Energy density as a probe of band representations in photonic crystals.

Topological quantum chemistry (TQC) has recently emerged as an instrumental tool to characterize the topological nature of both fermionic and bosonic band structures. TQC is based on the study of band representations and the localization of maximally localized Wannier functions. In this article, we study various two-dimensional photonic crystal structures analyzing their topological character through a combined study of TQC, their Wilson-loop (WL) spectra and the electromagnetic energy density. Our study demonstrates that the analysis of the spatial localization of the energy density complements the study of the topological properties in terms of the spectrum of the WL operator and TQC.

Quantum Simulation of the Bosonic Creutz Ladder with a Parametric Cavity.

There has been a growing interest in realizing quantum simulators for physical systems where perturbative methods are ineffective. The scalability and flexibility of circuit quantum electrodynamics make it a promising platform for implementing various types of simulators, including lattice models of strongly coupled field theories. Here, we use a multimode superconducting parametric cavity as a hardware-efficient analog quantum simulator, realizing a lattice in synthetic dimensions with complex hopping interactions. The coupling graph, i.e., the realized model, can be programmed in situ. The complex-valued hopping interaction further allows us to simulate, for instance, gauge potentials and topological models. As a demonstration, we simulate a plaquette of the bosonic Creutz ladder. We characterize the lattice with scattering measurements, reconstructing the experimental Hamiltonian and observing important precursors of topological features including nonreciprocal transport and Aharonov-Bohm caging. This platform can be easily extended to larger lattices and different models involving other interactions.