Abstract
Parity-time (PT)-symmetric Hamiltonians have widespread significance in non-Hermitian physics. A PT-symmetric Hamiltonian can exhibit distinct phases with either real or complex eigenspectrum, while the transition points in between, the so-called exceptional points, give rise to a host of critical behaviors that holds great promise for applications. For spatially periodic non-Hermitian systems, PT symmetries are commonly characterized and observed in line with the Bloch band theory, with exceptional points dwelling in the Brillouin zone. Here, in nonunitary quantum walks of single photons, we uncover a novel family of exceptional points beyond this common wisdom. These "non-Bloch exceptional points" originate from the accumulation of bulk eigenstates near boundaries, known as the non-Hermitian skin effect, and inhabit a generalized Brillouin zone. Our finding opens the avenue toward a generalized PT-symmetry framework, and reveals the intriguing interplay between PT symmetry and non-Hermitian skin effect.
Highlights
Parity-time (PT)-symmetric Hamiltonians have widespread significance in nonHermitian physics
Physical systems with PT symmetry are often based on spatially periodic structures [2, 13], where the notion of Bloch band greatly simplifies their characterization as each Bloch wave is treated independently
Whereas topological physics has been the focus in previous studies [19,20,21,22,23,24], a fundamental question remains whether the non-Hermitian skin effect has significant consequences beyond topology, among which the interplay of non-Hermitian skin effect and PT symmetry is arguably the most intriguing [25, 26]
Summary
For spatially periodic non-Hermitian systems, PT symmetries are commonly characterized and observed in line with the Bloch band theory, with exceptional points dwelling in the Brillouin zone. In non-unitary quantum walks of single photons, we uncover a novel family of exceptional points beyond this common wisdom. These “non-Bloch exceptional points” originate from the accumulation of bulk eigenstates near boundaries, known as the non-Hermitian skin effect, and inhabit a generalized Brillouin zone. Just as the framework with conventional Bloch bands has been universally adopted to describe periodic lattices in physical systems ranging from condensed matter to photonics, the generalized mechanism of PT symmetry, confirmed by our observation of “non-Bloch exceptional points”, is universally relevant to non-Hermitian platforms.
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