We propose a protocol of the long-distance atomic state teleportation via cavity decay, which allows for high-fidelity teleportation even with currently available optical cavities. The protocol is based on the scheme proposed by Bose emph{et al.} [Ph
ys. Rev. Lett. {textbf{83}}, 5158 (1999)] but with one important modification: it employs non-maximally-entangled states instead of maximally entangled states.
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. Con
ditional 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.
