EGAS41 - Swansea University

41 st EGAS CP 151 Gdańsk 2009
Negative refraction of matter-wave
M. Hamamda 1,∗ , G. Dutier 1 , F. Perales 1 , J. Baudon 1 , M. Ducloy 1
1 Laboratoire de Physique des Lasers, Universite Paris 13, 99 av J-B Clement,
93340 Villetaneuse, France
∗ Corresponding author: mehdi.hamamda@univ-paris13.fr,
Similarities and differences between light and matter-wave optics originate in the properties
of the associated particle. The extension of so-called ”left-handed” optical metamaterials
to negative-index media (NIM) for matter waves is a topic of particular importance
[1]. Since the seminal paper of V.G. Veselago [2], many works have been devoted
to optical NIM’s and their properties (negative refraction, perfect focussing, reversed
Doppler Effect, cloaking, etc.). Such artificial media are essentially characterised by a
negative value of the optical index, i.e. the reversal of the wave vector → k with respect
to the Poynting vector → R. What should be the ”de-Broglie optics” equivalent of those
meta-materials [1] To the energy flux corresponds the atomic probability flux, namely
the current density of probability, or equivalently the group velocity v g . Therefore, one
has to reverse v g with respect to → k, i.e. the phase velocity. However, contrarily to light
optics where → R remains directed outwards whereas → k is directed towards the light source
[3], for matter waves the direction of the phase velocity remains unchanged, whereas v g
is now directed towards the source [1]. Obviously, such an effect is necessarily transient.
Our approach relies on both position- and time-dependent magnetic potentials [1]. We
have shown that a novel class of potentials – ”comoving” potentials [2] – provides us with
a remarkably simple solution to devise negative-index media for matter waves [1]. These
co-moving potentials are oscillating magnetic potentials which, by an adequate choice of
the spatial period and oscillation frequency, can be made co-propagating with the atom
wave [4]. The calculation of the induced matter-wave phase-shift demonstrates the possibility
of producing transient negative group velocities for the atomic wave packet (see
figure 1). With an adequate time-dependence of the co-moving field, we can devise cylindrical
or spherical ”metalenses”. This extension of ”meta-optics” down to the nanometer
wavelength range opens novel applications in atom nano-lithography and interferometry.
Figure 1: Trajectories of the wave packet center.
References
[1] J. Baudon, M. Hamamda et al., Phys. Rev Lett. 102, 140403 (2009)
[2] V.G. Veselago, Sov. Phys. Usp. 10, 509 (1968)
[3] D.R. Smith, N. Kroll, Phys. Rev. Lett. 85, 2933 (2000)
[4] R. Mathevet et al., Phys. Rev. A 61, 033604 (2000)
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