The interplay between localization, quantum transport, and disorder is a central theme in physics. The traditional understanding, largely based on Anderson localization, posits that increasing disorder in one-dimensional systems leads to enhanced localization and a metal-insulator transition. However, recent theoretical work has challenged this view by predicting a reentrant localization transition in Su-Schrieffer-Heeger (SSH) chains with specific types of disorder, namely staggered quasiperiodic disorder and random-dimer disorder. This reentrant behavior implies that increasing disorder can initially localize states, then lead to a regime where both extended and localized states coexist, followed by a second localization phase with further disorder increase. This paper experimentally verifies this counterintuitive reentrant localization transition. The experimental platform leverages the advantages of integrated photonics, specifically using a photonic SSH lattice, allowing for precise control over the system parameters and enabling direct observation of wave function behavior. This provides a powerful and experimentally friendly approach to studying complex phenomena in condensed matter physics.

Anderson localization, first proposed by Philip W. Anderson, describes the absence of diffusive behavior in single-particle wave functions due to wave interference effects in disordered media, leading to a metal-insulator transition as disorder increases. Extensive research across various systems—electron gases, semiconductors, photonic lattices, and ultracold atoms—has confirmed this transition. In lower-dimensional systems (D ≤ 2), uncorrelated disorder typically leads to complete localization. However, quasiperiodic potentials can create an intermediate phase with coexisting extended and localized states, defined by a mobility edge. The traditional view held that the transition from extended to localized states was unidirectional. Recent theoretical studies, however, predicted and demonstrated the possibility of a reentrant localization transition in SSH chains with quasiperiodic or random-dimer disorder, suggesting the presence of both extended and localized states at intermediate disorder strengths.

The researchers employed a one-dimensional SSH model with random-dimer disorder, implemented experimentally using a fabricated Si3N4 waveguide array. Electron-beam lithography and reactive ion etching provided control over nearest-neighbor hopping amplitude, while waveguide width variations introduced a synthetic on-site potential. A Hamiltonian describing the SSH model with a bimodally distributed on-site potential was used. The on-site potential, ε, was tunable, allowing for probing various transport regimes. The localization-delocalization phase diagram was analyzed using the inverse participation ratio (IPR) and normalized participation ratio (NPR). These metrics quantify the extent of wave function localization. Specifically, the average IPR and NPR across the energy spectrum were calculated, with their simultaneous non-zero values indicating the coexistence of localized and extended states, a key characteristic of the reentrant localization transition. A parameter η, defined as log₁₀[(IPR) × (NPR)], further refined the identification of the coexistence regime. Experimentally, specific sites in the waveguide array were selectively excited, and the resulting light distribution at the array's end was imaged using a top imaging strategy. These intensity distributions were recorded for various disorder strengths (tuned via the on-site potential ε), allowing for extraction of the NPR and direct observation of the light transport regimes. The coupled mode theory was used to simulate the light propagation.

The experimental results showed a clear reentrant localization transition. The simulated light propagation patterns for different on-site potentials (ε = 0, 0.1, 0.185, and 0.3) revealed distinct behaviors. At low disorder (ε = 0), ballistic light propagation was observed. As disorder increased (ε = 0.1 and 0.3), the light became localized. However, at an intermediate disorder strength (ε = 0.185), a coexistence of localized and extended light was observed, indicating the reentrant localization. This observation aligns with numerical calculations of the spectral-averaged NPR, showing a non-monotonic behavior with a characteristic peak corresponding to the coexistence regime. The NPR values consistently showed this reentrant peak, even as the number of lattice sites was increased, confirming the robustness of the phenomenon. The experimental data on light intensity distribution closely matched the simulated patterns. The phase diagrams, both in the (Δ, ε) plane (dimerization parameter and on-site potential) and the (ε, p) plane (on-site potential and on-site probability), confirmed the existence and robustness of the reentrant localization region. The coexistence of localized and extended states was clearly observed.

The experimental observation of the reentrant localization transition validates recent theoretical predictions and provides a crucial step towards a more complete understanding of transport in disordered systems. The results demonstrate that the traditional view of a simple unidirectional metal-insulator transition is an oversimplification and highlight the importance of the interplay between disorder and other system parameters such as dimerization. The use of integrated photonics enabled high-precision control and direct observation of wave functions, offering a powerful tool for studying analogous phenomena in various other physical systems. This technique also opens up possibilities for exploring wave-packet manipulation for on-chip quantum state encoding.

This study successfully demonstrated the experimental observation of the reentrant metal-insulator transition in a one-dimensional disordered photonic SSH lattice. The precise control over system parameters and the direct wave function measurements offered by integrated photonics provided compelling evidence for this counterintuitive behavior. Future research could explore the influence of different disorder types, extend the study to higher dimensions, and investigate potential applications in quantum information processing and other areas of nanophotonics.

The study is limited to a specific model (SSH lattice with random-dimer disorder) and a particular experimental setup. While the results are robust within this context, generalizability to other systems with different types of disorder or lattice structures requires further investigation. The finite size of the experimental lattice might also affect the observation of the thermodynamic limit behavior. The experimental measurement of the light intensity distribution at the end of the lattice is an indirect measurement of the NPR, which introduces some level of uncertainty.