Population Inversion in Optical Adiabatic Rapid Passage with Phase Relaxation

Abstract

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