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Laser Physics

Dark and bright states of the coherently excited three-level atom

R. N. Shakhmuratov, J. Odeurs, Romain Coussement, A. Szabó

Published Jan 1, 2004• 3 citations
OpenAlex

Abstract

The dynamical evolution of the three-level atom under the influence of a bichromatic excitation is studied in the basis of the dark and bright states.With the help of these states, the analysis can be reduced to the consideration of a two-level system interacting with one effective field.Then, a simple Bloch-vector model is applied to describe the evolution of the initially complicated system.Special attention is paid to the low frequency coherence excitation, nonadiabatic population transfer, and population trapping.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 20, 2000•0 citations
The dynamical evolution of the three-level atom under the influence of a bichromatic excitation is studied in the basis of the dark and bright states.With the help of these states, the analysis can be reduced to the consideration of a two-level system interacting with one effective field.Then, a simple Bloch-vector model is applied to describe the evolution of the initially complicated system.Special attention is paid to the low frequency coherence excitation, nonadiabatic population transfer, and population trapping.
The interaction between a three-level atom and a polychromatic field with an equidistant spectrum (Λ-scheme of the atom--field interaction) has been studied theoretically. It is shown that the interaction of an atom with such a field can be reduced to its interaction with a bichromatic field with additional light shifts of transition frequencies and an additional coupling of the lower atomic levels, which is proportional to the field intensity. Owing to this coupling, the idea of the coherent population trapping can be considered only as an approximation, because the dark state is not an eigenstate of the effective Hamiltonian in the general case of arbitrary dipole moments. The analyzed model gives a simple theoretical interpretation for the formation of the atomic state, which is close to the coherent population trapping, in the radiation field of a femtosecond laser.
Mathematical modeling of the population dynamics is performed for states of a three-level system (atom) with a V-type configuration transforming a light pulse. It is assumed that the excited eigenstates of the atom are degenerate and coupled by coherent interaction, one of the states being radiating (radiative), while the other state is nonradiating (“dark”). The population dynamics of atomic states is described on the basis of numerical solutions of equations for the matrix elements of the density operator. The dependence of the efficiency of population of the atomic dark state from the values of the parameters of an irradiation pulse and from the ratio of the period of population oscillations of excited atomic states (caused by their coherent interaction) to the lifetime of the atomic radiating state is determined. Typical examples of the time dependence of the population of states of the atom considered are presented for the cases of irradiation by a short (as compared to the lifetime of the radiating state) sinusoidal light pulse and by a long rectangular light pulse with the resonance carrier frequency.
The interaction of a pair of copropagating pulses with three-level \ensuremath{\Lambda}-type atoms is discussed in terms of time-dependent coupled and decoupled superpositions \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}〉 of the lower levels. Due to the explicit time dependence of these states there is a nonadiabatic coupling between the ``bright'' state \ensuremath{\Vert}+〉 and the ``dark'' state \ensuremath{\Vert}-〉 in addition to the strong coupling between \ensuremath{\Vert}+〉 and the upper level \ensuremath{\Vert}a〉 . We show that under quasiadiabatic conditions and in the presence of decay from the upper level this coupling can be treated perturbatively and the Maxwell-Bloch equations can be solved analytically. With the help of such a perturbation approach, coherent population transfer and formstable laser pulse propagation are studied. \textcopyright{} 1996 The American Physical Society.
We show that an arbitrary system described by two dipole moments exhibits coherent superpositions of internal states that can be completely decoupled from the dissipative interactions (responsible for decoherence) and an external driving laser field. These superpositions, known as dark or trapping states, can be completely stable or can coherently interact with the remaining states. We examine the master equation describing the dissipative evolution of the system and identify conditions for population trapping and also classify processes that can transfer the population to these undriven and nondecaying states. It is shown that coherent transfers are possible only if the two systems are nonidentical, that is the transitions have different frequencies and/or decay rates. In particular, we find that the trapping conditions can involve both coherent and dissipative interactions, and depending on the energy level structure of the system, the population can be trapped in a linear superposition of two or more bare states, a dressed state corresponding to an eigenstate of the system plus external fields or, in some cases, in one of the excited states of the system. A comprehensive analysis is presented of the different processes that are responsible for population trapping, and we illustrate these ideas with three examples of two coupled systems: single V- and $\ensuremath{\Lambda}$-type three-level atoms and two nonidentical two-level atoms, which are known to exhibit dark states. We show that the effect of population trapping does not necessarily require decoupling of the antisymmetric superposition from the dissipative interactions. We also find that the vacuum-induced coherent coupling between the systems could be easily observed in $\ensuremath{\Lambda}$-type atoms. Our analysis of the population trapping in two nonidentical atoms shows that the atoms can be driven into a maximally entangled state which is completely decoupled from the dissipative interaction.
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.