EGAS41 - Swansea University

41 st EGAS CP 91 Gdańsk 2009
Effective field theory for light transport in disorder atomic
medium
M.B. Smirnov 1 , M.A. Baranov 1,2
1 RRC Kurchatov Institute, Kurchatov sq. 1. 123182 Moscow, Russian Federation
2 Institut fur Theoretische Physik, Universitat Innsbruck, Austria
∗ Corresponding author: smirnov@imp.kiae.ru
The character of light transport in disorder atomic medium is determined by the multiply
elastic scattering of light. In a sample of randomly distributed scatters, the initial
direction of the wave is fully randomized by multiple scattering, and a diffusion picture
seems to be an appropriate description of light propagation in the case of small densities
of scatters. Despite successful predictions, this theory does not take into account interference
effects. In fact, wave interference affects the physics of light propagation and results
in so-called weak or strong localization regime [1-2]. A system of randomly distributed
atoms with an atomic transition frequency close to the light frequency provides necessary
conditions for experimental observation of the interference and non-linear phenomenon.
The photons can be transferred radiatively as well as non-raditiavely via the resonance
dipole-dipole interaction in such a medium. The last is equivalent to including the longitudinal
component of the electromagnetic field. Non-radiative transfer becomes more
important with increasing the density of atoms, when a typical energy of dipole-dipole
interactions is comparable with the excitation energy of atoms.
We have developed a field theory approach to light propagation in a gas of resonant
atoms, where both the atoms and the electromagnetic fields have been represented by
quantum fields throughout the analysis, and taken into account vector character of light.
The atomic number density n is assumed to be low or moderate (i.e. nλ 3 < 1) and the
atoms are treated as a (1 + 3)-level system, i.e. a resonant s − p transitions in atoms
are supposed to occur only. The dipole-dipole interaction between atoms is incorporated
into the approach non-petrubatively and the relativistic effects are allowed for. Starting
from the exact action included interatomic dynamics, atom-atom interaction and electric
field atom interaction; we have derived the Green function and its derivatives for the
dressed photon that describes both the inelastic processes like a spontaneous emission
of the atoms and elastic scattering photon in gas with density-density correlations via
resonant atom-field interaction. The applied approach is not restricted to the rotatingwave
approximation. We have shown that the energy associated with transition between
resonance states does not change for low atomic density where the coupling parameter
is (16πd 2 ρ/∆) is small. Influence of short-range and long-range correlations of the atom
densities on light propagation has been analyzed. Contrary to the case of short-range
atom density-density correlations, the long-range correlations result in anisotropic spatial
dispersion controlled by the direction of the wave vector. When the wave length exceeds
the typical scale for density-density correlations, the anisotropy in spatial dispersion disappears,
as it should be for the case.
References
[1] G. Labeyrie, D. Delande, R. Kaiser, C. Miniatura, cond-mat, 0603153 (2006)
[2] C.A. Muller, Th. Jonckheere, C. Miniatura, D. Delande, Phys. Rev. A 64, 053804
(2001)
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