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The propagation of a pair of quantized fields inside a medium of three-levelatoms in $\Lambda$ configuration is analyzed. We calculate the stationaryquadrature noise spectrum of the field after propagating through the medium inthe case where the field has a general (but small) noise spectrum and the atomsare in a coherent population trapping state and show electromagneticallyinduced transparency (EIT). Although the mean values of the field remainunaltered as the field propagates, there is an oscillatory interchange of noiseproperties between the probe and pump fields. Also, as the field propagates,there is an oscillatory creation and annihilation of correlations between theprobe and pump quadratures. We further study the field propagation of squeezedstates when there is two-photon resonance, but the field has a detuning$\delta$ from atomic resonance. We show that the field propagation is verysensitive to $\delta$. The propagation in this case can be explained as acombination of a frequency dependent rotation of maximum squeezed quadraturewith an interchange of noise properties between pump and probe fields. It isalso shown that the effect of the Doppler width in a squeezed state propagationis considerable.

Propagation of small fluctuations in electromagnetically induced transparency. Influence of Doppler width