Theory of attosecond transient absorption spectroscopy of strong-field-generated ions

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.