Dynamic Stark Splitting of Multiphoton Absorption Resonances

  • P. L. Knight
Part of the Springer Series in Chemical Physics book series (CHEMICAL, volume 6)


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:
$${R_N} = {\sum\limits_f {\left| {\sum\limits_{{\ell _1}{\ell _2}...{\ell _{n - 1}}} {\frac{{\left\langle {f\left| V \right|{\ell _1}} \right\rangle \left\langle {{\ell _1}\left| V \right|{\ell _1}} \right\rangle ...\left\langle {{\ell _{N - 1}}\left| V \right|S} \right\rangle }}{{\left( {{\omega _s} - {\omega _{{\ell _1}}}} \right)\left( {{\omega _s} - {\omega _{{\ell _1}}}} \right)...\left( {{\omega _s} - {\omega _{{\ell _{N - 1}}}}} \right)}}} } \right|} ^2}x\delta \left( {{\omega _s} - {\omega _f}} \right)$$
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, ω: 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.


Rabi Frequency Stark Shift Rabi Oscillation Multiphoton Absorption State Transition Frequency 
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  1. [1]
    P. L. Knight, Opt. Comm, 22, 173 (1977); J Phys. B (1978) in press, and Refs. therein.ADSCrossRefGoogle Scholar
  2. [2]
    M. V. Fedorov and A. E. Kazakov, Opt, Comm. 22, 421 (1977) and Refs. therein.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • P. L. Knight
    • 1
  1. 1.Physics Department, Royal Holloway CollegeUniversity of LondonEgham, SurreyGreat Britain

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