Many-body symmetry protected zero edge modes of synthetic photo-magnonic crystals

The ten-fold topological classification of free fermion systems, grounded on four many-body symmetries, has had a dramatic impact on many fields of physics. Therefore, it is important to investigate a similar approach for bosons. Here, we propose a self-contained theory of many-body symmetry-protected free boson topology based on three physical symmetries, namely time-reversal, particle number, and squeezing. We identify two symmetry classes that are topologically non-trivial in one dimension, and include systems with topologically-mandated and many-body symmetry-protected zero edge modes. These results are applicable to the bosonic Kitaev chain and the bosonic Su-Schriefffer-Heeger model.

To further support our theory, we introduce photo-magnonic crystals, and highlight their flexibility for engineering bosonic topological physics at microwave frequencies. We propose a one-dimensional crystal supporting topologically-mandated edge modes, as predicted by the theory. Using an electromagnetic finite-element modelling of the crystal we simulate the reflection and transmission, and identify the signatures of the edge mode. The engineering of the symmetry-protected phase is also discussed.