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Journal of Experimental and Theoretical Physics

Coherent population trapping in an ensemble of three-level atoms in the presence of cooperative relaxation

Boris G. Matisov, I. A. Grigorenko, I. E. Mazets

Published Sep 1, 1997• 0 citations
Publisher

Abstract

We derive equations that describe the dynamics of three-level atoms with a cascade system of levels interacting with two resonant coherent fields in conditions where cooperative relaxation dominates over incoherent spontaneous emission. We calculate the temporal dynamics of the values of the atomic populations. The possibility of coherent population trapping in the presence of the cooperative decay is established. Finally, we calculate the averaged population of the intermediate level as a function of detuning for different values of the coupling constant.

DOI
10.1134/1.558332

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We derive equations that describe the dynamics of three-level atoms with a cascade system of levels interacting with two resonant coherent fields in conditions where cooperative relaxation dominates over incoherent spontaneous emission. We calculate the temporal dynamics of the values of the atomic populations. The possibility of coherent population trapping in the presence of the cooperative decay is established. Finally, we calculate the averaged population of the intermediate level as a function of detuning for different values of the coupling constant.
Equations are derived which describe the dynamics of three-level atoms with a Λ level scheme, interacting with two coherent resonance fields under conditions such that cooperative relaxation predominates over incoherent spontaneous emission. A numerical calculation of the temporal dynamics of the values of the atomic populations is performed. It is shown that coherent population trapping in the presence of cooperative decay is possible. The quantities characterizing this phenomenon are calculated—the width of the black line and the transition time to coherent trapping in this scheme.
We derive the equations describing the dynamics of an ensemble of atoms with (Lambda) - scheme of levels driven by two coherent resonant fields in a case when cooperative relaxation prevails over usual incoherent spontaneous emission. We investigate numerically temporal dynamics of mean values of the collective atomic operators. When the two-photon resonance condition is fulfilled then all atoms tend to be trapped in a coherent dark state, so coherent population trapping arises in a case of cooperative decay. Most important values characterizing this phenomenon such as the width of the black line and the time of initial transient stage of evolution are evaluated.
The interaction between electromagnetic radiation and two three-level atoms is investigated. The atom-atom separation is assumed to be smaller than the corresponding mean resonance wavelength. The total radiance rate of the atomic system is calculated as a function of time. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some act as photon-trapping states. Instead of exponential decay, the oscillations appear in the time evolution of the radiation rate due to the correlation between atoms. The decay constants and coupling decay constants show strong effects on the emission rates. Completely differing from two identical double-level atoms, the cooperative effects always exist in the three-level atomic system except for the case in which the coupling decay constants ${\ensuremath{\gamma}}_{12}$ and ${\ensuremath{\gamma}}_{21}$ are zero.
Coherent population trapping effect is widely studied for simple three-level systems of different types ((Xi) 2, (Lambda) , V)1,2. For real atoms the situation is more complicated. Atomic levels are degenerated one and in the presence of external fields coupling of magnetic sublevels appears due to radiation, so magnetic fields leading to the systems of levels of the higher order. Our theory and method of calculation for interaction of multilevel atoms, with intense radiation fields in the presence of external magnetic fields have been applied for considering coherent population trapping effect for such systems. In the absence of magnetic field for considering sets of parameters, we can see the behavior of populations in function of time, detunings for both systems of coupled sublevels inherent to the coherent population trapping effect. In the presence of magnetic field, we can see novel features in the populations for the systems of coupled magnetic sublevels.
Coherent population trapping effect is widely studied for simple three-level systems of different types ((Xi) , (Lambda) , V). For real atoms situation is more complicated. Atomic levels are degenerated one and in the presence of external fields coupling of magnetic sublevels appears due to as radiation, so magnetic fields, leading to the systems of levels of the higher order. Our theory and model of calculation for interaction of multilevel atom with intense radiation field at the presence of external magnetic field have been applied for considering coherent population trapping effect for such systems.
The population dynamics of a four-level atom, with decay from the highest level, interacting with three arbitrarily intense laser fields is studied. In a previous paper [4], this four-level system was investigated with no decay included. For a specific set of input fields, it was found that substantial population could be transferred from the ground state to the highest excited state. In that study, the detunings required to obtain this maximum population transfer were not explained. In this present work, we have introduced a two-level atom model that explains this choice of detunings. They are such as to make the three fields resonant with the Stark-shifted