  We show the existence of dynamical purity swapping phenomena in the
Jaynes-Cummings model. Moreover we show that purity swapping between a qubit
and a generic quantum system is possible, provided they are coupled via
non-unitary matrix elements interaction. We particularize to the case of a
quantum optical Ramsey interferometer. We show that using purity swapping, a
perfect interference pattern can be obtained at the output port of the
interferometer even if we start from totally unpolarized sources. This feature
is shown to be associated with the phenomena of recreation of the state vector
at half of the revival time. In fact, we show that the Gea-Banacloche attractor
is robust against degradation of the purity of the qubit input state. We also
show that the Tsallis entropy T2 is a useful entanglement monotone allowing one
to relate directly entanglement with purity exchange in interacting systems. We
conjecture an Araki-Lieb type inequality for T2 that bounds the maximum
interchange of purity between interacting systems.
