Observation of topologically protected bound states in photonic quantum walks

Takuya Kitagawa,Erez Berg,Alan Aspuru-Guzik,Andrew G White,Mark S Rudner,Alessandro Fedrizzi,Ivan Kassal,Matthew A Broome,Eugene Demler

doi:10.1109/cleoe.2011.5943396

Abstract

Topological phenomena in physical systems are a direct consequence of the topology of the underlying wave-functions and are robust against perturbations; for example, the Hall conductance induced by the integer quantum Hall effect is very precisely quantified—independent of intrinsic (e.g. impurities) or extrinsic (size, shape) characteristics of the studied samples. The study of these phenomena in condensed matter physics is often hard, due to the rapid decoherence of electrons—which are strongly coupled to their environment—and the difficulty of directly imaging electronic wave functions. Artificial quantum systems, such as in quantum optics, can in contrast be precisely controlled and provide an ideal setting for realizing, manipulating, and probing topological phases. The study of topological phases then does not have to remain limited to static or quasi-static/adiabatic situations, it can be extended to periodically driven systems, which have recently been proposed to also exhibit topological behaviors [1].

Highlights

These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems [1], the gapless surface states of topological insulators [2, 3], and elementary excitations with non-abelian statistics in fractional quantum Hall systems and topological superconductors[4]
The photon evolution simulates the dynamics of topological phases which have been predicted to arise in, for example, polyacetylene
The distinguishing feature of topological phases is the existence of a winding in the ground state wave function of the system, which cannot be undone by gentle changes to the microscopic details of the system

Summary

Introduction

To probe the existence of the bound states, we initialize a photon next to the boundary between two topologically distinct quantum walks, Fig. 1. For case 2 in Fig. 3b with parameters chosen to create a boundary between topologically distinct phases W−=1 and W+=0, we observe the existence of at least one bound state as a peak in the probability distribution near the origin after four steps.

Results

Conclusion