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Physical Review A

Dynamics of population of a four-level atom due to one- and three-photon processes

M. P. Sharma, José Antonio Roversi

Published Jun 1, 1984• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.29.3264

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 10, 1996•0 citations
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.
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
We have calculated the excitation spectra of a single electron in the excited state of a four-level atom interacting with three laser fields at low intensities, where two of them are on two-photon resonance with the three levels of the atom, while the third laser is a weak one operating between the fourth and excited level of the atom. It is shown that light is switched off at certain frequency due to the coherent population trapping while light is turned on at another frequency, where stimulated emission occurs leading to light amplification without population inversion.
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 spectroscopic properties of a single tightly trapped atom are studied, when the electronic levels are coupled by three laser fields in an NNN-shaped configuration of levels, whereby a $\ensuremath{\Lambda}$-type level system is weakly coupled to a metastable state. We show that depending on the laser frequencies the response can be tuned from coherent population trapping at two-photon resonance to a behavior at three photon resonance, where the metastable state can get almost unit occupation in a wide range of parameters. For certain parameter regimes the system switches spontaneously between dissipative and coherent dynamics over long time scales.