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arXiv:1911.04369 · Science Advances

Probing quantum walks through coherent control of high-dimensionally entangled photons

Poolad Imany, Navin B. Lingaraju, Mohammed S. Alshaykh, Daniel E. Leaird, Andrew M. Weiner

Published Jul 17, 2020• 39 citations
arXivHTMLPDF

Abstract

Control over the duration of a quantum walk is critical to unlocking its full potential for quantum search and the simulation of many-body physics. Here we report quantum walks of biphoton frequency combs where the duration of the walk, or circuit depth, is tunable over a continuous range without any change to the physical footprint of the system-a feature absent from previous photonic implementations. In our platform, entangled photon pairs hop between discrete frequency modes with the coupling between these modes mediated by electro-optic modulation of the waveguide refractive index. Through control of the phase across different modes, we demonstrate a rich variety of behavior: from walks exhibiting enhanced ballistic transport or strong energy confinement, to subspaces featuring scattering centers or local traps. We also explore the role of entanglement dimensionality in the creation of energy bound states, which illustrates the potential for these walks to quantify high-dimensional entanglement.

DOI
10.1126/sciadv.aba8066

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•Jan 1, 2021•17 citations
Control over the duration of a quantum walk is critical to unlocking its full potential for quantum search and the simulation of many-body physics. Here we report quantum walks of biphoton frequency combs where the duration of the walk, or circuit depth, is tunable over a continuous range without any change to the physical footprint of the system-a feature absent from previous photonic implementations. In our platform, entangled photon pairs hop between discrete frequency modes with the coupling between these modes mediated by electro-optic modulation of the waveguide refractive index. Through control of the phase across different modes, we demonstrate a rich variety of behavior: from walks exhibiting enhanced ballistic transport or strong energy confinement, to subspaces featuring scattering centers or local traps. We also explore the role of entanglement dimensionality in the creation of energy bound states, which illustrates the potential for these walks to quantify high-dimensional entanglement.
Quantum superpositions enable quantum walks (QWs) to potentially speedup certain computational tasks such as database searches, tests of graph isomorphism, ranking nodes in a network, quantum many-body simulations, etc. [1] . To implement QWs, photonic platforms have the advantages of being robust at room temperature and immune to decoherence [2] . However, photonic circuits either require huge overhead or necessitate modifying the physical layout to attain the tunability of the QW. Recently, QWs exhibiting enhanced ballistic transport (bosonic) or strong energy confinement (fermionic) have been demonstrated [3] using high-dimensional bi-photon quantum frequency combs (QFCs) [4] , which do not require any change of the device arrangement.
Quantum walks are central to a wide range of applications such as quantum search, quantum information processing, and entanglement transport. Gaining control over the duration and the direction of quantum walks (QWs) is crucial to implementing dedicated processing. However, in current systems, it is cumbersome to achieve in a scalable format. High-dimensional quantum states, encoded in the photons' frequency degree of freedom in on-chip devices are great assets for the scalable generation and reliable manipulation of large-scale complex quantum systems. These states, viz. quantum frequency combs (QFCs) accommodating huge information in a single spatial mode, are intrinsically noise tolerant, and suitable for transmission through optical fibers, thereby promising to revolutionize quantum technologies. Existing literature aimed to generate maximally entangled QFCs excited from continuous-wave lasers either from nonlinear microcavities or from waveguides with the help of filter arrays. QWs with flexible depth/duration have been lately demonstrated from such QFCs. Here, instead of maximally-entangled QFCs, we generate high-dimensional quantum photonic states with tunable entropies from periodically poled lithium niobate waveguides by exploiting a novel pulsed excitation and filtering scheme. We confirm the generation of QFCs with normalized entropies from ∼0.35\sim 0.35∼0.35 to 111 by performing quantum tomography with high fidelities. These states can be an excellent testbed for several quantum computation and communication protocols in nonideal scenarios and enable artificial neural networks to classify unknown quantum states. Further, we experimentally demonstrate the steering and coherent control of the directionality of QWs initiated from such QFCs with tunable entropies. Our findings offer a new control mechanism for QWs as well as novel modification means for joint probability distributions.
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.
Unlike discrete photonic circuits, which manipulate photons step-by-step using a series of optical elements, arrays of coupled waveguides enable photons to interfere continuously across the entire structure. When composed of a nonlinear material, such arrays can also directly generate quantum states of light within the circuit. To clarify the similarities and distinctions between these two approaches of quantum walks, we conduct here a systematic comparison between linear waveguide arrays, injected with photons produced externally, and nonlinear arrays, where photon pairs are continuously generated via parametric down-conversion. We experimentally validate these predictions using III-V semiconductor nonlinear waveguide lattices with varied geometries, enabling us to tune the depth of the quantum walks over an order of magnitude and reveal the gradual emergence of non-classicality in the output state. Finally, we demonstrate an inverse-design approach to engineer \textit{aperiodic} waveguide arrays, whose optimized coupling profiles generate maximally entangled states such as the biphoton W-state. These results highlight the potential of continuously-coupled photonic systems to harness high-dimensional entanglement within compact architectures.
The generation and control of quantum correlations in high-dimensional systems is a major challenge in the present landscape of quantum technologies. Achieving such non-classical high-dimensional resources will potentially unlock enhanced capabilities for quantum cryptography, communication and computation. We propose a protocol that is able to attain entangled states of d-dimensional systems through a quantum-walk (QW)-based transfer & accumulate mechanism involving coin and walker degrees of freedom. The choice of investigating QW is motivated by their generality and versatility, complemented by their successful implementation in several physical systems. Hence, given the cross-cutting role of QW across quantum information, our protocol potentially represents a versatile general tool to control high-dimensional entanglement generation in various experimental platforms. In particular, we illustrate a possible photonic implementation where the information is encoded in the orbital angular momentum and polarization degrees of freedom of single photons.