Polarization-addressed weak measurements for separating orbital angular momentum from particle localization in a single-path quantum Cheshire Cat

Weak measurements, which enable access to weak values with minimal disturbance to the quantum system, have significantly advanced the study of counterintuitive quantum phenomena, including the quantum Cheshire Cat (QCC). Building on this methodology, we report a single-path realization of the QCC effect by mapping the two interferometric arms onto orthogonal polarization states of a single photon within the orbital angular momentum (OAM) degree of freedom. This approach demonstrates that the pre- and post-selected quantum states yield weak measurement statistics consistent with the polarization and OAM observables behaving as although they are localized differently, effectively decoupling the OAM property from its polarization-encoded carrier. Using a polarization-addressed spatial light modulator, we implement two programmable weak couplings on the same hardware: a weak absorptive perturbation (probing particle-like localization) that yields the particle-detectability weak value from the slope of the normalized post-selection probability and a small OAM rotation (probing wave-like OAM) that yields the OAM-related weak value from the slope of the interference visibility—both operating within the linear weak-coupling regime. By comparing the statistics from these two measurements, we experimentally confirm the effective decoupling of the photon’s particle localization and its OAM. This pointer-free, single-platform architecture preserves full weak-value readout capability while substantially reducing alignment and stabilization complexity, offering a compact and resource-efficient route to QCC-based property separation well suited for high-dimensional quantum applications.