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We theoretically investigate the role of complex dipole phase in theattosecond probing of charge migration. The iodobromoacetylene ion (ICCBr$^+$)is considered as an example, in which one can probe charge migration byaccessing both the iodine and bromine ends of the molecule with differentspectral windows of an extreme-ultraviolet (XUV) pulse. The analyticalexpression for transient absorption shows that the site-specific information ofcharge migration is encoded in the complex phase of cross dipole products forXUV transitions between the I-$4d$ and Br-$3d$ spectral windows. Ab-initioquantum chemistry calculations on ICCBr$^+$ reveal that there is a constant$\pi$ phase difference between the I-$4d$ and Br-$3d$ transient-absorptionspectral windows, irrespective of the fine-structure energy splittings.Transient absorption spectra are simulated with a multistate model includingthe complex dipole phase, and the results correctly reconstruct thecharge-migration dynamics via the quantum beats in the two element spectralwindows, exhibiting out-of-phase oscillations.

Theoretical analysis of the role of complex transition dipole phase in XUV transient-absorption probing of charge migration