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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Coherent population trapping in high-intensity electromagnetic fields

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

Published May 10, 1996• 0 citations
Publisher

Abstract

We consider a case of interaction of a three-level atom with high-intensity electromagnetic field when the Rabi frequencies are greater than the atomic transition frequencies. We show that coherent population trapping can exist under the certain phase conditions in this case of the rotating wave approximation violation.
DOI
10.1117/12.239486

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We consider the case of interaction of a three-level atom with a high intensity pulse electromagnetic field. Rabi frequencies are assumed to be of the order of the transition frequency or greater. We demonstrate that coherent population trapping exists even in such a case when the usual rotating-wave approximation is no longer valid. However, a certain condition on the phases of electromagnetic wave components has to be satisfied in order to make coherent population trapping possible. This condition is specific for the strong field case in contrast to the case where the rotating-wave approximation is valid. Also we point out some elements for which a model of an atom with a finite number of levels may still be valid while the rotating-wave approximation breaks down.
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 Schr\"odinger equation in the rotating-wave approximation has been solved nonperturbatively to study the temporal behavior of the occupation probabilities of different levels of a four-level atom interacting with four arbitrarily intense laser fields, such that the frequency of one of them equals the sum of the other three. The three-photon-excitation population dynamics, which is already complex, is strongly modified by one-photon excitation and detunings. Under certain conditions the three-photon excitation traps the population in the state initially populated; the population starts flowing into other states when one-photon excitation is also operative.
We consider the deflection of a three-level atom of Λ-type interacting with a light field of two coherent laser beams. We employ the dressed state formalism, which is suitable for large Rabi frequencies and/or large detunings. A full study of the interaction and relaxation processes is performed. We show that a beam of atoms is split into three beams once it crosses the light field. This is a three-state version of the well-known optical Stern–Gerlach effect, which has been theoretically studied and experimentally demonstrated for two-level atoms. Under coherent population trapping conditions, the splitting of the beam becomes twofold. This gives us, in principle, the opportunity of a mechanical demonstration of the coherent population trapping effect.
The poulation transfer and coherent population trapping of a three-level atom interacting with few cycle pulse train are studied.The density matrix equation in interation picture is numerical solved without rotating wave approximation.The research indicates that if a three-level atom interacts with a few cycle pulse train,the population transfer of level and the coherence of ground state will be gradual accumulated.When the repetition frequency of pulses is integer points of the ground-state splitting,the three atom interacts with pulse train can be seen as the atom interacts with two tenoning frequency of the frequency comb.So the system will be in the dark state and reach coherent population trapping.If the parameters of few-cycle pulse are appropriately selected,the coherence of three-level system will evolute into stable value in 0.5 nanosecond.The coherent population trapping in the three-level is generated.Comparing with the pulse that the pulse width is 100 femtoseconds,the build-up time of coherent population trapping by few cycle pulse train is shortened two orders of magnitude.When the ground-state splitting is wided enough and the carrier frequency of pulse is ω=(ω1+ω2)/2,where,are the atomic transition frequency,the doppler frequency shift that is aroused by the movement of atom won't destroy the coherent population trapping of atom.The reason is that all tenoning frequencies of the frequency comb have the same frequency shift,so the condition of coherent population trapping is still meeted.
In a previous paper, we have already considered the system composed by a two level atom interacting with a coherent external electromagnetic field. No application whatsoever has been made of the rotating wave approximation. Being specially interested in the problem of higher harmonic generations for the case of very intense laser fields, we have developed in this letter a much more efficient way to obtain these solutions as well as to carry out some calculations in a range in which the parameters take extreme values. Also the formalism allows us now to provide analytic expressions in the WKB regime for the electric dipole moment and the population inversion. The spectrum can be decomposed in periodic and non-periodic contributions. Only the latter depends upon the Floquet exponent and can be responsible of the main complexities of the observed Rabi revivals and the hyper-Raman shift.