Floquet SSH Model Hosts Anomalous Edge States with Defined Quasienergies

The behaviour of light within carefully designed structures can reveal surprising quantum phenomena, and researchers are increasingly exploring how periodic, or ‘Floquet’, driving influences these effects. Changsen Li, Yujie Zhou, and colleagues at Nanjing University of Posts and Telecommunications, along with Xingping Zhou et al., have now demonstrated a novel system exhibiting a three-period evolution of light, extending beyond the more commonly observed two-period dynamics. They achieve this by constructing a unique waveguide array based on a modified Su-Schrieffer-Heeger model, incorporating both periodic driving and long-range couplings between light pathways. This innovative design gives rise to anomalous edge states with unusual quasienergies, and the team confirms through simulation that these states underpin the observed three-period behaviour, potentially opening new avenues for manipulating light in quantum technologies and exploring more complex periodic dynamics.

Periodic driving can induce the emergence of topological modes, and their superposition with zero modes leads to two-period dynamics. Introducing long-range couplings enables the realization of larger topological winding numbers, which correspond to multiple pairs of degenerate edge states under open boundary conditions. In this work, researchers construct a Floquet extended Su-Schrieffer-Heeger (SSH) model by introducing a two-step periodic driving and next-nearest-neighbor coupling into the static SSH chain simultaneously. Remarkably, the team identifies anomalous edge states with quasi-energy characteristics arising from this extended model.

Periodic Driving Reveals Quasi-Periodic Localization

This research investigates the behavior of a periodically driven system, focusing on identifying and characterizing topological states and their temporal evolution. The core finding is the observation of a quasi-periodic localization phenomenon, where the system tends to return to its initial state after multiples of a driving period, specifically three periods. This behavior is linked to the emergence of topological states and is confirmed through both time-domain and frequency-domain analysis. A tight-binding model, a simplified representation of electrons in a material, forms the basis of this investigation.

Topological insulators are materials that behave as insulators internally but conduct electricity on their surfaces, exhibiting robust conducting states. Floquet theory provides a mathematical framework for analyzing systems subjected to periodic forces, allowing researchers to identify effective stationary states. Dynamical localization describes the confinement of a particle or wave due to a time-periodic potential, differing from localization caused by disorder. Quasi-periodic localization represents a form of localization that isn’t strictly periodic but exhibits a tendency to return to a specific state after multiples of the driving period.

Researchers utilize a Fourier transform, a mathematical tool for decomposing signals into their constituent frequencies, to analyze the system’s behavior. The key results demonstrate the observation of this quasi-periodic localization, where the intensity at the initial excitation site returns to a high value after multiples of the driving period (3T). This behavior is confirmed by analyzing the system’s evolution in both the time and frequency domains. Frequency spectrum analysis reveals peaks at integer multiples of 1/3, supporting the claim of a three-period dynamic. The research employs rigorous analysis with both time and frequency domain methods, providing strong confidence in the results. Future research could explore how the quasi-periodic localization behavior changes with system size, how sensitive the behavior is to changes in model parameters, and how the presence of disorder affects the localization. Investigating potential experimental realizations in systems like photonic waveguide arrays or cold atom lattices, and exploring potential applications in quantum information processing or sensing, are also promising avenues.

Driven Topological Modes and Anomalous Quasienergies

Researchers have discovered a new way to control energy flow in a specifically designed material, revealing unusual properties and potential applications in quantum technologies. The team constructed a model system inspired by the Su-Schrieffer-Heeger chain, a common structure in materials science, but enhanced it with a periodic, or “driven”, structure and additional connections between the building blocks. This combination allows for the emergence of unique energy states at the edges of the material, known as topological modes. The key breakthrough lies in the creation of these anomalous edge states, which possess energies distinct from those typically observed in similar materials.

Specifically, the researchers identified states with unusual quasienergies, indicating a fundamentally different way energy is localized within the system. By carefully adjusting the driving parameters, the team demonstrated that the system can support multiple pairs of these edge states, effectively multiplying the number of pathways for energy to flow along the material’s boundaries. The team then mapped this theoretical model onto a physical system, a waveguide array, and successfully observed a three-period evolution of energy, meaning the energy cycles through a pattern repeating every three steps. This is a significant result, as it confirms the theoretical predictions and demonstrates the ability to dynamically control energy flow in a predictable manner.

The team also explored scenarios where the number of zero-energy states differs from the number of these anomalous states, leading to a two-period evolution, showcasing further control over the system’s behavior. This research expands the understanding of topological phases of matter, which are characterized by unique properties arising from the material’s overall structure rather than its local composition. By combining periodic driving with extended connections, the team has created a platform for manipulating energy flow with unprecedented precision, potentially paving the way for new devices in quantum computing and other advanced technologies.

Driven SSH Model Reveals Anomalous Edge States

This work demonstrates the construction of a Floquet extended Su-Schrieffer-Heeger (SSH) model, identifying anomalous edge states beyond conventional topological classifications. Researchers achieved this by combining periodic driving with next-nearest-neighbor coupling within the SSH chain, leading to the discovery of edge modes with specific quasienergies. Through numerical simulation of a photonic waveguide array, they successfully observed a characteristic three-period evolution of these states, representing a novel form of period-multiplied dynamics. The findings offer a new approach to designing systems exhibiting complex periodic behavior, potentially circumventing the need for multiple energy gaps typically required for topological characterization. While these anomalous edge states differ from recently studied topological modes, they also induce period-multiplied evolution, broadening the possibilities for manipulating wave propagation. The simulation’s alignment with realistic physical systems suggests potential for experimental verification using laser-written waveguide arrays, with possible applications in quantum computing.