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Physical Review A

Raman Processes in Intense Fields

Man Mohan, R. K. Thareja

Published Jan 1, 1973• 12 citations
Publisher

Abstract

Transition amplitudes corresponding to bound-bound multiphoton transitions with the emission or absorption of one and two Raman photons in the hydrogen atom have been evaluated following a recent method of Reiss. Results show that the transition probability varies smoothly for low values of $N$, where $N$ is the number of intense photons absorbed or emitted during the transition. For larger values of $N$ the amplitude, however, has oscillatory behavior. A particular feature of the present method of calculation is that we find the "reduced" transition amplitude for induced emission of two Raman photons is enhanced compared with single-Raman-photon emission. Another distinctive feature is the appearance of many more extrema in the transition amplitude for higher transitions for multiphoton processes at high intensity.

DOI
10.1103/physreva.7.34

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Physical Review A•Nov 1, 1971•139 citations
Transition amplitudes corresponding to bound-bound multiphoton transitions with the emission or absorption of one and two Raman photons in the hydrogen atom have been evaluated following a recent method of Reiss. Results show that the transition probability varies smoothly for low values of NNN, where NNN is the number of intense photons absorbed or emitted during the transition. For larger values of NNN the amplitude, however, has oscillatory behavior. A particular feature of the present method of calculation is that we find the "reduced" transition amplitude for induced emission of two Raman photons is enhanced compared with single-Raman-photon emission. Another distinctive feature is the appearance of many more extrema in the transition amplitude for higher transitions for multiphoton processes at high intensity.
The reduced transition amplitude for the multiphoton excitation with the emission of one Raman photon of the hydrogen molecule due to an intense EM field from the ground state 1s sigma 1 Sigma g + to the excited state B2p sigma 1 Sigma u + has been calculated using a method due to Reiss (1970). The intensity dependence of the transition probability has been numerically investigated. A major feature of the curve is the oscillatory behaviour for larger values of N where N is the number of photons absorbed in the process.
Using the hydrogenic model for the helium atom, the amplitude of transition from states He(ls) to He(ls, nl) by absorption of N photons of an intense field together with the emission of one Raman photon is evaluated. From the general expression for the transition amplitude, the particular case of transition from He(ls) to He(ls, 2p) is considered. The 'reduced' transition amplitude is plotted against the number of photons N involved and against the intensity parameter y st;parately. It is found that the s wave contributes maximaly to the transition amplitude. An important feature of the calculations is the appearance of nonlinear behaviour at high intensity. The dominance of higher order processes over lower ones at high intensity is also found.
Results valid for arbitrarily high intensity of electromagnetic field are presented for induced emission from an excited state of an atom. Comparison with perturbation theory shows that perturbative calculations fail quantitatively and qualitatively at lower intensity than had been expected. Distinctive intense-field features are discussed such as vanishing of the transition probability for certain intensities and photon multiplicities, and appearance of two extrema of the transition amplitude for multiphoton processes at very high intensities.
Two-Raman-photon emission in hydrogen atoms in the presence of an intense electromagnetic field has been calculated utilizing the method of Dalgarno and Lewis. We give a general formulation for ($n\ensuremath{-}2$)-photon absorption and two-photon emission and also give numerical results for two-photon emission in the $1s\ensuremath{-}2p$ transition in hydrogen atoms. It is found that the emission of two spontaneous Raman photons could become important when the energy of the intense photon approaches the ionization energy. Finally, in the spectrum of the emitted Raman photon, faint lines are expected corresponding to the resonant peaks in the cross section.
Within the framework of time-dependent perturbation theory, general expressions are derived for the cross section of multiphoton processes induced by radiation acting on a hydrogen atom. Bound-bound transitions involving emission of a single quantum and bound-free transitions are calculated for a wide range of photon energies. In the case of resonance, the transition probability is also discussed. The procedure used to evaluate the sums over intermediate states is described. The numerical computation allows one to compare the results obtained for various competing processes.