Nonchiral Non-Bloch Invariants and Topological Phase Diagram in Nonunitary Quantum Dynamics without Chiral Symmetry

The non-Bloch topology leads to the emergence of various counterintuitive phenomena in non-Hermitian systems under the open boundary condition, which can not find a counterpart in Hermitian systems. However, in the non-Hermitian system without chiral symmetry, being ubiquitous in nature, exploring its non-Bloch topology has so far eluded experimental effort. Here, by introducing the concept of nonchiral non-Bloch invariants, we theoretically predict and experimentally identify the non-Bloch topological phase diagram of a one-dimensional (1D) non-Hermitian system without chiral symmetry in discrete-time nonunitary quantum walks of single photons. Interestingly, we find that such topological invariants not only can distinguish topologically distinct gapped phases, but they also faithfully capture the corresponding gap closing in open-boundary spectrum at the phase boundary. Different topological regions are experimentally identified by measuring the featured discontinuities of the higher moments of the walker's displacement, which amazingly match excellently with our defined non-Bloch invariants. Our work provides a useful platform to study the interplay among topology, symmetries, and the non-Hermiticity.