Super-Heisenberg-limited Sensing via Collective Subradiance in Waveguide QED

We explore the quantum-metrological potential of subwavelength-spaced emitter arrays coupled to a one-dimensional nanophotonic waveguide. In this system, strong dipole--dipole interactions profoundly modify the collective optical response, leading to the emergence of ultranarrow subradiant resonances. Through an eigenmode analysis of the effective non-Hermitian Hamiltonian, we derive a universal scaling law for the decay rate of the most subradiant state, which exhibits an N^-3 scaling with even-odd oscillatory behavior in the deep-subwavelength regime. This scaling is directly observable in the single-photon scattering spectrum, enabling the detection of minute changes in atomic separation with a figure of merit that scales as N³. The quantum Fisher information (QFI) scales as N⁶ and can be closely approached by measuring spectral shifts near the steepest slope of the most subradiant resonance. These enhancements remain robust under realistic positional disorder, confirming that dipole--dipole-engineered subradiance provides a viable resource for quantum metrology. Our work bridges many-body waveguide quantum electrodynamics and high-precision sensing, opening a route toward scalable quantum sensors on integrated nanophotonic platforms.