The Bloch equation for multiphoton absorption. I. Derivation

Kenneth G. Kay

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23 Scopus citations


A Bloch equation describing infrared multiphoton absorption in an isolated polyatomic molecule is derived from first principles. The molecule is divided into a "system" mode which interacts directly with the laser field and a "bath" consisting of the remaining modes which interact with each other and the system mode via intramolecular vibrational coupling. In addition to describing the evolution of the system, the derived equation keeps track of changes in the bath state and the resulting changes in the bath-system interaction which occur as the bath gains energy. Unlike the master (or rate) equation for optical pumping, the Bloch equation is valid for arbitrary ratios W/Ω of the intramolecular relaxation rate W/ℏ to the Rabi frequency of the system mode Ω/ℏ. The equation derived differs from certain Bloch equations previously proposed on phenomenological grounds by the appearance of off-diagonal coupling terms. These terms may significantly reduce the vibrational dephasing rate and thus affect net pumping rates and optical line shapes for vibrationally excited molecules.

Original languageEnglish
Pages (from-to)1690-1711
Number of pages22
JournalJournal of Chemical Physics
Issue number4
StatePublished - 1981
Externally publishedYes


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