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Optics and Spectroscopy

Suppression of coherent population trapping upon spontaneous decay of an excited state

V. M. Datsyuk, Boris G. Matisov, Igor M. Sokolov

Published Feb 1, 2005• 0 citations
Publisher

Abstract

The interaction of a model three-level Λ system with electromagnetic radiation is considered under the conditions where a coherence (an off-diagonal matrix element) between lower sublevels arises upon spontaneous decay of an excited state. The cases of bichromatic and incoherent broadband fields are analyzed. It is shown that the occurrence of coherence may significantly change the character of evolution of the system under study with time. These changes are most pronounced for broadband fields. Some features of this phenomenon are considered for multilevel atomic systems.

DOI
10.1134/1.1870052

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The interaction of a model three-level Λ system with electromagnetic radiation is considered under the conditions where a coherence (an off-diagonal matrix element) between lower sublevels arises upon spontaneous decay of an excited state. The cases of bichromatic and incoherent broadband fields are analyzed. It is shown that the occurrence of coherence may significantly change the character of evolution of the system under study with time. These changes are most pronounced for broadband fields. Some features of this phenomenon are considered for multilevel atomic systems.
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.
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.
The work presented considers a new coherent phenomenon, i.e. the influence of the phases of electromagnetic fields interacting with a multilevel system on the character of excitation of this system. On the basis of analysing the equation for an N-level quantum system density matrix, it was established that in multilevel systems containing a closed contour of transitions, resonantly interacting with the field, stationary populations always depend on the total interaction contour phase Phi . For the simplest multilevel systems, i.e. three-level, the authors have obtained analytical expressions, connecting populations with the relative field phase in such systems. Thus, for a Lambda system, interacting with three resonant electromagnetic fields, it is discovered that, depending on the total phase value of the transition contour, both destruction and successive restoration of a coherent trapping state can take place. The work provides qualitative explanations of phase effects and suggests some possibilities for their application.
Near-degenerate lower levels in a $\ensuremath{\Lambda}$ system have an additional coherence term due to interaction with the vacuum of the radiation field. We report the effects of this spontaneously generated coherence on the formation of a trapped state in the presence of two coherent fields of arbitrary intensity. We show that such coherence preserves both electromagnetically induced transparency and coherent population trapping (CPT) phenomena. However, it changes the time scales associated with the formation of the CPT state, and brings about quantitative changes in the line profiles. We present a clear analytical explanation for our numerical results. We also report the dependence of line shapes on the relative phase between the two applied fields.
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.
We study the steady state in three-level lambda (\ensuremath{\Lambda}) and ladder systems. It is well known that in a \ensuremath{\Lambda} system this steady state is the coherent population trapping state, independent of the presence of spontaneous emission. In contrast, the steady state in a ladder system is in general not stable against radiative decay and exhibits a minimum in the population of the ground state. We show that incoherent population pumping destroys the stability of the coherent population trapping state in the \ensuremath{\Lambda} system and suppresses a previously discovered sharp dip in the steady-state response. In the ladder system the observed minimum disappears in the presence of an incoherent pump on the upper transition.