The Berry phase can be induced in a quantum system not only by adiabatic evolution but also via a sequence of projective measurements (in which case it is known as the Pancharatnam phase). We explored what happens upon replacing the projective (“strong”) measurements with so-called weak measurements. It turns out that the induced phase exhibits a drastic change of behaviour as the measurement strength is changed from infinitely strong to infinitely weak. This drastic change happens at a certain critical measurement strength and is related to a change in the topology of the surface spanned by measurement-induced quantum trajectories.

[1] V. Gebhart, K. Snizhko, T. Wellens, A. Buchleitner, A. Romito, and Y. Gefen, Topological transition in measurement-induced geometric phases, arXiv:1905.01147.