Switching from positive to negative dispersion in transparent degenerate and near-degenerate systems

Abstract

We investigate realistic atomic systems whose dispersion at line center switches from positive to negative and vice versa, as a particular experimental parameter is changed. We concentrate on those systems which have low probe absorption or gain at line center leading to a high figure of merit, and simultaneously have low pump absorption. For this purpose, we study both open and artificially closed ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=1$ and ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=2$ transitions in ${}^{87}\mathrm{Rb},$ in the absence and presence of an applied magnetic field. We find that the preferred system for observing switchover in the sign of the dispersion from positive to negative, as the pump Rabi frequency increases, is the open near-degenerate ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=1$ system. In the presence of Doppler broadening, the dispersion is positive for all realistic experimental parameters. Thus the switchover in the sign of the dispersion is only observable in the absence of Doppler broadening.