Quantum Walks in Quasi-Periodic Arrays of Waveguides

In this paper, we present results of numerical investigation of quantum walks (QWs) in different type arrays of single-mode waveguides: (i) regular arrays of identical waveguides (AIW), (ii) periodic arrays of two different waveguides (PAW), (iii) quasi-periodic arrays of waveguides with Fibonacci sequences (FAW), (iv) quasi-periodic arrays of waveguides with Thue-Morse sequences (TMAW). Our simulations show in contrast with randomly disordered systems, localized QWs in quasi-periodic arrays of waveguides FAWs and TMAWs are predictable and controllable due to the deterministic disorder nature of the quasi-periodic systems.