Light-Wave Engineering for Selective Polarization of a Single $\mathbf{Q}$ Valley in Transition Metal Dichalcogenides

The selective control of specific momentum valleys lies at the core of valleytronics, a field that has thus far focused primarily on the $\mathbf{K}$ and $\mathbf{K'}$ valleys in transition metal dichalcogenides (TMDs). However, direct optical access to other low-lying yet conventionally inaccessible valleys such as the sixfold degenerate $\mathbf{Q}$ valleys has remained an outstanding challenge, fundamentally limiting the exploitation of the full valley degree of freedom for information processing. Here, we theoretically introduce an emergent light-wave valley selection rule that enables deterministic and high fidelity excitation of any single $\mathbf{Q}$ valley in monolayer TMDs. By coherently combining a circularly polarized pump pulse with a linearly polarized driver pulse, we engineer distinct quantum pathways that unambiguously excited electrons into a targeted $\mathbf{Q}$ valley, completely decoupled from the conventional $\mathbf{K}/\mathbf{K'}$ valleys. This all-optical scheme achieves near-unity ($\sim$100\%) valley polarization across an exceptionally broad ultrafast window, from the terahertz ($10^{12}$~Hz) to petahertz ($10^{15}$~Hz) regimes, enabling single $\mathbf{Q}$ valley polarization on femtosecond timescales. Our findings establish a new paradigm of light-wave quantum metrology in valleytronics, unlocking the $\mathbf{Q}$-valley subspace for scalable multi-state valley information processing.