Topology with broken parity-time symmetry

Abstract

Topological edge states arise in parity-time ($\mathcal{P}\mathcal{T}$)-symmetric non-unitary quantum dynamics but have so far only been discussed in the $\mathcal{P}\mathcal{T}$-symmetry-unbroken regime. Here we report the experimental detection of robust topological edge states in one-dimensional photonic quantum walks with spontaneously broken $\mathcal{P}\mathcal{T}$ symmetry, thus establishing the existence of topological phenomena therein. We theoretically prove and experimentally confirm that the global Berry phase in non-unitary quantum-walk dynamics unambiguously defines topological invariants of the system in both the $\mathcal{P}\mathcal{T}$-symmetry-unbroken and broken regimes. As topological edge states exist in both $\mathcal{P}\mathcal{T}$ unbroken and broken regimes, we reveal that topological phenomena are not driven by $\mathcal{P}\mathcal{T}$ symmetry.

arXiv comment15 pages, 7 figures

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