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People have been paying attention to the role of atoms' complex internallevel structures in the research of electromagnetically induced transparency(EIT) for a long time, where the various degenerate Zeeman levels usuallygenerate complex linkage patterns for the atomic transitions. It turns out,with special choices of the atomic states and the atomic transitions' linkagestructure, clear signatures of quantum interference induced by the probe andcoupling light's polarizations can emerge from a typical EIT phenomena. Wepropose to study a four state system with double-V linkage pattern for thetransitions and analyze the polarization induced interference under the EITcondition. We show that such interference arises naturally under mildconditions on the optical field and atom manipulation. Its anticipatedproperties and its potential application of all optical switching inpolarization degree of freedom are also discussed. Moreover, we construct avariation form of double-M linkage pattern where the polarization inducedinterference enables polarization-dependent cross-modulation between incidentlights that can be effective even at the few-photon level. The theme is to gainmore insight into the essential question: how can we build non-trivial opticalmedium where incident lights will induce polarization-dependent non-linearoptical interactions, covering a wide range of the incidence intensity from themany-photon level to the few-photon level, respectively.

Polarization induced interference within electromagnetically induced transparency for atoms of double-V linkage