Quantum Walks in Periodic and Quasiperiodic Fibonacci Fibers

Abstract

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.

Figure 1

Diagram of MCRF with 39 identical SM cores (a), image of the fabricated fiber (b), and the image of the fiber that is overfilled with light of wavelength 1.550 μm.

Figure 2

Diagram of ring of cores: 4^th order FCRF4 with 13 cores (a), 5^th order FCRF5 with 23 cores (b), and 6^th order FCRF6 fiber with 39 cores (c). Red arrow indicates input core.

Figure 3

Probability distribution of photons in quantum walks: (a) regular MCRF with 13 cores, (b) regular MCRF with 23 cores and (c) regular MCRF with 39 cores, (d) FMCRF4 with 13 cores, (e) FMCRF5 with 23 cores and (f) FMCRF6 with 39 cores. Signal wavelength λ = 1.550 μm.

Figure 4

(a) Schematic of multicore fibers MCRF of 39 cores that are regular-spacing in a ring of radius R₁. All cores have same index difference Δn and core size a and are single mode, (b) Image of cross section of MCRF fabricated with 39 cores. (c) Schematic of Fibonacci multicore ring fiber FMCRF of 39 cores that are regular-spacing in a ring of radius R. There are two different SM waveguides A (blue) and B (orange) having same core diameter a but difference Δn_A = n_coreA − n_clad and Δn_B = n_coreB − n_clad. The circles around groups of cores are for different Fibonacci elements defined in Eq. (2). (d) Image of cross section of FMCRF fabricated with 39 cores. All parameters of the two fabricated fibers are detailed in the main text.

Figure 5

Experimental set up. A coherent 1550 nm laser output is coupled into a single mode fiber (SMF) attached onto an XYZ stage. Light from SMF is then butt-coupled to the MCRF at the central core indicated by the black inset with red circle. The output from MCRF is imaged onto a CCD camera, green inset. The SMF fiber is chosen such that the MFD matches that of the MCRF.

Figure 6

(a) Calculated probability photon distribution of quantum walks in the MCRF, and (b) experimental data of photon distribution at ~4.1 cm of MCRF. Both simulation and experimental results show the typical feature of QWs with two strong lobes at the end of walking length. (c) calculated probability photon distribution of quantum walks in the FMCRF, and (d) experimental data of the photon distribution at ~4.15 cm of FMCRF. The simulation and experimental results show strong localization at the center core. Details of the fibers and experiments are presented in the main text.