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IntechOpen eBooks

Topology in Photonic Discrete-Time Quantum Walks: A Comprehensive Review

Graciana Puentes

Published Feb 23, 2022• 1 citation
Publisher

Abstract

We present a comprehensive review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains. Moreover, we introduce a novel scheme for DTQWs using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects in photonic systems.

DOI
10.5772/intechopen.95111

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We present a comprehensive review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains. Moreover, we introduce a novel scheme for DTQWs using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects in photonic systems.
We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme for photonic DTQW, using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. Unlike all previous mode-multiplexed implementations, this scheme enables simulation of an arbitrary step of the walker, only limited, in principle, by the SLM resolution. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects and the use of non-local coin operations based on two-photon hybrid entanglement.
Controlling quantum states of light is of central importance to many fields of modern physics. The technology to do so underpins the only feasible means for long-distance quantum communication using quantum-key-distribution, and plays a pivotal role in the application of quantum computing, quantum metrology and investigations of fundamental physics. Motivated by these applications, in this thesis we present a number of experimental results that demonstrate an enhanced level of control over photonic states. First, we tackle one of the most important technological issues currently facing the field, namely the creation of pure multi-photon Fock states from pulsed parametric downconversion. Our technique shows a marked improvement over previous photon sources when employed for quantum information tasks. At a more foundational level, we experimentally examine the properties of quantum correlations in the temporal domain, where our results highlight surprising differences between its spatial-domain counterpart of multipartite entanglement. Finally, we experimentally implement single- and multi-photon quantum walks in the discrete- and continuous-time regimes respectively. Quantum walks have received much attention in recent years due to their vast applicability in quantum information science, especially for quantum simulation and emulation. On this front we use the quantum walk formalism to perform a full experimental simulation of topological phases in a 1-dimensional configuration. Aside from being the first demonstration of topological phases in this regime, our system exhibits unprecedented control over the topological properties in a quantum system. As such we are able to observe the exotic behaviour of trapped bound states, and discover the new phenomenon of paired bound states—a feature unique to periodically driven systems.
Quantum walks, a counterpart of classical random walks, have many applications due to their neoteric features. Since they were first proposed, quantum walks have been explored in many fields theoretically and have also been demonstrated experimentally in various physical systems. In this paper, we review the experimental realizations of discrete-time quantum walks in photonic systems with different physical structures, such as bulk optics and time-multiplexed framework. Then, some typical applications using quantum walks are introduced. Finally, the advantages and disadvantages of these physical systems are discussed.
The manipulation of the spatial structure of a light beam has many application in both classical and quantum physics. The possibility to exploit high dimensional degrees of freedom carried by a light beam can be employed, among the various applications, for simulating the dynamics on quantum particles in multidimensional spaces. Coupling these degrees of freedom, like the orbital angular momentum or the transverse linear momentum, with the polarization of light (also associated with the spin) allows to implement quantum walks on one and two dimensional lattices. This work presents a series of experiments where these implementations of photonic quantum walks were realized exploiting patterned liquid crystal devices. In particular, the experimental setup allows to investigate interesting effects of the non-trivial topological features of the simulated processes, and test methods for the experimental measurement of topological invariants. This research has also led to the introduction of a novel method of characterizing unknown structured light beams and to the study of the stability of polarization singularities in laser beams.