Observation of topologically protected bound states in a one dimensional photonic system (1105.5334v1)

Abstract: One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems, the gapless surface states of topological insulators, and elementary excitations with non-abelian statistics in fractional quantum Hall systems and topological superconductors. Many of these states hold promise in the applications to quantum memories and quantum computation. Artificial quantum systems, with their precise controllability, provide a versatile platform for creating and probing a wide variety of topological phases. Here we investigate topological phenomena in one dimension, using photonic quantum walks. The photon evolution simulates the dynamics of topological phases which have been predicted to arise in, for example, polyacetylene. We experimentally confirm the long-standing prediction of topologically protected localized states associated with these phases by directly imaging their wavefunctions. Moreover, we reveal an entirely new topological phenomenon: the existence of a topologically protected pair of bound states which is unique to periodically driven systems. Our experiment demonstrates a powerful new approach for controlling topological properties of quantum systems through periodic driving.

• The paper experimentally confirms the existence of topologically protected bound states using a split-step quantum walk protocol.
• The authors utilize controlled rotations and translations with half-wave plates and beam displacers, effectively simulating the SSH model.
• The observed bound states exhibit strong robustness against perturbations, highlighting potential applications in fault-tolerant quantum simulations and computing.

Observation of Topologically Protected Bound States in a One-Dimensional Photonic System

This paper presents an exploration into topological phenomena using photonic quantum walks, with particular emphasis on the experimental observation of topologically protected bound states in a one-dimensional system. Utilizing a split-step quantum walk protocol, the authors have achieved direct visualization of these bound states, which have long been theorized but never directly observed in prior experiments.

Methodology and Experimental Design

In their experimental setup, the authors studied topological phases through quantum walks employing photons with specific internal states—horizontal and vertical polarizations—on a one-dimensional lattice. The lattice dynamics were controlled via rotation and translation operations facilitated by half-wave plates and beam displacers, respectively. Such a setup enabled a quantum simulation analogous to known models within solid-state physics, such as the Su-Schrieffer-Heeger (SSH) model.

A notable methodological detail of this work is the execution of a split-step quantum walk protocol. The authors engineered spatial inhomogeneity via modifications in rotation angles, specifically using inhomogeneous rotations to induce boundaries within the simulated system. By doing so, they successfully created a scenario where topologically protected edge states could be probed.

Numerical Results and Key Findings

The paper reports several important findings:

1. Direct Imaging of Topologically Protected States: The experimental results confirm the existence of topologically robust bound states. These states, unique to regions characterized by differing winding numbers, present as peaks in the measured probability distribution, which would otherwise exhibit ballistic spreading.
2. Novel Topological Phenomena in Periodically Driven Systems: The researchers discovered a pair of bound states, distinctively topologically protected due to their periodic driving dynamics—a phenomenon absent from static systems. These states exhibited quasi-energy differences of π, providing a new lens through which to examine topological protection in time-dependent quantum systems.
3. Robustness Against Perturbations: The bound states maintained their integrity upon modulating parameters, highlighting the robustness typical of topologically protected states against weak perturbations.

Implications and Future Directions

The paper offers significant implications for both theoretical and practical perspectives:

• Quantum Simulations and Topological Studies: The direct imaging technique used in this research positions itself as a powerful tool for probing topological materials and can be utilized in other complex systems, enabling deeper understandings of topological insulators and superconductors.
• Extensions to Higher Dimensions and Other Models: The work may lead to further explorations into higher-dimensional systems and other topologically nontrivial phases.
• Applications in Quantum Computing: With these robust states holding potential for information storage, the advances made pave the way for applications involving fault-tolerant quantum computation.

In conclusion, the investigation presents concrete evidence and insights into the dynamics of periodically driven topological systems, challenging traditional perspectives and expanding the understanding of topological mechanics in one-dimensional quantum systems. The techniques and findings will likely catalyze ongoing research in quantum simulation and topological phase studies, with promising implications for the field of quantum information science.