Dynamic Stark Splitting of Multiphoton Absorption Resonances

Abstract

When a discrete state is coupled to a set of continuum states by interaction with laser radiation, what is the distribution of energies produced? Perturbation theory gives for the rate of N-quantum absorption:$${R_N} = {\sum\limits_f {\left| {\sum\limits_{{\ell _1}{\ell _2}...{\ell _{n - 1}}} {\frac{{\left\langle {f\left| V \right|{\ell _1}} \right\rangle \left\langle {{\ell _1}\left| V \right|{\ell _1}} \right\rangle ...\left\langle {{\ell _{N - 1}}\left| V \right|S} \right\rangle }}{{\left( {{\omega _s} - {\omega _{{\ell _1}}}} \right)\left( {{\omega _s} - {\omega _{{\ell _1}}}} \right)...\left( {{\omega _s} - {\omega _{{\ell _{N - 1}}}}} \right)}}} } \right|} ^2}x\delta \left( {{\omega _s} - {\omega _f}} \right)$$ (1)Where the interaction V couples the initial state s through the intermediate states ℓ to a set of final states continuum. As long as the concept of a time-independent rate is applicable, sautration effects in the form of induced widths and Stark shifts only modify the energies ω s, ωℓ: the energy-conserving delta-function remains to indicate that only a very narrow range of final state energies are admissible. In reality we expect that a range of energies would be produced whose width (and possibly centre) would be intensity dependent. We will examine how non-perturbative approaches to this problem predict power broadening and (for multiphoton absorption) an AC Stark splitting of the continuum states produced by the laser excitation.