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Experimental two-dimensional quantum walk on a photonic chip

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Science Advances  11 May 2018:
Vol. 4, no. 5, eaat3174
DOI: 10.1126/sciadv.aat3174

Figures

  • Fig. 1 Experimental layout.

    (A) Schematic diagram of 3D waveguide array fabrication using the femtosecond laser direct writing technique. (B) Photographed cross section of a photonic lattice studied in this experiment. (C) Schematic diagram of one waveguide coupling to other waveguides in the 3D waveguide arrays, and (D) the corresponding coupling coefficient C for different center-to-center waveguide spacings in horizontal and vertical directions. (E) Setup of single-photon experiment. Each photonic chip to be tested incorporates many sets of 3D waveguide arrays. APD, avalanched photo diode; PBS, polarized beam splitter; HWP, half-wave plate; QWP, quarter-wave plate; LPF, long-pass filter; PPKTP, periodically poled KTP crystal.

  • Fig. 2 2D QWs of different propagation lengths.

    (A to E) Experimentally obtained probability distribution of heralded single photons and (F to J) theoretical probability distribution. The propagation lengths are 1.81 mm for (A) and (F), 3.31 mm for (B) and (G), 4.81 mm for (C) and (H), 7.31 mm for (D) and (I), and 9.81 mm for (E) and (J).

  • Fig. 3 The transport properties of QWs.

    (A) The variance against propagation length for experimental 2D QWs, theoretical 2D QWs, and theoretical 1D QWs. a.u., arbitrary units. (B) An evolution pattern of a 2D QW from heralded single-photon experiment at a propagation length z = 4.31 mm and its projection profile onto the x and y axes. (C) A theoretical evolution pattern of a 2D classical random walk in a 2D Gaussian distribution with a sigma of 1.5 spacing units and its projection profile onto the x and y axes.

  • Fig. 4 The recurrent properties.

    (A) Probability at the initial position against propagation length and (B) Pólya number against propagation length for experimental 2D QWs, theoretical 2D QWs, and theoretical 1D QWs.