  We present an analytic description of the effects of dephasing processes on
stimulated Raman adiabatic passage in a tripod quantum system. To this end, we
develop an effective two-level model. Our analysis makes use of the adiabatic
approximation in the weak dephasing regime. An effective master equation for a
two-level system formed by two dark states is derived, where analytic solutions
are obtained by utilizing the Demkov-Kunike model. From these, it is found that
the fidelity for the final coherent superposition state decreases exponentially
for increasing dephasing rates. Depending on the pulse ordering and for
adiabatic evolution the pulse delay can have an inverse effect.
