Topology-protected displacement metrology using broadband unpolarized light

We introduce topological invariants into displacement metrology and show that robust topological structures in momentum space can be used to retrieve the displacement of a small particle. Owing to its topological nature, the proposed scheme is general. It does not require phase or polarization stability and works even under broadband unpolarized illumination with randomly fluctuating phases. Remarkably, unpolarized illumination can achieve a superior performance to its coherent counterpart, owing to closely packed in-plane polarization singularity structures with very high displacement sensitivities nearby. Our work opens an avenue for developing topologically protected ultrasensitive metrological methods with randomly fluctuating fields.