Non-Hermitian topological microwave photonics with synthetic non-Abelian gauges. (arXiv:1812.02610v1 [quant-ph])

Topological phases in spinless non-Hermitian models have been widely studied
both theoretically and experimentally in some artificial materials using
photonics and photonics. In this work, we investigate the interplay between
non-Hermitian loss and gain and non-Abelian gauge potential realized in a
two-component superconducting circuit. In our model, the non-Hermiticity along
only gives rise to trivial gain and loss to the states; while the non-Abelian
gauge along gives rise to flying butterfly spectra and associated edge modes,
which in photonics can be directly measured by the intensity of photons at the
boundaries. These two terms do not commute, and their interplay can give rise
to several intriguing non-Hermitian phases, including the fully gapped quantum
spin Hall (QSH) phase, gapless QSH phase, trivial gapped phase and gapless
metallic phase. The bulk-edge correspondence is absent, and we find that during
the closing of energy gap in the gapped QSH phase, the system enters the
gapless QSH phase regime which still supports topological edge modes. Our
proposed model in this work has potential to be realized immediately, in
regarding of the huge progresses achieved in quantum computation based on
superconducting circuits.

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