  An evolution of a two-level system (qubit) interacting with a single-photon
wave packet is analyzed. It is shown that a hierarchy of master equations gives
rise to phase covariant qubit evolution. {The temporal correlations in the
input field} induce nontrivial memory effects for the evolution of a qubit. It
is shown that in the resonant case whenever time-local generator is regular
(does not display singularities) the qubit evolution never displays information
backflow. However, in general the generator might be highly singular leading to
intricate non-Markovian effects. A detailed analysis of the exponential profile
is provided which allows to illustrate all characteristic feature of the qubit
evolution.
