  The time-dependent behavior of a two-level system interacting with a quantum
oscillator system is analyzed in the case of a coupling larger than both the
energy separation between the two levels and the energy of quantum oscillator
($\Omega < \omega < \lambda $, where $\Omega $ is the frequency of the
transition between the two levels, $\omega $ is the frequency of the
oscillator, and $\lambda $ is the coupling between the two-level system and the
oscillator). Our calculations show that the amplitude of the expectation value
of the oscillator coordinate decreases as the two-level system undergoes the
transition from one level to the other, while the transfer probability between
the levels is staircase-like. This behavior is explained by the interplay
between the adiabatic and the non-adiabatic regimes encountered during the
dynamics with the system acting as a quantum counterpart of the Landau-Zener
model. The transition between the two levels occurs as long as the expectation
value of the oscillator coordinate is driven close to zero. On the contrary, if
the initial conditions are set such that the expectation values of the
oscillator coordinate are far from zero, the system will remain locked on one
level.
