Strong-field ionization generally produces ions in a superposition of ionic eigenstates. This superposition is generally not fully coherent and must be described in terms of a density matrix. A recent experiment [E. Goulielmakis et al., Nature (London) 466, 739 (2010)] employed attosecond transient absorption spectroscopy to determine the density matrix of strong-field-generated Kr
+ ions. The experimentally observed degree of coherence of the strong-field-generated Kr
+ ions is well reproduced by a recently developed multichannel strong-field-ionization theory, but there is significant disagreement between experiment and theory with respect to the degree of alignment of the Kr
+ ions. In the present paper, the theory underlying attosecond transient absorption spectroscopy of strong-field-generated ions is developed. The theory is formulated in such a way that the nonperturbative nature of the strong-field-ionization process is systematically taken into account. The impact of attosecond pulse propagation effects on the interpretation of experimental data is investigated both analytically and numerically. It is shown that attosecond pulse propagation effects cannot explain why the experimentally determined degree of alignment of strong-field-generated Kr
+ ions is much smaller than predicted by existing theory.
Strong field ionization injects a transient vacancy in the atom which is entangled to the outgoing photoelectron. When the electron is finally detached, the ion is populated at different excited states with part of coherence information lost. The preserved coherence of matter after interacting with intense short pulses has important consequences on the subsequent nonequilibrium evolution and energy relaxation. Here we employ attosecond transient absorption spectroscopy to measure the time-delay of resonant transitions of krypton vacancy during their creation. We have observed that the absorptions by the two spin-orbit split states are modulated at different paces when varying the time-delay between the near-infrared pumping pulse and the attosecond probing pulse. It is shown that the coupling of the ions with the remaining field leads to a suppression of ionic coherence. Comparison between theory and experiments uncovers that coherent Raman coupling induces time-delay between the resonant absorptions, which provides insight into laser-ion interactions enriching attosecond chronoscopy.