Negative-Index Media for Matter-Wave Optics (original) (raw)

2009, Physical Review Letters

We consider the extension of optical meta-materials to matter waves and then the down scaling of meta-optics to nanometric wavelengths. We show that the generic property of pulsed comoving magnetic fields allows us to fashion the wave-number dependence of the atomic phase shift. It can be used to produce a transient negative group velocity of an atomic wave packet, which results into a negative refraction of the matter wave. Application to slow metastable argon atoms Ar*( 3 P2) shows that the device is able to operate either as an efficient beam splitter or an atomic meta-lens. 03.75.Be, 37.10.Gh, Since the pioneering work of H. Lamb [1] and V.G. Veselago's seminal paper [2] about so-called "lefthanded" or "meta" media for light optics, a number of studies have been devoted to these new media and their applications (negative refraction, reversed Doppler effect, perfect lens, van der Waals atom-surface interaction, etc.) , in various spectral domains , some of them being even extended to acoustic waves . Such media are essentially characterised by a negative value of the optical index, which results into opposite directions of the wave vector k and the Poynting vector R. Our goal here is to extend this concept to matter waves, and the first arising question is the following: what should be the "de-Broglie optics" equivalent of those meta-materials? To the energy flux in electromagnetism (R vector) corresponds the atomic probability flux, namely the current density of probability J, or equivalently the group velocity v g = |ψ| −2 J, where ψ is the wave-function. Therefore, here also, one has to reverse v g with respect to the wave vector k or the phase velocity. However, as discussed below, contrarily to what occurs in light optics where R remains directed outwards whereas k is directed towards the light source [10], for matter waves the direction of the phase velocity (k) remains unchanged, whereas v g is now directed towards the source. Obviously, because of the conservation of probability, such an effect is necessarily a transient effect.