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Shedding light (and dark) on quantum probabilities

27 April 2017

A tenet of quantum mechanics is, in principle, testable with the double-slit experiment, thanks to classically nonsensical light paths.

For more than a century, Thomas Young’s seminal double-slit experiment was seen as a convincing demonstration that light is a wave phenomenon. The modern interpretation provided by quantum mechanics is radically different: Light comprises discrete entities called photons, and the photon wavefunction at a given location on a detector screen receives contributions from all paths that pass from the photon source through the slits (call them A and B) and on to the screen. The intensity at any location on the screen is proportional to the probability that the photon arrives at that location. According to the Born rule, that probability is given by the absolute square of the wavefunction. Interference was famously observed with light, but it is not a phenomenon limited to light. Any particle can, in theory, exhibit an interference pattern determined by the absolute square of its wavefunction.

Shedding light (and dark) on quantum probabilities

You can destroy the characteristic double-slit interference by determining which slit the particle passes through. As textbooks typically describe it, when you check, paths passing through slit A are distinguishable from paths passing through slit B, and the slit-A intensity adds to the slit-B intensity. But as emphasized in a new theoretical paper by James Quach, a postdoc at the Institute of Photonic Sciences in Barcelona, Spain, if a detector registers a particle traversing slit A, it could be that the particle followed a classically nonsensical path that passed through both slits in succession. Such paths typically have only a small effect on the intensity pattern, but their contribution can become significant when the light’s wavelength is commensurate with or larger than the slit separation.

Observations of interference patterns can serve as a direct test of the Born rule. In particular, as observed by the Perimeter Institute’s Rafael Sorkin, the Born rule implies that a cleverly chosen combination of three-slit-experiment intensities will vanish. Last year Urbasi Sinha and colleagues from the Raman Research Institute implemented Sorkin’s intensity combination with microwaves and found a nonzero value. The Sorkin observation, however, assumes that classically nonsensical paths may be ignored.

Theoretically, the Sorkin prescription can be corrected to account for those neglected paths, but the exact calculation is currently beyond theorists’ reach. The classically nonsensical paths mean that the Sorkin approach cannot be simply implemented. But in return they generate a new simplicity: As Quach demonstrates, the strange paths mean that the Born rule can be tested with an appropriate combination of intensities observed in two-slit experiments in which zero, one, or both slits are monitored. Quach’s suite of observations requires two kinds of experiment in which a detector monitors both slits. In one, the detector can tell whether the particle passes through slit A, slit B, or both. In the other, the detector can tell whether the particle passes through one slit or both, but cannot distinguish passage through A from passage through B. Before experimenters can carry out Quach’s suggested test, however, they’ll need to meet the challenge of fabricating reliable detectors that don’t destroy the particles they register. (J. Q. Quach, Phys. Rev. A 95, 042129, 2017.)

Editor’s note, 3 May: The article was updated to better represent the findings made by Urbasi Sinha’s group. Also see Sinha’s comment below.

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