Virginia TechNayfeh, Munir H.Nayfeh, Ali H.2014-04-252014-04-251977-03-01Nayfeh, M. H.; Nayfeh, A. H., "adiabatic following in two-photon transition," Phys. Rev. A 15, 1169 (1977); DOI: http://dx.doi.org/10.1103/PhysRevA.15.11691050-2947http://hdl.handle.net/10919/47703The coherent interaction of two smoothly varying, near-resonant, two-photon pulses with a three-level system can be described by "two-photon damped Bloch equations" which are analogous to those for a one-photon transition in a two-level system except for the presence of a two-photon coupling and a frequency shift. These equations are solved for the cases γ1, γ2≪Ω, γ1=γ2, and γ2k2ε4Ω2, γ1≪Ω, where γ1 and γ2 are the atomic energy and phase relaxation widths, respectively, and Ω is the Rabi frequency. The leading contribution to the refractive index is intensity dependent, caused by the level shifts inherent in multiphoton processes; it includes a relaxation dependent part which is important at times shorter than γ−11. The second-order contributions depend on the square of the intensity and the time-integrated square of the intensity. The latter contribution, which is relaxation dependent, causes line asymmetry at the long-wavelength wing; it consists of a term proportional to γ2−γ1 and only important at early times and a term proportional to 2γ2−γ1.application/pdfen-USIn CopyrightArticle - Refereedhttp://journals.aps.org/pra/abstract/10.1103/PhysRevA.15.1169https://doi.org/10.1103/PhysRevA.15.1169