Eigenstate-Selective Entangled Two-Photon Absorption in Monolayer WSe$_2$

Abstract

We show that the Bell-state phase of a polarization-entangled photon pair controls the biexciton eigenstate distribution produced by entangled two-photon absorption in monolayer WSe$_2$. In a frequency-nondegenerate ladder scheme, two independent valley pathways ($K$ and $K'$) share no intermediate state, so the biphoton phase sets the relative amplitude between them. Within the valley-symmetric limit, the phase dependence is contained in the prefactors $1\pm e^{i\varphi}$, which are independent of the material response. The resulting selection rule partitions the excitation among biexciton eigenstates according to the Bell-state phase $\varphi$. The symmetric Bell state ($\varphi = 0$) selectively drives bright eigenstates, while the antisymmetric state ($\varphi = π$) drives the exchange-dark eigenstate. No separable polarization state reproduces this $\varphi$-dependent eigenstate distribution. At equal total pair flux, the dark-state pumping rate of the Bell state is twice the upper bound for any separable polarization state. Exceeding this bound certifies polarization entanglement of the source. Including valley dephasing, intervalley scattering, source imperfections, and residual amplitude errors at 4~K, the estimated phase-scan visibility of the eigenstate-resolved pair-absorption rates is $V\gtrsim0.95$ for broadband spontaneous parametric down-conversion (entanglement time $T_e \sim 100$ fs) with high source concurrence and picosecond-scale valley coherence.