Photonic Exceptional Points in Holography and QCD

TL;DR

The work builds a holographic QCD–inspired toy model to study photonic third-order exceptional points in a ternary resonator system by mapping gain/loss and inter-resonator couplings to a soft-wall AdS5 framework with flavor-brane dynamics. It demonstrates how EPs manifest as bulk spectral degeneracies tied to confinement-like end-walls, enables analytic results in symmetric-coupling limits, and tests spectral-weight conservation via an EP-aware Ferrell-Glover-Tinkham sum rule, including inhomogeneous lattice extensions. The study further connects EPs to timelike entanglement entropy and Kirkwood-Dirac-type distributions, and finally explores links between EPs and QCD topology through θ-vacua and winding numbers, finding a real second-order EP upon perturbation. Overall, the approach provides a unifying holographic perspective on non-Hermitian photonics, spectral phase transitions, and topological aspects of QCD, with potential implications for chaotic dynamics, edge states, and enhanced sensing in open quantum systems.

Abstract

In this work, based on an analogy of holographic confining geometries and using complexified fields, we build the 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, in our holographic model, 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.

Figures (28)

• Figure 1: The relationship between the real and imaginary parts of the eigenvalues versus frequency $f$ and the gain/loss parameter $\gamma$ is shown.
• Figure 2: A ternary system, consisting of three coupled microrings. On the left, a PT-symmetric and on the right, an anti-PT-symmetric system with dissipative coupling are depicted. This setup with single-mode operation could lead to various orders of exceptional points.
• Figure 3: Modeling EPs using flavor branes in the bulk, showing the couplings and where the exceptional point occurs along $z$.
• Figure 4: Two runs for finding eigenvalue trajectories in the complex plane as $\gamma$ is varied for the ternary coupled microcavity model (anti-PT sweep). In the left $N_z=20$ (grid points along holographic z) and in the right $N_z=200$.
• Figure 5: Two runs for finding imaginary parts versus $\gamma$ (growth rates of modes) for the ternary coupled microcavity model (anti-PT sweep). In the left $N_z=20$ (grid points along holographic z) and in the right $N_z=200$.