Complementarity of which-path information in induced and stimulated coherences via four-wave mixing process from warm Rb atomic ensemble.

Complementarity, a fundamental tenet of quantum optics, is indispensable for elucidating the fundamental principles of quantum physics and advancing quantum information processing applications. In the context of wave–particle duality, induced-coherence experiments were understood through the lens of which-path information. Conversely, the stimulated-coherence experiments were explained by using the indistinguishability of the photon statistics of conjugate photons as a means of realizing complementarity. Here, we report a systematic approach for establishing a complementary relationship between the interference visibility, concurrence, and predictability in the crossing of induced and stimulated coherences of two-mode squeezed coherent states. This is achieved using a double-path interferometer involving two independent four-wave mixing (FWM) atomic samples generated via spontaneous and stimulated FWM processes from a warm atomic ensemble of 87 Rb. We demonstrate that the transition from quantum to classical behavior can be characterized by the induced coherence effect, distinguishing between the two-mode squeezed vacuum and coherent states. Moreover, our experimental scheme, employing two FWM atomic ensembles with long-coherent photons, provides valuable insights into the complementarity of which-path information in induced and stimulated coherences.