  In the present paper an example of entanglement between two different kinds
of interacting particles, photons and electrons is analysed. The initial-value
problem of the Schroedinger equation is solved non-perturbatively for the
system of a free electron interacting with a quantized mode of the
electromagnetic radiation. Wave packets of the dressed states so obtained are
constructed in order to describe the spatio-temporal separation of the
subsystems before and after the interaction. The joint probability amplitudes
are calculated for the detection of the electron at some space-time location
and the detection of a definite number of photons. The analytical study of the
time evolution of entanglement between the initially separated electron wave
packet and the radiation mode leads to the conclusion that in general there are
non-vanishing entropy remnants in the subsystems after the interaction. On the
basis of the simple model to be presented here, the calculated values of the
entropy remnants crucially depend on the character of the switching-on and off
of the interaction.
