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Optics Express

Localized quantum walks in quasi-periodic Fibonacci arrays of waveguides

Dan Trung Nguyen, Daniel A. Nolan, Nicholas F. Borrelli

Published Jan 11, 2019• 18 citations
Publisher

Abstract

New quasi-periodic arrays of waveguides (AWs) constructed with Fibonacci sequences are proposed to realize localized quantum walks (LQWs). The proposed Fibonacci arrays of waveguides (FAWs) are simple and straightforward to make, but have a rich set of properties that are of potential use for applications in quantum communication. Our simulations show that, in contrast with randomly disordered AWs, LQWs in FAWs are highly controllable due to the deterministic disorder nature of quasi-periodic systems. Furthermore, unique LQWs with symmetrical probability distribution can be conveniently realized in the FAWs.

DOI
10.1364/oe.27.000886

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New quasi-periodic arrays of waveguides (AWs) constructed with Fibonacci sequences are proposed to realize localized quantum walks (LQWs). The proposed Fibonacci arrays of waveguides (FAWs) are simple and straightforward to make, but have a rich set of properties that are of potential use for applications in quantum communication. Our simulations show that, in contrast with randomly disordered AWs, LQWs in FAWs are highly controllable due to the deterministic disorder nature of quasi-periodic systems. Furthermore, unique LQWs with symmetrical probability distribution can be conveniently realized in the FAWs.
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We present construction rules for a new class of quasiperiodic photonics lattices (QPL) to realize localized quantum walks (LQWs) deterministically.The new quasiperiodic structures are constructed symmetrically with Fibonacci, Thue-Morse, and other quasiperiodic sequences.Our construction rules allow us to build the symmetrical quasiperiodic photonics lattices.As a result, LQWs with symmetrical probability distributions can be realized in these QPLs.Furthermore, the proposed QPLs are composed with different waveguides providing both on-and off-diagonal deterministic disorders.We show LQWs in the proposed QPLs are highly programmable and controllable.
Quantum walks (QWs) have emerged from fundamental research to be one of key processes in quantum information technology including quantum computing and quantum communication. In this paper, we present results of our numerical investigation of quantum walks (QWs) in different types of 2D arrays of waveguides. We show (i) the localized QWs in quasiperiodic arrays based on Fibonacci sequences are highly controllable due to the deterministically disordered nature of quasiperiodic photonic lattices, (ii) 2D arrays of waveguides can also be used as platforms to realize important effects for special applications such as exponential speedup in quantum search and quantum topology photonics and finally, (iii) results of multiple photons QWs in 2D programable directional couplers can be useful for designing quantum photonics gates.
Quantum walk is a key operation in quantum computing, simulation, communication and information. Here, we report for the first time the demonstration of quantum walks and localized quantum walks in a new type of optical fibers having a ring of cores constructed with both periodic and quasiperiodic Fibonacci sequences, respectively. Good agreement between theoretical and experimental results has been achieved. The new multicore ring fibers provide a new platform for experiments of quantum effects in low-loss optical fibers which is critical for scalability of real applications with large-size problems. Furthermore, our new quasiperiodic Fibonacci multicore ring fibers provide a new class of quasiperiodic photonics lattices possessing both on- and off-diagonal deterministic disorders for realizing localized quantum walks deterministically. The proposed Fibonacci fibers are simple and straightforward to fabricate and have a rich set of properties that are of potential use for quantum applications. Our simulation and experimental results show that, in contrast with randomly disordered structures, localized quantum walks in new proposed quasiperiodic photonics lattices are highly controllable due to the deterministic disordered nature of quasiperiodic systems.
Waveguide quantum electrodynamics (QED) provides a powerful framework for engineering quantum interactions, traditionally relying on periodic photonic arrays with continuous energy bands. Here, we investigate waveguide QED in a fundamentally different environment: A one-dimensional photonic array whose hopping strengths are structured aperiodically according to the deterministic Fibonacci-Lucas substitution rule. These "Fibonacci waveguides" lack translational invariance and are characterized by a singular continuous energy spectrum and critical eigenstates, representing a deterministic intermediate between ordered and disordered systems. We demonstrate how to achieve decoherence-free, coherent interactions in this unique setting. We analyze two paradigmatic cases: (i) Giant emitters resonantly coupled to the simplest aperiodic version of a standard waveguide. For these, we show that atom photon bound states form only for specific coupling configurations dictated by the aperiodic sequence, leading to an effective atomic Hamiltonian, which itself inherits the Fibonacci structure; and (ii) emitters locally and off-resonantly coupled to the aperiodic version of the Su-Schrieffer-Heeger waveguide. In this case the mediating bound states feature aperiodically modulated profiles, resulting in an effective Hamiltonian with multifractal properties. Our work establishes Fibonacci waveguides as a versatile platform, which is experimentally feasible, demonstrating that the deterministic complexity of aperiodic structures can be directly engineered into the interactions between quantum emitters.