Photonic Exceptional Points in Holography and QCD

In this work, based on an analogy with holographic confining geometries and using complexified fields, we build a holographic toy model of third order photonic exceptional points (EPs) of ternary coupled microrings with gain and loss, which makes an open, non-Hermitian quantum system. In our model, we discuss the Ferrell-Glover-Tinkham sum rule for various combinations of gain and loss systems, and numerically find the behavior of spectra which matches with the experiments. We also discuss the inhomogeneous case of a holographic lattice for three-site photonic EPs. Additionally, we numerically find the behavior of phase rigidity and the Petermann factor around EPs versus various parameters of the model. We also discuss the connections between recent developments in complexified, time-dependent entanglement entropy and EPs, and finally, we connect EPs and the $θ$-vacuum of QCD through topological structures, partition functions, and winding numbers, and find a second-order EP in a perturbed $θ$-vacuum model.

💡 Research Summary

This paper establishes a novel interdisciplinary bridge between non‑Hermitian photonics, holographic models of confinement, and the topological aspects of quantum chromodynamics (QCD). The authors start from an experimentally realized ternary microring system that exhibits a third‑order photonic exceptional point (EP) when gain and loss are appropriately balanced. The dynamics of the three coupled resonators are encoded in a 3 × 3 non‑Hermitian Hamiltonian containing resonance frequencies (ω₁‑₃), gain/loss parameters (λ₁‑₃) and a symmetric coupling constant κ. By tuning these parameters the eigenvalues coalesce at a third‑order branch point, producing a single‑mode laser with distinctive spectral signatures.

To map this optical setup onto a holographic framework, the authors construct a bottom‑up five‑dimensional AdS model with three flavor branes representing the three microrings. The bulk metric ds² = (R²/z²)(η_{μν}dx^μdx^ν + dz²) is supplemented by a soft‑wall dilaton profile ϕ(z)=κ²z², which mimics the gain‑loss background. Off‑diagonal components of the bulk gauge field strength F_{MN} or interaction terms involving a scalar X encode the inter‑resonator coupling and the PT/anti‑PT symmetry. Complex bulk masses and couplings are introduced solely as computational devices to reproduce non‑Hermitian effects on the boundary; no claim is made about a fundamentally non‑Hermitian gravity theory.

The holographic analysis reveals that the “end‑wall” (the UV cutoff in the bulk) plays a role analogous to the EP in the photonic system. In both cases a critical parameter value triggers a phase transition: PT symmetry breaking in the optical device and confinement–deconfinement transition in the holographic QCD model. Near the EP the bulk wavefunctions lose their norm, the spectral lines coalesce, and the corresponding spectral weight (analogous to a meson decay constant) spikes, mirroring the behavior of nuclei near drip lines.

A major part of the work is devoted to testing the Ferrell‑Glover‑Tinkham (FGT) sum rule in a non‑Hermitian context. Numerical integration of the optical conductivity shows that, despite asymmetric gain/loss, the total spectral weight remains conserved across the EP, indicating that sum‑rule conservation can survive non‑Hermitian perturbations.

The authors also compute phase rigidity and the Petermann factor as functions of the EP parameters. Phase rigidity collapses to zero while the Petermann factor diverges, confirming the expected extreme sensitivity and linewidth narrowing of lasers operating at EPs. Time‑dependent entanglement entropy is evaluated using a complexified evolution operator; the entropy growth rate exhibits a sharp kink at the EP, reflecting a rapid redistribution of quantum information in non‑Hermitian dynamics.

In the QCD sector, the paper introduces a non‑Hermitian deformation of the θ‑vacuum. By complexifying the θ angle and adding a small angular coupling, the authors numerically locate a second‑order EP in the spectrum of the θ‑vacuum model. This EP is characterized by a coalescence of two topological sectors distinguished by winding numbers, offering a fresh perspective on the strong CP problem and on how topological vacua may undergo non‑Hermitian phase transitions.

The inhomogeneous case is explored through a holographic lattice of three sites, where spatially varying gain/loss patterns generate a “holographic lattice EP”. The presence of both an end‑wall and an EP enhances chaotic indicators, suggesting that EPs can serve as proxies for confinement walls in holographic QCD.

Overall, the paper delivers a comprehensive theoretical framework that maps third‑order photonic EPs onto critical points in holographic confinement models and further extends the analogy to topological structures in QCD. By systematically analyzing spectra, sum rules, phase rigidity, Petermann factors, entanglement entropy, and winding numbers, the authors demonstrate that disparate physical systems share a common mathematical structure centered on exceptional points. This work opens new avenues for cross‑disciplinary research, suggesting that experimental photonic platforms could be used to simulate and probe non‑perturbative QCD phenomena, while holographic insights may guide the design of next‑generation non‑Hermitian photonic devices.