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

People have been paying attention to the role of atoms' complex internal level structures in the research of electromagnetically induced transparency (EIT) for a long time, where the various degenerate Zeeman levels usually generate complex linkage patterns for the atomic transitions. It turns out, with special choices of the atomic states and the atomic transitions' linkage structure, clear signatures of quantum interference induced by the probe and coupling light's polarizations can emerge from a typical EIT phenomena. We propose to study a four state system with double-V linkage pattern for the transitions and analyze the polarization induced interference under the EIT condition. We show that such interference arises naturally under mild conditions on the optical field and atom manipulation. Its anticipated properties and its potential application of all optical switching in polarization degree of freedom are also discussed. Moreover, we construct a variation form of double-M linkage pattern where the polarization induced interference enables polarization-dependent cross-modulation between incident lights that can be effective even at the few-photon level. The theme is to gain more insight into the essential question: how can we build non-trivial optical medium where incident lights will induce polarization-dependent non-linear optical interactions, covering a wide range of the incidence intensity from the many-photon level to the few-photon level, respectively.