Line shapes in V-type electromagnetically induced transparency for 87Rb atoms: theory and experiment

We present a theoretical and experimental study of electromagnetically induced transparency (EIT) in V-type systems of $^{\mathrm{87}}$Rb atoms. The probe beam frequency is locked to the F$_{\mathrm{g}}=$2$\to $F$_{\mathrm{e}}=$2 and F$_{\mathrm{g}}=$2$\to $F$_{\mathrm{e}}=$1 transitions of D$_{\mathrm{1}}$ line and the coupling beam frequency is scanned around the F$_{\mathrm{g}}=$2$\to $F$_{\mathrm{e}}=$1,2,3 transitions of D$_{\mathrm{2}}$ line. The polarizations of the probe and coupling beams are linear in parallel or perpendicular direction. We calculate accurate line shapes of V-type EIT spectra using density matrix equations by considering all the magnetic sub-levels and compare them with experimental results. To discriminate the contribution of coherence term, we perform similar calculations by ignoring the coherences between the sublevels in the 5P$_{\mathrm{1/2}}$ state and those in the 5P$_{\mathrm{3/2}}$ state. We find that the coherence effect is significant only for the cycling transition line.