Research ArticlePHYSICS

Observing momentum disturbance in double-slit “which-way” measurements

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Science Advances  14 Jun 2019:
Vol. 5, no. 6, eaav9547
DOI: 10.1126/sciadv.aav9547
  • Fig. 1 Experimental setup.

    Heralded signal photons (SPs) are separated into two paths by a beam displacer (BD 30). A half-wave plate HWP1 is used to change the relative phase between these two paths, while HWP2 is used to make the polarization of both paths the same. A birefringent crystal (PC) is inserted into one of the paths to compensate the difference in the optical length. The photon is prepared in the diagonal polarization state by HWP3 and then goes through a thin calcite crystal to perform weak measurement. The optic axis of the calcite crystal is in the xz plane oriented at 42° to the z axis. A quarter wave plate (QWP) and a beam displacer (BD 40) are used to detect the polarization of the photon. A combination of three lenses, L1 (plano-convex), L2 (aspherical and moveable), and L3 (plano-convex cylindrical), is used to image different planes on the intensified charge-coupled device (ICCD) camera.

  • Fig. 2 Experimental velocities and trajectories.

    (A) The weak value of the transverse velocities or momenta (v/c = λp/h) at z117 = 8.612 m. The red squares and blue dots represent experimental data with the relative phase ϕ being 0 and π, respectively. (B) Trajectories beginning at the same initial condition, x = ±1.02 mm, for ϕ = 0 (red) and ϕ = π (blue). The trajectories are reconstructed from 117 imaging planes. If a trajectory locates on a point that is not at the center of a pixel, then a cubic spline interpolation between neighboring momentum values is used.

  • Fig. 3 Bohmian momentum disturbance, in units of ℏ/D, for the photons subject to a minimally disturbing WWM with η0 = ηπ = 1/2.

    (A) The mean absolute momentum disturbance pzB as a function of the propagation distance z. The nonclassicality of the momentum change is evident from the fact that it accrues gradually during propagation from near to far field. (B) Complete distribution of the Bohmian momentum disturbance at the last plane and the first plane (inset). Red is for ϕ = 0 and blue for ϕ = π.

  • Fig. 4 The relationship between the total mean absolute momentum disturbance pzB (in units of ℏ/D) and fringe visibility V.

    The blue dots represent the experimental data for various partial WWMs kinds of measurements in the plane z117 = 8.612 m. The red solid line represents the theoretical prediction (5) under ideal conditions. The black dashed line represents the theoretical prediction, calculated with the same experimental conditions. Error bars are estimated from the counting statistics.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Section SI. Momentum in Bohmian mechanics and related theories
    • Section SII. Single photon generation
    • Fig. S1. Experimental setup for single-photon generation.
    • References (3234)

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