Geometric phases arising from strong measurements of weak values

Geometric phases and weak values (WVs) are two fundamental concepts that were originally introduced in the realm of quantum mechanics. In the course of time, it became clear that the two concepts apply in both the quantum domain and the classical domain. Moreover, the two concepts proved to be intimately connected with one another, as disclosed by Sjöqvist some years ago (Sjöqvist 2006 Phys. Lett. A 359 187). WVs were so named in reference to very weak couplings between a system’s observable, e.g. light polarization, and its measuring device, the ‘pointer’. However, the actual definition of WVs does not involve the system-pointer coupling strength. We have addressed the strong coupling regime both theoretically and experimentally, thereby obtaining geometric phases out of WVs. We report experimental results as a proof-of-concept, using classical light beams and single-shot images. Our approach applies without essential modifications also to single photons.