  The entanglement between a Pauli-like two-level system and a quantum harmonic
oscillator enhanced by an interaction between them and a $\delta$-pulse
sequence is studied, with the decoherence due to their coupling with a
Markovian bath. Without the Markovian bath, the entanglement is enhanced to
maximum possible values. With the Markovian bath, the entanglement is enhanced
up to some time and then dissipated, with the system in thermal equilibrium
with the Markovian bath after a very long time. The time for achieving the
maximum entanglement shows discontinuous jumps over the parameters of
decoherence.
