A new sublattice polarimeter enables full reconstruction of Bloch wavefunctions in bipartite photonic lattices, granting direct access to the quantum metric and Berry curvature across the Brillouin zone.

Demonstrations include coupling between S- and P-orbitals and validation of theoretical predictions within a two-band model through second-neighbor coupling.

The approach is general and scalable beyond two-band systems, with potential to explore Chern insulators, trigonal warping, Euler curvature, and fragile or non-abelian topologies in multi-band settings.

A reconfigurable spatial light modulator is used to isolate light from individual lattice sites and project it between crossed polarizers, enabling precise control over phase retardation and amplitude imbalance between sublattice fields.

Reconstruction of Bloch eigenstates from measured Stokes parameters allows extraction of the full Bloch Hamiltonian and topological invariants such as band Chern numbers, with an experimental value of 0.25 ± 0.01 at K’.

The technique applies to hexagonal, bipartite lattices and can extend to higher orbitals and multiple internal degrees of freedom, offering a robust tool for probing quantum geometry and topology in light-matter systems.

The method analyzes wavefunction overlaps around Brillouin-zone plaquettes and uses a tight-binding framework to connect sublattice polarization to Bloch states, with high polarization enabling precise measurements.