  We investigate signatures of non-Markovianity in the dynamics of a
periodically-driven qubit coupled to a dissipative bosonic environment. We
propagate the dynamics of the reduced density matrix of the qubit by
integrating the numerically exact hierarchical equations of motion.
Non-Markovian features are quantified by comparing on an equal footing the
predictions from diverse and complementary approaches to quantum dissipation.
In particular, we analyze the distinguishability of quantum states, the decay
of the volume accessible to the qubit on the Hilbert space, the negativity of
the canonical rates in the generalized Lindblad equation and the relaxation of
the memory kernels in the Nakajima-Zwanzig generalized quantum master equation.
We study the effects of controlled driving on the coherent dynamics of the
system. We show that a suitable external field can offset the ergodic
relaxation of time correlation functions, increase distinguishability over time
and strengthen non-Markovian effects witnessed by the canonical dissipation
channels. We furthermore observe the phenomenon of eternal non-Markovianity for
sufficiently small system-bath coupling and we discuss how this can be enhanced
by modulating the frequency of the external drive. The present work provides a
broad theoretical analysis of quantum dissipation in the framework of open
quantum dynamics and quantum information.
