Direct experimental access to the bulk band inversion in a topological metamaterial

Abstract

Topological phases in exciton-polaritons and other metamaterial platforms have attracted significant attention due to their flexibility as Hamiltonian simulators. In previous works, signatures of topology have mainly been investigated from the perspective of edge states - strongly localised modes with exponentially decaying intensity into the bulk. While these edge states have become the hallmark of topological systems as they can facilitate non-reciprocal transport in potential applications, the topology is fundamentally encoded in the bulk band structure. In particular, the momentum-dependence of the eigenstates, i.e., the wave functions, determines the topology, usually reflected in a bulk band inversion. We present a band inversion in the paradigmatic Su-Schrieffer-Heeger (SSH) model, characterised by a reversal of the sublattice symmetry, quantified by the expectation value $\langle \sigma_\mathrm{x} \rangle$, when going from the centre of the Brillouin zone to the zone boundary. Here, we show direct experimental access to this bulk band inversion in SSH exciton-polariton chains, using two-dimensional momentum-space ($k$-space) mapping - without the need for real-space imaging. This technique enables the direct observation of the momentum-dependent inversion of the sublattice symmetry in the bulk bands, providing a unique perspective on topological phases beyond conventional edge state measurements. Our approach establishes effective momentum-resolved sublattice phase measurements as a powerful tool for accessing the wave function and bulk topology in photonic and polaritonic systems and beyond.