No 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 [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]. Many of these states hold promise in the applications to quantum memories and quantum computation [4][5][6][7][8]. Artificial quantum systems, with their precise controllability, provide a versatile platform for creating and probing a wide variety of topological phases [9][10][11][12][13][14]. Here we investigate topological phenomena in one dimension, using photonic quantum walks [10]. 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 [15]. Our experiment demonstrates a powerful new approach for controlling topological properties of quantum systems through periodic driving.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. Such topological structures appear in a variety of physical contexts, from condensedmatter [2-7, 17, 18] and high-energy physics [19] to quantum optics [9] and atomic physics [10][11][12][13][14]. These systems provide diverse platforms for studying the universal features of topological phases and their potential for technological applications.In this paper we study topological phenomena in periodically driven systems using the discrete time quantum walk [20], a protocol for controlling the motion of quantum particles on a lattice. In particular, we demonstrate that quantum walks stroboscopically simulate topological phases [10] which belong to the same topological class as that of the Su-Schrieffer-Heeger (SSH) model of polyacetylene [21] and the Jackiw-Rebbi model of a one-dimensional spinless Fermi field coupled to a Bose field [19]. These two models, devel-oped in entirely different fields, share a common underlying topological structure, which has been predicted to result in the existence of topologically protected bound states with exactly zero energy. Intriguingly, such zero-energy bound states are responsible for the existence of solitons with fractional fermion number in both models [22]. However, to date such zero-energy bound states have never been directly observed. In this experiment, we confirm the existence of these topologically robust bound states for the first time by directly imagi...
Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The number of optical elements required scales linearly with the number of steps. We measure walks with up to 6 steps and explore the quantum-to-classical transition by introducing tunable decoherence. Finally, we also investigate the effect of absorbing boundaries and show that decoherence significantly affects the probability of absorption.
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