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Physical Review A

Local-field effects in a dense ensemble of resonant atoms: Model of a generalized two-level system

Anatoly A. Afanas'ev, Andrey G. Cherstvy, R. A. Vlasov, Vasily M. Volkov

Published Aug 1, 1999• 9 citations
Publisher

Abstract

The local-field effects are considered which are feasible in a dense ensemble of resonant atoms modeled by multilevel quantum systems. Our approach is based on the generalized two-level system [V.S. Butylkin, A.E. Kaplan, and Yu.G. Khronopulo, Zh. \'Eksp. Teor. Fiz. 59, 921 (1970)]. Making use of this model, we take account of the nonresonant polarization and Stark shift of the absorption line due to the difference in linear polarizabilities of atoms in ground and excited states. With near dipole-dipole interaction and quadratic Stark effect included simultaneously, new features of the hysteresis behavior of the population difference as a function of the external-field intensity are predicted.

DOI
10.1103/physreva.60.1523

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The local-field effects are considered which are feasible in a dense ensemble of resonant atoms modeled by multilevel quantum systems. Our approach is based on the generalized two-level system [V.S. Butylkin, A.E. Kaplan, and Yu.G. Khronopulo, Zh. 'Eksp. Teor. Fiz. 59, 921 (1970)]. Making use of this model, we take account of the nonresonant polarization and Stark shift of the absorption line due to the difference in linear polarizabilities of atoms in ground and excited states. With near dipole-dipole interaction and quadratic Stark effect included simultaneously, new features of the hysteresis behavior of the population difference as a function of the external-field intensity are predicted.
Transient processes are analyzed based on modified Bloch equations describing the interaction of optical radiation with dense resonant media with allowance for dipole-dipole interaction between atoms (the local-field effect). An analytical solution to the equation for the population difference of resonant atomic levels, taking into account the up-conversion processes, is obtained for a rectangular pulse in the quasi-stationary approximation. Computer simulation is performed for the kinetics of the population difference of resonant atomic levels in the field of a long sine-shaped pulse. It is shown that the time dynamics of the population difference of resonant atomic levels manifests characteristic features inherent in the intrinsic optical bistability effect under adiabatically slow variation of the acting field.
Transient processes are analyzed based on modified Bloch equations describing the interaction of optical radiation with dense resonant media with allowance for dipole-dipole interaction between atoms (the local-field effect). An analytical solution to the equation for the population difference of resonant atomic levels, taking into account the up-conversion processes, is obtained for a rectangular pulse in the quasi-stationary approximation. Computer simulation is performed for the kinetics of the population difference of resonant atomic levels in the field of a long sine-shaped pulse. It is shown that the time dynamics of the population difference of resonant atomic levels manifests characteristic features inherent in the intrinsic optical bistability effect under an adiabatically slow variation of the acting field.
We investigate the effect of a linear host medium on the dynamics of a dense collection of resonant atoms. We find that near dipole-dipole interaction is enhanced by the presence of the host dielectric, resulting in a lower threshold density and a greater hysteresis area for intrinsic optical bistability. Cooperative decay terms appear that represent the interaction of near dipoles mediated by the absorptive component of the dielectric function of the host medium. These terms are part of the local response and correspond to local cooperative decay effects. \textcopyright{} 1996 The American Physical Society.
The numerical simulation of multiple scattering in dense ensembles is the mostly adopted solution to predict their complex optical response. While the scalar- and vectorial-light-mediated interactions are accurately taken into account, the computational complexity still limits current simulations to the low saturation regime and ignores the internal structure of atoms. Here, we propose to go beyond these restrictions, at constant computational cost, by describing a multilevel system by an effective two-level system that best reproduces the coherent and total scattering properties in any saturation regime. The correspondence of our model is evaluated for different experimentally realistic conditions such as the modification of the driving field polarization, the presence of stray magnetic fields, or an incoherent resonant electromagnetic field background. The trust interval of the model is quantified for the D2{\mathrm{D}}_{2}D2​ line of 87Rb^{87}\mathrm{Rb}87Rb atoms, but it could be generalized to any closed transition of a multilevel quantum system.
The theory of interaction of intense bichromatic field of laser radiation with multilevel atomic system in the external magnetic field is considered. The magnitudes of interaction are much larger than the width of atomic levels. The vector-potential of radiation field consisting of two monochromatic components with the frequencies resonant to adjacent transitions is taken in electric dipole approximation. The eigenvalues and eigenstates of the Hamiltonian, including spin-orbit interaction and interactions with laser radiation and external magnetic fields, are found without perturbation theory using resonant approximation. When the effects of resonantly excited radiation are considered the Hamiltonian of interaction with the weak field of scattered radiation is included also. Its eigenfunctions are found with the help of perturbation theory. We consider tow types of effects: polarization effects and effects of resonantly excited radiation. As the atomic system is multilevel we use the numerical methods. The influence of the magnetic field on coherent population trapping effect for multilevel systems is considered. Some of our theoretical results coincide with known experimental ones.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations