Exact solution of the Bloch equations for the nonresonant exponential model in the presence of dephasing

An exact analytic solution is presented for a two-state quantum system driven by a time-dependent external field with an exponential temporal shape in the presence of dephasing. In the absence of dephasing the model reduces to the well-known Demkov model originally introduced in slow atomic collisions. The solution is expressed in terms of the generalized hypergeometric function ${}_{1}{F}_{2}(a;{b}_{1},{b}_{2};x)$. Various limiting cases are examined in the limits of weak and strong dephasing, strong driving field, and exact resonance.