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Physical Review A

Effects of Debye plasmas on two-photon transitions in lithium atoms

S. Paul, Y. K. Ho

Published Oct 27, 2008• 40 citations
Publisher

Abstract

We have studied two-photon transition rates of atomic lithium within model potential by using the pseudostate summation approach. Transition amplitudes and absorption coefficients have been computed for $2s\text{\ensuremath{-}}3s$, $2s\text{\ensuremath{-}}4s$, and $2s\text{\ensuremath{-}}3d$ transitions with various Debye lengths. In the case of $2s\text{\ensuremath{-}}3s$ transition, two-photon transparency vanishes for smaller Debye length. Reverse incident occurred for $2s\text{\ensuremath{-}}3d$ transition. Here, we have found a two-photon transparency for lower values of Debye length. These two situations occur due to energy level shifting in the presence of a plasma environment. A detailed description of resonance enhancement frequency and transition amplitude has been analyzed.

DOI
10.1103/physreva.78.042711

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We have studied two-photon transition rates of atomic lithium within model potential by using the pseudostate summation approach. Transition amplitudes and absorption coefficients have been computed for 2s\ensuremath-3s2s\text{\ensuremath{-}}3s2s\ensuremath-3s, 2s\ensuremath-4s2s\text{\ensuremath{-}}4s2s\ensuremath-4s, and 2s\ensuremath-3d2s\text{\ensuremath{-}}3d2s\ensuremath-3d transitions with various Debye lengths. In the case of 2s\ensuremath-3s2s\text{\ensuremath{-}}3s2s\ensuremath-3s transition, two-photon transparency vanishes for smaller Debye length. Reverse incident occurred for 2s\ensuremath-3d2s\text{\ensuremath{-}}3d2s\ensuremath-3d transition. Here, we have found a two-photon transparency for lower values of Debye length. These two situations occur due to energy level shifting in the presence of a plasma environment. A detailed description of resonance enhancement frequency and transition amplitude has been analyzed.
The rate of absorption of entangled photon pairs is linear in the photon-flux density. We demonstrate that the two-photon absorption cross section is a nonmonotonic function of the entanglement time; it vanishes for certain energy-level configurations and values of the entanglement time. This entanglement-induced two-photon transparency arises from the coherent summation of transition-amplitude contributions over the finite entanglement time. As an example, the entangled two-photon cross section for the $1S\ensuremath{-}2S$ electronic transition in atomic hydrogen is obtained.
The propagation of two pulses in a three-level absorber is treated by using Maxwell's equations and an effective "two-photon Bloch equations" which are analogous to the one-photon Bloch equations, except for two-photon coupling and frequency shifts. I derive relaxation-dependent shifts in the equilibrium $2n\ensuremath{\pi}$ Lorentzian pulses. Part of these shifts depends on weighted time integrals of harmonics of the area and hence remove the propagation degeneracy of pulses having equal areas but different shapes. Absorption of small-area pulses is studied as a function of absorption length, input energies, and relaxation, and it is found that a local enhancement in the transmission occurs as a function of the absorption length.
The two-photon transition rate for hydrogen is evaluated with the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}}$ and the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ interactions including the continuum. We find that the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}}$ interaction approaches the final result with a small number of intermediate states and consequently is the one to be used in any approximate calculation. Numerical values of the two-photon absorption coefficient as a function of frequency are given and the resonance enhancement is exhibited.