Double-Λ electromagnetically induced transparency with degenerate atomic levels

Abstract

The general expression for the transformation matrix of the two input weak arbitrarily polarized probe fields passing through the medium under the conditions of double-Λ electromagnetically induced transparency is obtained for arbitrary values of the amplitudes, phases and polarizations of the control fields and arbitrary values of the angular momenta of resonant levels. The conditions are found for the two input weak probe fields linearly polarized in perpendicular planes to exchange their polarizations after the passage through the medium without absorption. The polarization rotation of the probe fields is studied for the atoms being initially in the equilibrium state.