Theory of attosecond delays in molecular photoionization.

We present a theoretical formalism for the calculation of attosecond delays in molecular photoionization. It is shown how delays relevant to one-photon-ionization, also known as Eisenbud-Wigner-Smith delays, can be obtained from the complex dipole matrix elements provided by molecular quantum scattering theory. These results are used to derive formulae for the delays measured by two-photon attosecond interferometry based on an attosecond pulse train and a dressing femtosecond infrared pulse. These effective delays are first expressed in the molecular frame where maximal information about the molecular photoionization dynamics is available. The effects of averaging over the emission direction of the electron and the molecular orientation are introduced analytically. We illustrate this general formalism for the case of two polyatomic molecules. NO serves as an example of a polar linear molecule characterized by complex photoionization dynamics resulting from the presence of molecular shape resonances. HO illustrates the case of a non-linear molecule with comparably simple photoionization dynamics resulting from a flat continuum. Our theory establishes the foundation for interpreting measurements of the photoionization dynamics of all molecules by attosecond metrology.