Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2511.06844

Observation of Non-Hermitian Spectral Deformation in Complex Momentum Space

Mu Yang, Yue Li, Mingtao Xu, Wei Yi, Jin-Shi Xu, Chuan-Feng Li, Guang-Can Guo

quant-phSubmitted Nov 10, 2025• Announced Nov 11, 2025
arXivHTMLPDF

Abstract

Open systems feature a variety of phenomena that arise from non-Hermitian physics. Recent theoretical studies have offered much insights into these phenomena through the non-Bloch band theory, though many of the theory's key features are experimentally elusive. For instance, the correspondence between complex momenta and non-Hermitian bands, while central to non-Bloch band theory, has so far defied direct experimental observation. Here we experimentally study the non-Hermitian spectral deformation in complex-momentum space, by implementing a non-Hermitian lattice with long-range couplings in the synthetic orbital-angular-momentum (OAM) dimension of photons inside a degenerate cavity. Encoding the complex momenta in the phase and amplitude modulations of the OAM modes, and devising a complex-momentum-resolved projective detection, we reconstruct the spectral deformation in momentum space, where the eigenspectrum on the complex plane morphs through distinct geometries. This enables us to experimentally extract key information of the system under the non-Bloch band theory, including exceptional points in the complex-momentum space, the open-boundary spectra, and the generalized Brillouin zone. Our work demonstrates a versatile platform for exploring non-Hermitian physics and non-Bloch band theory, and opens the avenue for direct experimental investigation of non-Bloch features in the complex-momentum space.

Related papers

Tomographic characterization of non-Hermitian Hamiltonians in reciprocal space

Francesco Di Colandrea, Fabrizio Pavan, Sarvesh Bansal +6 more

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.

quant-pharXiv:2512.09870•Dec 11, 2025

Optimal spectral transport of non-Hermitian systems

Mingtao Xu, Zongping Gong, Wei Yi

The optimal transport problem seeks to minimize the total transportation cost between two distributions, thus providing a measure of distance between them. In this work, we study the optimal transport of the eigenspectrum of one-dimensional non-Hermitian models as the spectrum deforms on the complex plane under a varying imaginary gauge field. Notably, according to the non-Bloch band theory, the deforming spectrum continuously connects the eigenspectra of the original non-Hermitian model (with vanishing gauge field) under different boundary conditions. It follows that the optimal spectral transport should contain key information of the model. Characterizing the optimal spectral transport through the Wasserstein metric, we show that, indeed, important features of the non-Hermitian model, such as the (auxiliary) generalized Brillouin zone, the non-Bloch exceptional point, and topological phase transition, can be determined from the Wasserstein-metric calculation. We confirm our conclusions using concrete examples. Our work highlights the key role of spectral geometry in non-Hermitian physics, and offers a practical and convenient access to the properties of non-Hermitian models.

arXiv:2501.15209•Physical review. B./Physical review. B•Jun 2, 2025•1 citation

Non-Bloch Quantum Geometry of Non-Hermitian Systems

Junsong Sun, Huaiming Guo, Bohm-Jung Yang

We formulate quantum geometry for non-Hermitian systems under open boundary conditions. By defining quantum-geometric quantities in both real-space and non-Bloch representations, we establish a unified framework beyond conventional Bloch band theory. Our central result is an exact equivalence between the real-space integrated quantum metric and a non-Bloch integrated quantum metric defined on the generalized Brillouin zone. We further introduce localized non-Bloch Wannier functions in the presence of the non-Hermitian skin effect and show that the non-Bloch integrated quantum metric gives the gauge-invariant part of their spread functional. These results establish quantum geometry as a natural framework for characterizing open-boundary non-Hermitian band structures and the localization properties encoded in skin modes.

