Electromagnetically induced transparency with a standing-wave drive in the frequency up-conversion regime

We study electromagnetically induced transparency for a probe traveling-wave (TW) laser field in closed Doppler-broadened three-level systems driven by a standing-wave (SW) laser field of moderate intensity (its Rabi frequencies are smaller than the Doppler width of the driven transition). We show that probe windows of transparency occur for values of the probe to drive field frequency ratio R close to half-integer values. For optical transitions and typical values of Doppler broadening for atoms in a vapor cell, we show that for $R>\mathrm{}1\mathrm{}$ a SW drive field is appreciably more efficient than a TW drive in inducing probe transparency. As examples, we consider parameters for real cascade schemes in barium atoms with $R\approx 1.5$ and in beryllium atoms with $R\approx 3.5$ showing that probe transmission values well above 50% are possible for conditions in which it is almost negligible either without driving field or with only one of the TW components of the drive. We show that a strongly asymmetric drive having two TW components with unequal intensities is even more eficient than a symmetric SW drive in inducing probe transparency. The case of arbitrary probe intensity is also considered.