Topological phases in metamaterials are often inferred from localized edge states or from real-space wave-function measurements. Yet the topology is fundamentally encoded in the bulk eigenvectors and often manifests as a bulk band inversion. Here we directly access this band inversion in an exciton-polariton Su-Schrieffer-Heeger (SSH) chain using far-field spectroscopy with tuneable sublattice interference. The SSH chain provides an excellent benchmark model for establishing this measurement principle in an exciton-polariton platform. We show that in the SSH model, the band inversion is characterized by a sign change of the sublattice symmetry $\langle {\sigma }_{\mathrm{x}}\rangle$ between the Brillouin-zone center and boundary. A transverse sublattice displacement maps the relative phase between sublattice wave functions onto a controllable far-field interference phase $\mathrm{\Delta }\theta$. Taking the difference of spectra at $\mathrm{\Delta }\theta =0$ and $\mathrm{\Delta }\theta =\pi$ yields a quantity proportional to $\langle {\sigma }_{\mathrm{x}}\rangle$, directly revealing the band inversion in the topological configuration. The tunable phase $\mathrm{\Delta }\theta$ further lets us reconstruct the effective $2\times 2$ Bloch Hamiltonian and its winding number, unequivocally linking the measured band inversion to the topological invariant. More generally, spectroscopy with a controllable sublattice phase allows for the measurement of bulk eigenvectors, granting access to band inversions for higher-dimensional systems.

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• Edge states
• Geometric & topological phases
• Symmetry protected topological states
• Topological effects in photonic systems
• Topological insulators