Recently, the research team led by Prof. Xue Peng and Associate Researcher Wang Shulin from the School of Physics, SEU, in collaboration with Prof. Stefano Longhi from Politecnico di Milano in Italy, has made new progress in non-Hermitian anomalous scaling and its manipulation. The related findings were published in Physical Review Letters, a top-tier physics journal in the United States, under the title “Non-Hermitian anomalous scaling engineering.”
The non-Hermitian skin effect (NHSE) refers to the phenomenon in which all eigenstates of an asymmetrically coupled lattice are localized at the boundary. This effect challenges the bulk–boundary correspondence, a cornerstone concept in conventional topological physics, and has thus attracted extensive attention in recent years. Beyond its conceptual breakthroughs, the NHSE also exhibits unique application value, particularly in the field of optics. For instance, leveraging the boundary-localized nature of the NHSE, researchers have designed a topological optical funnel for highly robust energy harvesting; exploiting the interplay between the NHSE and nonlinear self-localization, they have also realized nonlinear optical routing with flexibly tunable output ports. However, since real physical systems are generally finite in size, the impact of system dimensions must be considered when constructing practical devices based on these application paradigms. Therefore, clarifying the scaling law of the NHSE is of great significance for the development of real-world devices. In recent years, theoretical physicists have discovered that the NHSE exhibits unconventional anomalous scaling behavior. In the presence of the NHSE, the system-size scaling can significantly alter the energy spectrum and eigenstate distribution, and can even induce topological phase transitions—a stark contrast to the nearly invariant energy spectrum and eigenstate distribution observed in conventional Hermitian systems. Nevertheless, due to the lack of an experimentally accessible platform that is both easy to reconfigure and amenable to probing, robust experimental evidence for the anomalous scaling behavior of the NHSE remains elusive. Moreover, as an important branch of the NHSE, the scaling behavior of the nonlinear NHSE also awaits further investigation.
Fig. 1. (a) Schematic diagram of the construction principle of the temporal photonic lattice. The temporal photonic lattice is constructed based on time-division multiplexing of optical pulses in a dual-fiber-loop system. Its evolution dimension is given by the number of round trips,m, that the optical pulse travels in the loops, and its transverse dimensionn is determined by the position of the pulse within the pulse sequence in each round. The two ends of the lattice are labeled as−N andN, which are connected via an additional coupling. (b) and (c): Simulated and experimental results of eigenstate evolution under different lattice lengths.
The research team constructed a nonlinear non-Hermitian temporal photonic lattice based on a dual-fiber-loop system with optoelectronic feedforward circuitry, successfully verifying the non-Hermitian anomalous scaling law in the presence of the NHSE and its nonlinear manipulation. To observe the non-Hermitian anomalous scaling phenomenon, the team built two fiber loops with slightly different lengths connected by a coupler. Through time-division multiplexing of optical pulses in the loops, they equivalently constructed a discrete photonic lattice in the time domain, as illustrated in Fig. 1 (a). In addition, by introducing gain and loss into the two fiber loops respectively, they created the asymmetric coupling required for realizing the NHSE in the temporal lattice. By coupling the two ends of the lattice together, they further implemented generalized boundary conditions that are more versatile than conventional open and periodic boundary conditions. Taking advantage of the temporal photonic lattice's ease of reconfiguration and detection, they monitored the real-time evolution of all eigenstates under different system sizes, thereby experimentally directly verifying the anomalous changes in the energy spectrum and eigenstate distribution induced by lattice scaling.
Fig. 2 (a) and (b): Inverse participation ratio (IPR) of nonlinear eigenmodes as a function of lattice length under weak Kerr nonlinearity and strong Kerr nonlinearity, respectively.
As shown in Figs. 1 (b) and 1(c), when the system size is small, the energy spectrum is entirely real, and the eigenstates maintain their intensity during propagation. As the system size increases, however, the emergence of imaginary parts in the spectrum enables the eigenstates to be continuously amplified during propagation. In addition, increasing the lattice length reduces the localization intensity of the eigenstates. Subsequently, the research team introduced Floquet modulation on the coupling (i.e., assigning different coupling coefficients to even and odd round trips) into the temporal photonic lattice, thereby constructing a Su-Schrieffer-Heeger (SSH)-type lattice system with topological characteristics. The team found that scaling the lattice length can induce a non-Hermitian topological phase transition. Finally, by embedding optoelectronic feedforward circuitry into the fiber loops, they equivalently introduced Kerr nonlinearity. As shown in Figure 2(a), the self-focusing and self-defocusing effects under weak nonlinearity can respectively increase or decrease the inverse participation ratio (i.e., the localization intensity) of the eigenmode intensity envelope, thereby effectively accelerating or decelerating the anomalous scaling behavior in the presence of the NHSE. Strong nonlinearity, on the other hand, can completely break this scaling behavior [Fig. 2(b)]. This work experimentally elucidates the anomalous scaling law in the presence of the NHSE, providing important guidance for the design of photonic devices based on the NHSE.
Associate Researcher Wang Shulin from the School of Physics, SEU, is the first author of this paper. Prof. Xue Peng from the School of Physics, SEU, and Prof. Stefano Longhi from Politecnico di Milano, Italy, are the corresponding authors. This work was supported by the National Key Research and Development Program of China and the National Natural Science Foundation of China.
Paper’s link:https://doi.org/10.1103/39t1-94yh
Source: School of Physics, SEU
Translated by: Melody Zhang
Edited by: Leah Li