cond-mat.mes-hallCross-listedarXiv:2605.19272•May 20, 2026•0 citations

Momentum-Space Path Integral Approach to Non-Hermitian Symmetry Breaking

Zhuo-Ting Cai, Wei Chen

A quantum-classical correspondence for non-Hermitian symmetry breaking has recently been established using coordinate-space path integrals, providing a semiclassical understanding of spectral transitions at the level of individual eigenstates. Here we develop its dual formulation in momentum space by constructing the corresponding trace formula and quantization condition. We show that the real or complex nature of individual eigenvalues is determined by the symmetry properties of the associated semiclassical orbits, as in the coordinate-space path-integral approach. Moreover, we demonstrate that the topology of semiclassical orbits determines the natural formulation of the quantization condition: the coordinate- and momentum-space formulations are equivalent for contractible periodic orbits in phase space, whereas for noncontractible orbits, the quantization condition along the winding direction remains valid, but its dual form must be corrected by a boundary term. In particular, real-space-winding and Brillouin-zone-winding orbits naturally select coordinate- and momentum-space quantization, respectively. As a nontrivial application, we investigate the boundary-induced spectral transition of Bloch oscillations in a finite non-Hermitian lattice, where Bloch-oscillation orbits winding across the Brillouin zone preserve the relevant symmetry and yield real energy levels, whereas boundary-reflected orbits form symmetry-related pairs and give rise to complex-conjugate eigenvalues. Our work completes the quantum-classical correspondence framework for non-Hermitian symmetry breaking, extending its applicability to a broader class of non-Hermitian problems.

quant-pharXiv:2610.05702•Oct 6, 2026

Non-Bloch band theory for finite banded non-Hermitian Toeplitz matrices

Yannick De Bruijn, Erik Orvehed Hiltunen

Non-Bloch band theory recovers the open-boundary spectrum of a non-Hermitian chain from its Bloch Hamiltonian evaluated along the generalised Brillouin zone rather than the unit circle. We develop its finite-size counterpart for banded Toeplitz matrices with real open-boundary spectrum. Reality of the spectrum forces the generalised Brillouin zone to be parametrised by an analytic polar curve, so the known sufficient condition for a real spectrum is also necessary under some mild non-degeneracy conditions. At finite size $n$, the eigenvalues of the original and the symmetrised Bloch Hamiltonians are given by samples at $n$ quantised momenta from the same limiting band, although separated by a phase mismatch of order $1/n$ which we obtain in closed form. Iterating this correction $K$ times yields a quantisation rule on the generalised Brillouin zone reproducing the finite spectrum with an error $\mathcal{O}(n^{-K-1})$ for any fixed $K$. At finite size, the generalised Brillouin zone itself is unchanged and only its parametrisation depends on $n$.

arXiv:2610.13715•Oct 9, 2026•0 citations

Spatiotemporal Topological Phase Transition in non-Hermitian Photonic System

Zimeng Zeng, Zhuoyang Li, Jiayao Liu +2 more

While energy band topology in spatial photonic crystals (PCs) and momentum-band topology in temporal crystals have each served as powerful probes of topological phases in their respective domains, their unification in a static platform remains unexplored. In this Letter, we bridge this gap by introducing a waveguide assisted non-Hermitian SSH model, in which controlled tuning of loss and coupling drives PT-symmetry breaking and enables a continuous transition between energy- and momentum-gap regimes. This allows us to construct a complete spatiotemporal topological phase diagram in a unified parameter space. By mapping this phase diagram onto a spatially graded PC, we experimentally observe multiple Bloch momentum-band gaps and a continuous spatiotemporal topological transition via translating across the static sample, enabling real-time control over the evolution pathway of the band topology. Our work creates a versatile, bias-free platform for exploring synthetic spacetime physics and opens new avenues for controlling light via non-Hermitian band engineering.

