Probing $PT$-Symmetry Breaking of Non-Hermitian Topological Photonic States via Strong Photon-Magnon Coupling

Light-matter interaction is crucial to both understanding fundamental phenomena and developing versatile applications. Strong coupling, robustness, and controllability are the three most important aspects in realizing light-matter interactions. Topological and non-Hermitian photonics have provided frameworks for robustness and control flexibility, respectively. How to engineer the properties of the edge state such as photonic density of state by using non-Hermiticity while ensuring topological protection has not been fully studied. Here we construct a parity-time-symmetric dimerized photonic lattice and probe the spontaneous $PT$-symmetry breaking of the edge states by utilizing the strong coupling between the photonic mode and a spin ensemble. Our Letter presents an accurate and almost noninvasive approach for investigating non-Hermitian topological states, while also offering methodologies for the implementation and manipulation of topological light-matter interactions.

Figure 1

(a),(b) Schematic of the Hermitian and non-Hermitian SSH chains. (c),(e) Eigenmodes of the Hermitian and non-Hermitian SSH chain plotted in the complex energy plane. (d),(f) Transmission spectra of the Hermitian and non-Hermitian SSH chains. The solid curves are the measured spectra, and the dashed curves show the simulation results by utilizing the electromagnetic simulation and analysis software CST Studio Suite.

Figure 2

Photograph of the Hermitian SSH chain. The chain contains six unit cells and twelve SRRs. The SRRs are labeled by a site index $s$. The YIG sphere is placed on the top of the device. (b),(e) The mappings of the transmission spectra are plotted versus the electromagnet current and probe frequency when a YIG sphere is placed at site 1 and site 12, respectively. Strong coupling between the edge (bulk) mode and the magnon mode is indicated by the large (small) level repulsion. The squares of the coupling strengths (c) $g_{m,s}^2$ ($m=8$, bulk state, blue dots) and (d) $g_{m,s}^2$ ($m=6$,7, edge states, red dots) are extracted when the YIG sphere is positioned at the $s$th site, where $m$ is the eigenmode index. The gray bars represent the intensity distributions of wave function $|{\phi }_{m,s}{|}^2$.

Figure 3

Photograph of the non-Hermitian SSH chain. The integrated resistors induce on site losses. (b),(e) When the YIG sphere is placed at site 1 and site 12, respectively, the mappings of the transmission spectra are plotted versus the electromagnet current and probe frequency. Strong coupling between the edge (bulk) mode and the magnon mode is indicated by the large (small) level repulsion. At the bulk-mode frequency, the data measured at site 1 and site 12 are completely symmetric, which is reflected in both the coupling strength and the linewidth of the hybridized modes. Owing to the SPTB of the edge mode, the coupling strengths measured at the edge-mode frequency are still symmetric, but the linewidths of the hybridized modes become different. The squares of the coupling strengths (c) $g_{8,s}^2$ (blue dots) and (d) $g_{m,s}^2$ ($m=6$,7, blue and red dots respectively) are plotted versus site index $s$. The intensity distributions of wave function $|{\phi }_{m,s}{|}^2$ are denoted by gray ($m=8$, bulk mode), blue ($m=6$, low-loss edge state), and red ($m=7$, high-loss edge state) bar diagrams.

Figure 4

(a),(b) The measured absorptivity spectra for both Hermitian and non-Hermitian SSH chains, where $\delta \gamma /2(w+v)=0$ and 0.034, respectively. ${\mathrm{A}}_1$ (${\mathrm{A}}_2$) is measured when loading signal to port 1 (2), as shown by the blue (red) curve. (c),(d) The real and imaginary parts of normalized eigenvalues, which are plotted versus $\delta \gamma /2(w+v)$. The inset between (a) and (b) shows the $PT$-symmetry spontaneous breaking point (${\mathrm{EP}}_1$) of the edge states. The EPs divide the system into three representative regions, as labeled by regions I, II, and III [42].