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There are many ways to spin a photon: Half-quantization of a total optical angular momentum

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Science Advances  29 Apr 2016:
Vol. 2, no. 4, e1501748
DOI: 10.1126/sciadv.1501748
  • Fig. 1 The generalized total angular momentum of light.

    (A) Experimental arrangement to study the generalized total angular momentum of light J1/2. Photons in a variable superposition of two angular momentum eigenstates |j = ±1/2〉 can be generated from the Gaussian input beam using a linear polarizer (LP), a quarter–wave plate (QWP), and a biaxial crystal (BC). The angular momentum currents can then be measured using an interferometer, introducing rotations in the optical paths to sort the beam according to angular momentum. Measuring J1/2 entails rotating the image and polarization by different angles, in this case using two polarization-preserving Dove prisms (DP1 and DP2) to rotate the image by 180° and two half–wave plates (HWP1 and HWP2) to rotate the polarization by 90°. BS1 and BS2 are beam splitters used to separate and recombine the optical paths; DP1 and DP2 are at 90° to one another, and HWP1 and HWP2 are at 45°. The piezo delay is tuned such that each eigenstate interferes constructively at one output and destructively at the other. (B) Calculated intensity (grayscale) and polarization (red arrows) for the |j = 1/2〉 component of the input beam.

  • Fig. 2 Experimental results.

    (A) Average of the total angular momentum J1/2 per photon, in beams comprising a variable superposition of its eigenstates |j = 1/2〉 and |j = −1/2〉. The solid line is the predicted result, corrected for the measured visibility of the interferometer. (B) Measured fluctuations in the angular momentum current quantified by its Fano factor. At the minima, the noise is predominantly shot noise reflecting the discreteness of angular momentum. The corresponding charge goes below ħ and approaches the expected value of ħ/2, showing that the quantized angular momentum of the photon is a fraction of ħ. The solid lines show the predicted result in the ideal case, with full visibility and no classical noise.

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