physics.opticsCross-listedarXiv:2602.05475•Feb 6, 2026
Open systems feature a variety of phenomena that arise from non-Hermitian physics. Recent theoretical studies have offered much insights into these phenomena through the non-Bloch band theory, though many of the theory's key features are experimentally elusive. For instance, the correspondence between complex momenta and non-Hermitian bands, while central to non-Bloch band theory, has so far defied direct experimental observation. Here we experimentally study the non-Hermitian spectral deformation in complex-momentum space, by implementing a non-Hermitian lattice with long-range couplings in the synthetic orbital-angular-momentum (OAM) dimension of photons inside a degenerate cavity. Encoding the complex momenta in the phase and amplitude modulations of the OAM modes, and devising a complex-momentum-resolved projective detection, we reconstruct the spectral deformation in momentum space, where the eigenspectrum on the complex plane morphs through distinct geometries. This enables us to experimentally extract key information of the system under the non-Bloch band theory, including exceptional points in the complex-momentum space, the open-boundary spectra, and the generalized Brillouin zone. Our work demonstrates a versatile platform for exploring non-Hermitian physics and non-Bloch band theory, and opens the avenue for direct experimental investigation of non-Bloch features in the complex-momentum space.
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.
The optimal transport problem seeks to minimize the total transportation cost between two distributions, thus providing a measure of distance between them. In this work, we study the optimal transport of the eigenspectrum of one-dimensional non-Hermitian models as the spectrum deforms on the complex plane under a varying imaginary gauge field. Notably, according to the non-Bloch band theory, the deforming spectrum continuously connects the eigenspectra of the original non-Hermitian model (with vanishing gauge field) under different boundary conditions. It follows that the optimal spectral transport should contain key information of the model. Characterizing the optimal spectral transport through the Wasserstein metric, we show that, indeed, important features of the non-Hermitian model, such as the (auxiliary) generalized Brillouin zone, the non-Bloch exceptional point, and topological phase transition, can be determined from the Wasserstein-metric calculation. We confirm our conclusions using concrete examples. Our work highlights the key role of spectral geometry in non-Hermitian physics, and offers a practical and convenient access to the properties of non-Hermitian models.
We formulate quantum geometry for non-Hermitian systems under open boundary conditions. By defining quantum-geometric quantities in both real-space and non-Bloch representations, we establish a unified framework beyond conventional Bloch band theory. Our central result is an exact equivalence between the real-space integrated quantum metric and a non-Bloch integrated quantum metric defined on the generalized Brillouin zone. We further introduce localized non-Bloch Wannier functions in the presence of the non-Hermitian skin effect and show that the non-Bloch integrated quantum metric gives the gauge-invariant part of their spread functional. These results establish quantum geometry as a natural framework for characterizing open-boundary non-Hermitian band structures and the localization properties encoded in skin modes.
A quantum-classical correspondence for non-Hermitian symmetry breaking has recently been established using coordinate-space path integrals, providing a semiclassical understanding of spectral transitions at the level of individual eigenstates. Here we develop its dual formulation in momentum space by constructing the corresponding trace formula and quantization condition. We show that the real or complex nature of individual eigenvalues is determined by the symmetry properties of the associated semiclassical orbits, as in the coordinate-space path-integral approach. Moreover, we demonstrate that the topology of semiclassical orbits determines the natural formulation of the quantization condition: the coordinate- and momentum-space formulations are equivalent for contractible periodic orbits in phase space, whereas for noncontractible orbits, the quantization condition along the winding direction remains valid, but its dual form must be corrected by a boundary term. In particular, real-space-winding and Brillouin-zone-winding orbits naturally select coordinate- and momentum-space quantization, respectively. As a nontrivial application, we investigate the boundary-induced spectral transition of Bloch oscillations in a finite non-Hermitian lattice, where Bloch-oscillation orbits winding across the Brillouin zone preserve the relevant symmetry and yield real energy levels, whereas boundary-reflected orbits form symmetry-related pairs and give rise to complex-conjugate eigenvalues. Our work completes the quantum-classical correspondence framework for non-Hermitian symmetry breaking, extending its applicability to a broader class of non-Hermitian problems.
Non-Bloch band theory recovers the open-boundary spectrum of a non-Hermitian chain from its Bloch Hamiltonian evaluated along the generalised Brillouin zone rather than the unit circle. We develop its finite-size counterpart for banded Toeplitz matrices with real open-boundary spectrum. Reality of the spectrum forces the generalised Brillouin zone to be parametrised by an analytic polar curve, so the known sufficient condition for a real spectrum is also necessary under some mild non-degeneracy conditions. At finite size nnn, the eigenvalues of the original and the symmetrised Bloch Hamiltonians are given by samples at nnn quantised momenta from the same limiting band, although separated by a phase mismatch of order 1/n1/n1/n which we obtain in closed form. Iterating this correction KKK times yields a quantisation rule on the generalised Brillouin zone reproducing the finite spectrum with an error O(n−K−1)\mathcal{O}(n^{-K-1})O(n−K−1) for any fixed KKK. At finite size, the generalised Brillouin zone itself is unchanged and only its parametrisation depends on nnn.
While energy band topology in spatial photonic crystals (PCs) and momentum-band topology in temporal crystals have each served as powerful probes of topological phases in their respective domains, their unification in a static platform remains unexplored. In this Letter, we bridge this gap by introducing a waveguide assisted non-Hermitian SSH model, in which controlled tuning of loss and coupling drives PT-symmetry breaking and enables a continuous transition between energy- and momentum-gap regimes. This allows us to construct a complete spatiotemporal topological phase diagram in a unified parameter space. By mapping this phase diagram onto a spatially graded PC, we experimentally observe multiple Bloch momentum-band gaps and a continuous spatiotemporal topological transition via translating across the static sample, enabling real-time control over the evolution pathway of the band topology. Our work creates a versatile, bias-free platform for exploring synthetic spacetime physics and opens new avenues for controlling light via non-Hermitian band engineering.