wavesâ are located outside the corresponding Mach cones, and oblique dark solitons are found inside the wider cone. An analytical theory is developed for the linear patterns. A particular dark-soliton solution is also obtained, its stability is investigated, and two unstable modes of transverse perturbations are identified. It is shown that for a sufficiently large flow velocity, this instability has a convective character in the reference frame attached to the moving body, which makes the dark soliton effectively stable. The analytical findings are corroborated by numerical simulations
Ball lightning an electromagnetic knot?
© 1996 Nature Publishing Group.Depto. de Estructura de la Materia, FĂsica TĂ©rmica y ElectrĂłnicaFac. de Ciencias FĂsicasTRUEpu