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arXiv:1305.1387 · Physical Review A

Spatial distribution of optically induced atomic excitation in a dense and cold atomic ensemble

Ya. A. Fofanov, A. S. Kuraptsev, Igor M. Sokolov, Mark D. Havey

Published Jun 24, 2013• 43 citations
arXivHTMLPDF

Abstract

On the basis of our general theoretical results developed previously [I. M. Sokolov et al., J. Exp. Theor. Phys. 112, 246 (2011)], we calculate the spatial distribution of atoms excited in a dense and cold atomic cloud by weak monochromatic light. We also study the atomic distribution over different Zeeman sublevels of the excited state in different parts of the cloud. The dependence of this distribution of atomic excitation on the density of the atomic ensemble and the frequency of external emission is investigated. We show that in the boundary regions of the cloud, the orientation and alignment of atomic angular momentum takes place. Analysis of the spatial distribution of atomic excitation shows no noticeable signs of light localization effects, even in those parameter regimes where the Ioffe-Regel criterium of strong localization is satisfied. However, comparative calculations performed in the framework of the scalar approximation to the dipole-dipole interaction reveal explicit manifestation of strong localization under some conditions.

DOI
10.1103/physreva.87.063839

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On the basis of our general theoretical results developed previously [I. M. Sokolov et al., J. Exp. Theor. Phys. 112, 246 (2011)], we calculate the spatial distribution of atoms excited in a dense and cold atomic cloud by weak monochromatic light. We also study the atomic distribution over different Zeeman sublevels of the excited state in different parts of the cloud. The dependence of this distribution of atomic excitation on the density of the atomic ensemble and the frequency of external emission is investigated. We show that in the boundary regions of the cloud, the orientation and alignment of atomic angular momentum takes place. Analysis of the spatial distribution of atomic excitation shows no noticeable signs of light localization effects, even in those parameter regimes where the Ioffe-Regel criterium of strong localization is satisfied. However, comparative calculations performed in the framework of the scalar approximation to the dipole-dipole interaction reveal explicit manifestation of strong localization under some conditions.
Based on the already-developed general theory (I.M. Sokolov, D.V. Kupriyanov, and M.D. Havey, JETP 112 (2), 246 (2011)), we have studied the spatial distribution of excited atoms and of the atomic polarization that a weak monochromatic field creates in a dense ultracold atomic medium. We show that, in the case of a homogeneous random spatial distribution of atoms, the amplitude of atomic polarization averaged over spatial configurations decreases outside boundary regions according to an exponential law, while its phase linearly increases. Based on this, we have numerically determined the extinction coefficient and the light wavelength in the medium, as well as its dielectric permittivity. The dispersion of the permittivity at different concentrations has been studied. We show that, for dense clouds, the real part of the dielectric permittivity acquires negative values in a certain frequency range. Based on the calculation of the spatial distribution of excited atoms, we have analyzed the character of the transfer and trapping of quasi-resonant radiation in atomic clouds of differing density.
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.
On the basis of general theoretical results developed previously in [JETP 112, 246 (2011)], we analyze the atomic polarization created by weak monochromatic light in an optically thick, dense, and cold atomic ensemble. We show that the amplitude of the polarization averaged over a uniform random atomic distribution decreases exponentially beyond the boundary regions. The phase of this polarization increases linearly with increasing penetration into the medium. On these grounds, we determine numerically the wavelength of the light in the dense atomic medium, its extinction coefficient, and the complex refractive index and dielectric constant of the medium. The dispersion of the permittivity is investigated for different atomic densities. It is shown that, for dense clouds, the real part of the permittivity is negative in some spectral domains.
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.
Light propagation in disordered media is a fundamental and important problem in optics and photonics. In particular, engineering light-matter interaction in disordered cold atomic ensembles is one of the central topics in modern quantum and atomic optics. The collective response of dense atomic gases under light excitation, which crucially depends on the spatial distribution of atoms and the geometry of the ensemble, has important impacts on quantum technologies like quantum sensors, atomic clocks and quantum information storage. Here we analyze near-resonant light transmission in two-dimensional dense ultracold atomic ensembles with short-range positional correlations. Based on the coupled-dipole simulations under different atom number densities and correlation lengths, we show that the collective effects are strongly influenced by those positional correlations, manifested as significant shifts and broadening or narrowing of transmission resonance lines. We also analyze the eigenstate distribution of different atomic ensembles. This work may provide profound implications on collective and cooperative effects in cold atomic ensembles as well as the study of mesoscopic physics concerning light transport in strongly scattering disorder media.