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arXiv:0811.2068 · AIP conference proceedings

Testing Born’s Rule in Quantum Mechanics with a Triple Slit Experiment

Urbasi Sinha, Christophe Couteau, Zachari Medendorp, Immo Söllner, Raymond Laflamme, Rafael D. Sorkin, Gregor Weihs, Luigi Accardi, Guillaume Adenier, Christopher A. Fuchs, Gregg S. Jaeger, Andrei Yu. Khrennikov, Jan-Åke Larsson, Stig Stenholm

Published Jan 1, 2009• 50 citations

Abstract

In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the resulting interference violates the (Kolmogorov) sum rule expressing the additivity of probabilities of mutually exclusive events. However, there is a higher order sum rule that quantum mechanics does obey, involving the probabilities of three mutually exclusive possibilities. We could imagine a yet more general theory by assuming that it violates the next higher sum rule. In this paper, we report results from an ongoing experiment that sets out to test the validity of this second sum rule by measuring the interference patterns produced by three slits and all the possible combinations of those slits being open or closed. We use attenuated laser light combined with single photon counting to confirm the particle character of the measured light.

DOI: 10.1063/1.3109942

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Recent high-precision measurements in a three-slit diffraction experiment [Sinha et al., Science 329, 418 (2010)] have been performed as an explicit test of the validity of Born's rule for quantum probabilities. This experiment aims to establish an upper limit to the possibility of higher-order interference, which, if observed, could support generalization of quantum probability theory. We reproduce this three-slit experiment using position-resolved detection, compare our results to a computational model, and find significant limitations to the normalization scheme proposed by Sinha et al. that influence interpretation. We further show that the dependence of the measurements on detector size and position must be taken into account for proper interpretation of results and meaningful comparison with other experimental schemes.

Quantum mechanics predicts that interference arising from multiple slits can be reduced to a sum of outcomes from the simpler one- and two-slit counterparts. Testing deviations from these results has been discussed as testing the validity of Born's rule. Here an experiment that considers the evolution between three levels of an atom as the quantum paths is devised, providing precision tools that can be used to test universality of Born's and to constrain theories designed to supersede quantum mechanics.

Interference between two waves is a well-known concept in physics, and its generalization to more than two waves is straightforward. The order of interference is defined as the number of paths that interfere in a manner that cannot be reduced to patterns of a lower order. In practice, second-order interference means that in, say, a triple-slit experiment, the interference pattern when all three slits are open can be predicted from the interference patterns between all possible pairs of slits. Quantum mechanics is often said to only exhibit second-order interference. However, this is only true under specific assumptions, typically single particles undergoing linear evolution. Here we experimentally show that nonlinear evolution can in fact lead to higher-order interference. The higher-order interference in our experiment can be understood using a simple classical or quantum description, namely optical coherent states interacting in a nonlinear medium. Our work shows that nonlinear evolution could open a loophole for experiments attempting to verify Born's rule by ruling out higher-order interference.