Quantum phase gate via stimulated Raman adiabatic passage with time-dependent two-photon detuning

We investigate a quantum phase gate (QPG) in a four-level system where the system is manipulated using adiabatic passage by lasers with a time-dependent two-photon detuning. The QPG cannot employ the dark state, because the two-photon detuning is indispensable for phase shifts of the gate. All the eigenstates have population in the excited state, which cause errors of the QPG. In this paper, we investigate optimal conditions of the two-photon detuning which would maximize the fidelity and minimize the errors due to the excited state for various values of the phase shifts. Finally we find the conditions of the detuning for improvement of the QPG performance.