Topological invariants characterising filled Bloch bands attract enormous interest, underpinning electronic topological insulators and analogous artificial lattices for Bose-Einstein condensates, photons, and acoustic waves. In the latter bosonic systems there is no Fermi exclusion principle to enforce uniform band filling, which makes measurement of their bulk topological invariants challenging. Here we show how to achieve controllable filling of bosonic bands using leaky photonic lattices. Leaky photonic lattices host transitions between bound and radiative modes at a critical energy, which plays a role analogous to the electronic Fermi level. Tuning this effective Fermi level into a band gap results in disorder-robust dynamical quantization of bulk topological invariants such as the Chern number. Our findings establish leaky lattices as a novel and highly flexible platform for exploring topological and non-Hermitian wave physics.
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