Simultaneous EIT of two circularly polarized optical fields driven by a linearly polarized optical field in a $\omega$-system

We analyze the possibility of slowing down simultaneously two circularly polarized optical fields using a linearly polarized control field in a four level atom $\omega $-system placed in a weak magnetic field. The goal is to propose a new type of optical quantum memory [1] using binary recording. Our prototype $\omega $-system is an ensemble of alkali-atoms on the $\vert ^{1}$S$_{0}>$ground state and the three M = 0, $\pm $1 Zeeman states of the first excited atomic state, $\vert ^{1}$P$_{1}>$. The energy separation between the Zeeman states is set up with a weak magnetic field of 0.006 $<$ B $<$ 0.035 T chosen so that (1) the Larmor frequency does not exceed the characteristic time of the spin-orbit interaction between $\vert ^{1}$S$_{0}>$ and $\vert ^{1}$P$_{1}>$ states, and (2) the bandwidths of the $\vert ^{1}$P$_{1}$; M $>$ Zeeman states do not overlap. We report atomic coherences calculated from the density matrix master equation which includes the radiative relaxations $\vert ^{1}$P$_{1}$; M= 0, $\pm $1 $> \quad \to \quad \vert ^{1}$S$_{0}>$. We explain the mechanism of slowing down simultaneously two optical fields using a variable control field by adopting a dressed state representation. We also analyze the evolution of the Autler-Townes doublets associated to the two probe fields from a proto-EIT phase into a stable EIT phase [2]. [1] Lvovsky A I, Sanders B C and Tittel W 2009 \textit{Nature Photonics }\textbf{3} 706. [2] Fleischhauer M, Imamoglu A and Marangos J P 2005 \textit{Rev. Mod. Phys.}\textbf{ 77} 633.