Beyond Quantum interference and Optical pumping: invoking a Closed-loop phase

Atomic coherence effects arising from coherent light-atom interaction are conventionally known to be governed by quantum interference and optical pumping mechanisms. However, anisotropic nonlinear response driven by optical field involves another fundamental effect arising from closed-loop multiphoton transitions. This closed-loop phase dictates the tensorial structure of the nonlinear susceptibility as it governs the principal coordinate system in determining, whether the light field will either compete or cooperate with the external magnetic field stimulus. Such a treatment provides deeper understanding of all magneto-optical anisotropic response. The magneto-optical response in all atomic systems is classified using closed-loop phase. The role of quantum interference in obtaining electromagnetically induced transparency or electromagnetically induced absorption in multi-level systems is identified.