  We study the dynamics of a quantum spin ensemble controlled by trains of
ultrashort pulses. To model disturbances of the kicks, we consider that the
spins are submitted to different kick trains which follow regular, random,
stochastic or chaotic dynamical processes. These are described by dynamical
systems on a torus. We study the quantum decoherence and the population
relaxation of the spin ensemble induced by these classical dynamical processes
disturbing the kick trains. For chaotic kick trains we show that the
decoherence and the relaxation processes exhibit a signature of chaos directly
related to the Lyapunov exponents of the dynamical system. This signature is a
horizon of coherence, i.e. a preliminary duration without decoherence followed
by a rapid decoherence process.
