Observation and theoretical simulation of dispersive properties of an electromagnetically induced transparent 87Rb atomic medium

The dispersive properties of Rb-87 atomic medium in electromagnetically induced transparency (EIT) have been studied experimentally as well as theoretically. To measure the dispersion signal, a balanced homodyne detection technique was used by forming a Mach-Zehnder interferometer. We studied the system in a Lambda-type configuration. From the slope of the dispersive EIT signal, the group index (n(g)) of the atomic medium, the group velocity (nu(g)) and the time delay (Delta t(g)) of the light wave through the atomic medium were calculated. We measured the group index of the atomic medium from the dispersion signal and observed that it non-linearly depends on the pump power. This non-linearity signifies that to achieve the maximum reduced group velocity, optimization of the pump power is needed. We got the maximum reduction in the group velocity of the probe beam as nu(g) = (c/130.4) m s(-1). The corresponding time delay was Delta t(g) = 21.73 ns. To support our experimental observation, we have performed a theoretical simulation by taking the semi-classical approach of density matrix formalism of a Lambda-type three level system. To get the probe response we solved the optical Bloch equation analytically assuming the Lorentzian velocity distribution of the atom. We have observed that our analytical solution matched exactly with the numerical solution. Our experimental observation of non-linear variation of the group index with the pump Rabi frequency matched quite well with both of our numerical and analytical simulations.