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-$\mathsf{\text{V}}$ 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 techniques. Moreover, we construct a variation form of double-M linkage pattern where the polarization-induced interference enables polarization-dependent cross modulation between incident weak 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 a nontrivial optical medium where incident lights experience polarization-dependent nonlinear optical interactions, valid for a wide range of incidence intensities down to the few-photon level?

• Received 6 September 2017

DOI:https://doi.org/10.1103/PhysRevA.97.023815