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Physical Review A

Electro-optical effects in dense and cold atomic gases

Igor M. Sokolov

Published Jul 17, 2018• 8 citations
Publisher

Abstract

On the basis of the general theoretical approach developed previously by Fofanov et al. [Ya. A. Fofanov et al., Phys. Rev. A 84, 053811 (2011)], we analyze the atomic polarization created by weak monochromatic light in an optically thick, dense, and cold atomic ensemble placed in an electrostatic field. On this basis, we determine complex refractive indexes and the permittivity tensor of the medium. We analyze the dispersion of the permittivity and its dependence on the strength of the field and on the density of the medium. We show that electro-optic effects in dilute and cold gases differ essentially from those in dense ones. In the latter case, electric field modifies the shape, amplitude, and typical linewidth of the atomic resonance. The electric field also modifies the collective Lamb shift. Observed peculiarities are explained as a result of the indirect influence of the field on optical properties of dense gases through modification of polyatomic collective effects caused by interatomic dipole-dipole interactions.

DOI
10.1103/physreva.98.013412

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On the basis of the general theoretical approach developed previously by Fofanov et al. [Ya. A. Fofanov et al., Phys. Rev. A 84, 053811 (2011)], we analyze the atomic polarization created by weak monochromatic light in an optically thick, dense, and cold atomic ensemble placed in an electrostatic field. On this basis, we determine complex refractive indexes and the permittivity tensor of the medium. We analyze the dispersion of the permittivity and its dependence on the strength of the field and on the density of the medium. We show that electro-optic effects in dilute and cold gases differ essentially from those in dense ones. In the latter case, electric field modifies the shape, amplitude, and typical linewidth of the atomic resonance. The electric field also modifies the collective Lamb shift. Observed peculiarities are explained as a result of the indirect influence of the field on optical properties of dense gases through modification of polyatomic collective effects caused by interatomic dipole-dipole interactions.
The permittivity tensor of dense and cold atomic ensembles exposed to an electrostatic field has been calculated in the microscopic quantum-mechanical approach. The anisotropic properties and dispersion of the systems under consideration have been analyzed. It has been shown that the electro-optical effects in dense ensembles are manifested in an essentially different manner than in diluted ones, where the resonant dipole–dipole interaction between atoms can be neglected. The discovered features have been explained by the influence of the electric field on the character of collective effects, which affect considerably the optical properties of the ensembles of interacting atoms.
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.
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.
We study light propagation through a slab of cold gas using both the standard electrodynamics of polarizable media and massive atom-by-atom simulations of the electrodynamics. The main finding is that the predictions from the two methods may differ qualitatively when the density of the atomic sample $\ensuremath{\rho}$ and the wave number of resonant light kkk satisfy $\ensuremath{\rho}{k}^{\ensuremath{-}3}\ensuremath{\gtrsim}1$. The reason is that the standard electrodynamics is a mean-field theory, whereas for sufficiently strong light-mediated dipole-dipole interactions the atomic sample becomes strongly correlated. The deviations from mean-field theory appear to scale with the parameter $\ensuremath{\rho}{k}^{\ensuremath{-}3}$, and we demonstrate noticeable effects already at $\ensuremath{\rho}{k}^{\ensuremath{-}3}\ensuremath{\simeq}{10}^{\ensuremath{-}2}$. In dilute gases and in gases with an added inhomogeneous broadening the simulations show shifts of the resonance lines in qualitative agreement with the predicted Lorentz-Lorenz shift and ``cooperative Lamb shift,'' but the quantitative agreement is unsatisfactory. Our interpretation is that the microscopic basis for the local-field corrections in electrodynamics is not fully understood.
Light–matter interaction in cold atomic ensembles is one of the central topics in modern quantum and atomic optics with important applications in various quantum technologies. The collective response of dense atomic gases under light excitation depends crucially on the spatial distribution of atoms and the geometry of the ensemble. We analyze near-resonant light transmission in two-dimensional dense ultracold atomic ensembles with short-range positional correlations. Based on coupled-dipole simulations, we show that the collective effects, manifested as notable shifts of transmission resonance frequency and considerable modification of optical depths, are influenced strongly by positional correlations. Mean-field theories such as the Lorentz–Lorenz relation are not capable of describing such collective effects. We also investigate the statistical distribution of eigenstates and provide a connection between the transmission spectra and eigenstate distribution by utilizing the population weighted detuning and decay rate of all eigenstates. We further demonstrate the intricate interplay between dipole–dipole interactions and positional correlations by increasing the number densities of atoms.
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.