  Strong-field ionization generally produces ions in a superposition of ionic
eigenstates. This superposition is generally not fully coherent und must be
described in terms of a density matrix. A recent experiment [E. Goulielmakis et
al., Nature 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.
