Tomographic characterization of non-Hermitian Hamiltonians in reciprocal space

Francesco Di Colandrea; Fabrizio Pavan; Sarvesh Bansal; Paola Savarese; Grazia Di Bello; Giulio De Filippis; Carmine Antonio Perroni; Donato Farina; Filippo Cardano

arXiv · 2512.09870

Tomographic characterization of non-Hermitian Hamiltonians in reciprocal space

Francesco Di Colandrea·Fabrizio Pavan·Sarvesh Bansal·Paola Savarese·Grazia Di Bello·Giulio De Filippis·Carmine Antonio Perroni·Donato Farina·Filippo Cardano

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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.

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Francesco Di Colandrea, Fabrizio Pavan, Sarvesh Bansal, Paola Savarese, Grazia Di Bello, Giulio De Filippis, Carmine Antonio Perroni, Donato Farina, Filippo Cardano. 2025-12-10. Tomographic characterization of non-Hermitian Hamiltonians in reciprocal space. https://arxiv.org/abs/2512.09870

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