Population Inversion in Optical Adiabatic Rapid Passage with Phase Relaxation

The transition probability $P$ in the optical adiabatic rapid passage is calculated for a two-level model with dephasing. In the limit $\frac{T_2}{{\tau }_p}\to 0$, where $T_2$ is the dephasing time and ${\tau }_p$ is the time scale of passage through the resonance region, $P$ is given by $P=\frac{[1-\exp (-\frac{\pi {\chi }^2}{\left|\dot{\omega }\right|}\left)\right]}{2}$ in which $\chi$ is the Rabi flopping frequency at resonance and $\dot{\omega }$ is the time derivative of the offset angular frequency. Generally, $P$ takes its maximum value at an intermediate $\dot{\omega }$ for fixed $\chi$ and is bounded by the above formula and by $P=1-\exp (-\frac{\pi {\chi }^2}{2\left|\dot{\omega }\right|})$, which gives the asymptotic value in the limit $\frac{T_2}{{\tau }_p}\to \infty$.