Research ArticleQUANTUM OPTICS

Two-photon quantum walk in a multimode fiber

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Science Advances  29 Jan 2016:
Vol. 2, no. 1, e1501054
DOI: 10.1126/sciadv.1501054
  • Fig. 1 Apparatus to control the propagation of photon pairs through an MMF.

    Photon pairs from a SPDC source (not shown) are injected in a graded-index MMF (50-μm core diameter) with orthogonal polarizations. Two SLMs (SLM H and SLM V) are used to shape the transverse spatial waveform of each photon. Output light is monitored by an EMCCD camera and two PMSMFs, F1 and F2, connected to APDs all imaging the output plane of the MMF. A half-wave plate and a PBS positioned just after the MMF permit selection of one specific polarization of the output field.

  • Fig. 2 Experimental measurement of the TTM.

    (A) Schematic of the experimental setup using a two-photon state injected into two different transverse spatial modes. (B) Recorded intensity images of the corresponding output speckle patterns for photon H only, photon V only, and H+V simultaneously, containing about 50 independent speckle grains. The scale bar represents 25 μm in the output plane of the MMF. The H+V speckle pattern corresponds to the incoherent sum of each individual case. (C) Coincidence detection patterns between F1 and F2 reconstructed for 16 two-photon input states programmed by the SLMs. F1 and F2 scan four output coincidence positions denoted |X1Y2〉, |X1Y2〉, |X1Y2〉, |X1Y2〉. The 16 × 4 coincidence matrix measured here represents a subset of the complete TTM that consists of approximately (380 × 380)2 elements. (D) For the same 16 × 4 elements, the differences observed in coincidence patterns measured with distinguishable (δ = 0.4 mm) or indistinguishable (δ = 0) photons are quantified by reconstructing the nonclassical contrast matrix. A contrast is given by the formula C = (Rδ=0Rδ=0.4 mm)/Rδ=0.4 mm, where Rδ is the coincidence rate of a two-photon output state at a path length difference of δ. This matrix is a clear signature of quantum interference effects occurring in the MMF. Coincidences are monitored for 900 s with a coincidence window of 2.5 ns.

  • Fig. 3 Focusing photon pairs in a targeted two-photon output state of the MMF.

    (A1 to A3) The first configuration (A1) directs photon H to output position |X2〉 of F1 and photon V to output position |Y3〉 of F2. This is visible in the direct images measured using the EMCCD camera (A2). Coincidence profiles (A3) are measured for 25 coincidence output fiber position pairs. Coincidence rates in the targeted two-photon state Embedded Image are about 100 times higher than the background, for both distinguishable and indistinguishable photons. (B1 to B3) The second configuration (B1) corresponds to photon H being prepared in a superposition of output states |X2〉 and |Y3〉 with a relative phase ϕH = 0 and photon V directed to a superposition of the same output states with a relative phase ϕV = 0. Direct images measured with the EMCCD confirm that both photons are directed to the two output states (B2). The effect of nonclassical interference is shown on the output coincidence speckle patterns (B3), where we observe an increase of 72% in the coincidences rate in the state Embedded Image in the indistinguishable case (δ = 0) compared to the distinguishable case (δ = 0.4 mm). Coincidence measurements are acquired for 900 s with a coincidence window of 2.5 ns. The white scale bars represent 25 μm in the output plane of the MMF.

  • Fig. 4 Deterministic control of quantum interferences.

    (A) Nonclassical interference contrast measured for two photons mapped onto a superposition of two output states with different phase settings (ϕH, ϕV). The nonclassical contrast is defined as C = (Rδ=0Rδ=0.4 mm)/Rδ=0.4 mm, where Rδ is the two-photon coincidence rate of the targeted output state Embedded Image at a path length difference of δ. Contrast values are measured with 8 × 8 = 64 phase settings. (B) Contrast values for three phase settings [(α), (ϕH = 0, ϕV = 0); (β), (ϕH = 0, ϕV = π/2); (γ), (ϕH = 0, ϕV = π)] as a function of the path length difference between input photons δ. The observed effects are consistent with the initial indistinguishability of the photons evaluated with a HOM experiment (see the Supplementary Materials). Data are acquired for 290 s with a coincidence window of 2.5 ns.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/1/e1501054/DC1

    Experimental details

    Controlling the two-photon field using the two-photon transmission matrix.

    Validation of the experimental data

    Table S1. Statistical analysis of experimental data presented in Fig. 3.

    Fig. S1. Characterization of the photon-pair indistinguishability by the Hong-Ou-Mandel experiment.

    Fig. S2. Dispersion characterization through the MMF.

    Fig. S3. Statistical analysis of experimental data represented in Fig. 2.

    Fig. S4. Statistical analysis of experimental data presented in Fig. 4.

    References (43, 44)

  • Supplementary Materials

    This PDF file includes:

    • Experimental details
    • Controlling the two-photon field using the two-photon transmission matrix
    • Validation of the experimental data
    • Table S1. Statistical analysis of experimental data presented in Fig. 3.
    • Fig. S1. Characterization of the photon-pair indistinguishability by the Hong-Ou-Mandel experiment.
    • Fig. S2. Dispersion characterization through the MMF.
    • Fig. S3. Statistical analysis of experimental data represented in Fig. 2.
    • Fig. S4. Statistical analysis of experimental data presented in Fig. 4.
    • References (43, 44)

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