Tomographic characterization of non-Hermitian Hamiltonians in reciprocal space

TL;DR

This paper introduces an experimental photonic platform for simulating non-Hermitian Hamiltonians via quantum walks, enabling direct tomographic reconstruction of their properties in reciprocal space, including band structures and exceptional points.

Contribution

It presents a novel method for directly accessing and reconstructing non-Hermitian Hamiltonians in reciprocal space using photonic quantum walks, advancing the study of non-Hermitian topological phenomena.

Findings

Successful reconstruction of complex band structures

Identification of exceptional points in momentum space

Detection of parity-time symmetry breaking

Abstract

Non-Hermitian Hamiltonians enrich quantum physics by extending conventional phase diagrams, enabling novel topological phenomena, and realizing exceptional points with potential applications in quantum sensing. Here, we present an experimental photonic platform capable of simulating a non-unitary quantum walk generated by a peculiar type of non-Hermitian Hamiltonian, largely unexplored in the literature. The novelty of this platform lies in its direct access to the reciprocal space, which enables us to scan the quasi-momentum across the entire Brillouin zone and thus achieve a precise tomographic reconstruction of the underlying non-Hermitian Hamiltonian, indicated by the comparison between theoretical predictions and experimental measurements. From the inferred Hamiltonian, it is possible to retrieve complex-valued band structures, resolve exceptional points in momentum space, and detect the associated parity-time symmetry breaking through eigenvector coalescence. Our results, presented entirely in quasi-momentum space, represent a substantial shift in perspective in the study of non-Hermitian phenomena.