%0 Journal Article
%T Metaoptics with Nonrelativistic Matter Waves
%A T. Taillandier-Loize
%A J. Baudon
%A M. Hamamda
%A G. Dutier
%A V. Bocvarski
%A M. Boustimi
%A F. Perales
%A M. Ducloy
%J Advances in OptoElectronics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/734306
%X The counterpart of metamaterials in light optics for nonrelativistic matter waves governed by the Schr£¿dinger equation can be found by transiently reversing the group velocity using a so called comoving potential. Possible applications to wave-packet dynamics, atom interferometry, and atom deceleration are described. 1. Introduction The genuine concept of ¡°meta¡± materials for electromagnetic waves originates from the now famous Veselago¡¯s paper published in 1967 [1]. The basic idea is that, in a material with negative electric permittivity and negative magnetic permeability , Maxwell equations impose that the wave vector k and the Poynting vector S of a planar wave have opposite directions and, because of causality, the effective optical index is real negative: . The realisation of such artificial or ¡°meta¡± materials, also called left-handed materials (LHM), in a wide range of wavelengths, has been¡ªand continues to be¡ªthe subject of considerable theoretical and experimental efforts [2¨C4]. Compared to an ordinary material with a positive index, a metamaterial has a similar group velocity, whereas its phase velocity is reversed. This gives rise to the negative refraction phenomenon, owing to which so-called ¡°meta¡± lenses are conceivable. The concept is rather easily extended to matter waves, provided that the effective mass of the particle be zero or close to zero, as it is the case for electrons in graphene, governed by a (relativistic) Dirac equation [5]. Paradoxically the situation is much more intricate with nonrelativistic particles, as atoms having a thermal velocity (a few hundreds ms£¿1), the dynamics of which is governed by the Schr£¿dinger equation. The first obstacle is the inability of atoms to penetrate dense matter: hence a ¡°material¡± should be replaced by a ¡°medium¡±, namely, some external potential created in vacuum. A second difficulty comes from the fact that, in this situation, the phase velocity is an ambiguous concept since it is gauge dependent and its inversion appears to be problematic, if not meaningless. Nevertheless the key property of a metamedium lies in the opposite directions of phase and group velocities, a property which will be realised in our case by simply reversing the group velocity. Obviously, given a source of atoms, this property has necessarily a transient character since the group velocity is associated to the density of the probability flux which should finally be oriented outwards from the source. As a consequence, the external potential, assumed to depend on a single spatial coordinate ( ), must be also time
%U http://www.hindawi.com/journals/aoe/2012/734306/