  A scheme for fine tuning of quantum operations to improve their performance
is proposed. A quantum system in $\Lambda$ configuration with two-photon Raman
transitions is considered without adiabatic elimination of the excited
(intermediate) state. Conditional dynamics of the system is studied with focus
on improving fidelity of quantum operations. In particular, the $\pi$ pulse and
$\pi/2$ pulse quantum operations are considered. The dressed states for the
atom-field system, with an atom driven on one transition by a classical field
and on the other by a quantum cavity field, are found. A discrete set of
detunings is given for which high fidelity of desired states is achieved.
Analytical solutions for the quantum state amplitudes are found in the first
order perturbation theory with respect to the cavity damping rate $\kappa$ and
the spontaneous emission rate $\gamma$. Numerical solutions for higher values
of $\kappa$ and $\gamma$ indicate a stabilizing role of spontaneous emission in
the $\pi$ and $\pi/2$ pulse quantum operations. The idea can also be applied
for excitation pulses of different shapes.
