Pulse delay and group velocity dispersion measurement in V-type electromagnetically induced transparency of hot $^{85}Rb$ atom

Pulse delay with the group velocity dispersion (GVD) characteristics was studied in the V-type electromagnetically induced transparency in the hyperfine levels of $^{85}Rb$ atoms with a closed system configuration. The phase coherency between the pump and the probe laser beams was maintained. We studied the pulse delay and the group velocity dispersion characteristics with the variation of the pump Rabi frequency taking temperature as a parameter. We observed a maximum of $268$ $ns$ pulse delay for $21.24 MHz$ pump Rabi frequency at $55^0C$ temperature of the Rb vapour cell. For a better understanding of the experimental results, we have derived an analytical solution for the delay characteristics considering the thermal averaging. The analytical solution was derived for a three level V-type system. The theoretical plots of the delay and the group velocity dispersion show the same characteristics as we observed in the experiment. This analytical approach can be further generalized for the higher level schemes to calculate different quantities such as susceptibility, group velocity delay or group velocity dispersion characteristics.