Tomographic Characterization of Non-Hermitian Hamiltonians Enables Reconstruction of Complex-Valued Band Structures in Reciprocal Space
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Non-Hermitian Hamiltonians are expanding the boundaries of modern physics, promising new topological states of matter and unique phenomena like exceptional points with potential technological applications.
Francesco Di Colandrea, Fabrizio Pavan, and Sarvesh Bansal, alongside colleagues Paola Savarese, Grazia Di Bello, and Giulio De Filippis, have developed a photonic platform that directly simulates these complex systems. This innovative approach provides unprecedented access to the reciprocal space, allowing the team to map the behaviour of non-Hermitian Hamiltonians with exceptional precision, effectively creating a tomographic reconstruction of their properties. The results reveal complex band structures, pinpoint exceptional points within momentum space, and detect the breakdown of parity-time symmetry, representing a significant advance in understanding these increasingly important physical systems.
Quantum Walk Experiments, Setup and Tomography Routines This document details the experimental methods and analysis techniques used to investigate non-Hermitian Hamiltonians using quantum walks. It provides a comprehensive overview of the experimental setup, data processing, and supplementary results not included in the main publication, focusing on understanding how these systems behave and how their properties can be accurately measured. The document is organized into three main sections: a description of the experimental setup, an explanation of the process used to reconstruct the system’s properties from measured data, and a presentation of additional experimental results. Each section provides detailed information necessary for understanding the research. The experimental setup utilizes a laser source, specialized optics, and liquid crystal metasurfaces to implement the quantum walk. These metasurfaces control the polarization of light, acting as the building blocks for simulating the quantum system, with precise control over birefringence and dichroism achieved through applied voltage allowing for fine-tuning of the system’s properties.
The team employed a process tomography routine, a mathematical procedure used to reconstruct the system’s Hamiltonian from measured polarization data. This involves defining a cost function that quantifies the difference between experimental data and theoretical predictions, and then minimizing this function to find the best-fit parameters, with constraints applied to ensure the physical validity of the results. Supplementary data includes additional experimental results for different parameter settings, tomographic reconstructions of energy bands and polarization eigenstates, and measurements of the winding number, validating the accuracy of the experimental setup and data analysis methods. Non-Hermitian Quantum Walks on Photonic Platforms Scientists engineered a novel photonic platform to simulate a non-unitary quantum walk governed by a specifically designed non-Hermitian Hamiltonian, directly accessing and reconstructing the Hamiltonian in reciprocal space to enable precise characterization of non-Hermitian phenomena.
The team designed the Hamiltonian to feature complex coupling coefficients between sites, introducing a non-unitary evolution and defining the non-Hermitian character of the system, allowing for the investigation of non-Hermitian effects beyond those typically observed in other models. To fully characterize the system, scientists scanned the quasi-momentum across the entire Brillouin zone, achieving a tomographic reconstruction of the underlying non-Hermitian Hamiltonian, validated through a direct comparison between theoretical predictions and experimental measurements. From the inferred Hamiltonian, the team retrieved complex-valued band structures, resolved exceptional points in momentum space, and detected parity-time symmetry breaking through eigenvector coalescence, demonstrating the platform’s capability to explore fundamental aspects of non-Hermitian physics, and offering a powerful tool for advancing quantum sensing and topological matter research. Non-Hermitian Hamiltonian Reconstruction via Quantum Walk Scientists have developed a photonic platform capable of simulating a non-Hermitian Hamiltonian and have achieved precise tomographic reconstruction of its underlying properties, utilizing a quantum walk to simulate complex lattice Hamiltonians and investigate non-Hermitian dynamics and topological phenomena. Experiments reveal a well-defined topological characterization of the Hamiltonian, demonstrated by a discontinuous jump in the winding number, which allowed reconstruction of the complete phase diagram, and identified critical quasi-momentum values where exceptional points appear, signifying a fundamental change in the system’s behavior. Measurements confirm the existence of spontaneous parity-time (PT) symmetry breaking within the Hamiltonian, a phenomenon where the balance between gain and loss is disrupted.
The team’s tomographic protocol establishes the properties of the non-Hermitian model implemented in the platform, revealing a complex interplay between topology, sublattice symmetry, and PT symmetry, and demonstrating a significant advancement unavailable in other implementations like transmon qubits or trapped ions, delivering a new capability for investigating non-Hermitian physics and exploring complex quantum phenomena. Non-Hermitian Physics via Photonic Simulation This research demonstrates a new photonic platform for simulating and exploring non-Hermitian Hamiltonians, systems that extend conventional physics by allowing for unusual topological phenomena and exceptional points, successfully creating an experimental setup with precise control over system parameters, enabling detailed reconstruction of the underlying Hamiltonian through measurements in reciprocal space. The platform allows for the mapping of complex-valued band structures, the identification of exceptional points in momentum space, and the observation of parity-time symmetry breaking through the coalescence of eigenstates, accurately characterizing the system and determining its topological invariant, confirming the platform’s ability to probe fundamental properties. Future work will focus on tracking dynamical observables to further investigate the winding number and exploring the behaviour of Liouvillian exceptional points and thermodynamic features across phase transitions, paving the way for a deeper understanding of non-Hermitian physics and its potential applications in quantum technologies. 👉 More information 🗞 Tomographic characterization of non-Hermitian Hamiltonians in reciprocal space 🧠 ArXiv: https://arxiv.org/abs/2512.09870 Tags: