Temporal-order-driven asymmetric quantum interference and temporal coherence enhancement in spontaneous six-wave mixing

Abstract

Narrow-band multiphoton entanglement sources serve as a core enabling resource for advanced quantum information technologies. Recently, researchers have directly generated energy-time entangled triphoton W states in a hot atomic medium via spontaneous six-wave mixing for the first time. However, a rigorous theoretical framework for this process remains lacking to date, confining our understanding to a mere extension of the biphoton model. Here, we analytically investigate the generation mechanism of energy-time entangled triphotons and their classically controllable optical properties in an electromagnetically induced transparency-assisted five-level cold atomic system. Notably, triphoton generation follows strict temporal ordering, resulting in asymmetric quantum interference in triple coincidence counts--unreplicable and unexplainable by the inherently symmetric biphoton model. These results establish a rigorous physical framework for spontaneous six-wave mixing-generated triphotons, clarify their distinctions from states produced via cascaded nonlinear models, and substantially advance their utility in quantum information protocols.

Figures (3)

• Figure 1: (a) Triple-photon generation in a five-level cold atomic system. (b) Spatial configuration of incident light and generated signals. $D_i$ represents the $i$th detector.
• Figure 2: The fifth-order nonlinear susceptibility $|\chi^{5}(\delta_2,\delta_3)|$ for $L=0.15$cm, $N=8.36\times10^{14}$, $\gamma_{31}=2\pi\times3$MHz, $\Omega_{c1}=\Omega_{c2}=40\gamma_{31}$, $\gamma_{41}=\gamma_{31}$, $\gamma_{51}=0.1\gamma_{31}$, $\gamma_{21}=0.02\gamma_{31}$, $\Delta_{c1}=\Delta_{c2}=0$, and $\Delta_p=-2\pi\times300$MHz.
• Figure 3: (a) Normalized triple-coincidence counts $R_{cc}(\tau_{12},\tau_{13})$ dominated by $\chi^{(5)}$, with parameters as in Fig. \ref{['fig2']} except $\Omega_{c1}=\Omega_{c2}=8\gamma_{31}$. In this regime, (b) $R_{cc}(\tau_{12})$ and (c) $R_{cc}(\tau_{13})$ for $\Omega_{c1}=\Omega_{c2}=2\gamma_{31}$, $4\gamma_{31}$, and $8\gamma_{31}$, respectively. (d) Normalized $R_{cc}(\tau_{12},\tau_{13})$ dominated by both $\chi^{(5)}$ and $\Phi$, with parameters as in Fig. \ref{['fig2']} except $\Omega_{c1}=\Omega_{c2}=2\gamma_{31}$ and $OD=111$. (e) $R_{cc}(\tau_{12})$ and (f) $R_{cc}(\tau_{13})$ in the hybrid regime for OD=37, 74, 111, with remaining parameters same as in (d).