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Journal of Physics Conference Series

Light localization in cold and dense atomic ensemble

Igor M. Sokolov

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We report on results of theoretical analysis of possibilities of light strong (Anderson) localization in a cold atomic ensemble. We predict appearance of localization in dense atomic systems in strong magnetic field. We prove that in absence of the field the light localization is impossible.
DOI
10.1088/1742-6596/793/1/012026

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On the basis of the general theoretical results developed previously (Sokolov et al 2011 J. Exp. Theor. Phys. 112 246) we calculate the light transmission coefficient of a disordered dense ensemble of motionless atomic scatterers. We analyze dependence of this coefficient on thickness of the ensemble as well as on frequency of the light. This analysis shows no manifestation of light localization effects, even in those parameter regimes where the Ioffe–Regel criterion of strong localization is satisfied. An analogous calculation made in the framework of scalar approximation when the vector character of light is neglected demonstrates strong localization under some conditions.
We propose to control light trapping in a large ensemble of cold atoms by an external, static magnetic field. For an appropriate choice of frequency and polarization of the exciting pulse, the field is expected to speed up the fluorescence of a dilute atomic system. In a dense ensemble, the field does not affect the early-time superradiant signal but amplifies intensity oscillations at intermediate times and induces a very slow, nonexponential long-time decay. The slowing down of fluorescence is due to the excitation of spatially localized collective atomic states that appear only under a strong magnetic field and have exponentially long lifetimes. Our results therefore pave a way towards experimental observation of the disorder-induced localization of light in cold atomic systems.
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We explore the potential of a static electric field to induce Anderson localization of light in a large three-dimensional cloud of randomly distributed, immobile atoms with a nondegenerate ground state (total angular momentum Jg=0{J}_{g}=0Jg​=0) and a threefold-degenerate excited state (Je=1{J}_{e}=1Je​=1). We study both the spatial structure of quasimodes of the atomic cloud and the scaling of the Thouless number with the size of the cloud. Our results indicate that unlike the static magnetic field, the electric field does not induce Anderson localization of light by atoms. We explain this conclusion by the incomplete removal of degeneracy of the excited atomic state by the field and the relatively strong residual dipole-dipole coupling between atoms which is weaker than in the absence of external fields but stronger than in the presence of a static magnetic field. A joint analysis of these results together with our previous results concerning Anderson localization of scalar waves and light suggests the existence of a critical strength of dipole-dipole interactions that should not be surpassed for Anderson localization to be possible in three dimensions.
We establish a localization phase diagram for light in a random three-dimensional (3D) ensemble of motionless two-level atoms with a threefold degenerate upper level, in a strong static magnetic field. Localized modes appear in a narrow spectral band when the number density of atoms $\ensuremath{\rho}$ exceeds a critical value ${\ensuremath{\rho}}_{c}\ensuremath{\simeq}0.1{k}_{0}^{3}$, where k0{k}_{0}k0​ is the wave number of light in the free space. A critical exponent of the localization transition taking place upon varying the frequency of light at a constant $\ensuremath{\rho}>{\ensuremath{\rho}}_{c}$ is estimated to be $\ensuremath{\nu}=1.57\ifmmode\pm\else\textpm\fi{}0.07$. This classifies the transition as an Anderson localization transition of 3D orthogonal universality class.