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arXiv:1610.06401 · Physical Review A

Which-way double-slit experiments and Born-rule violation

James Q. Quach

Published Apr 24, 2017• 18 citations
arXivHTMLPDF

Abstract

In which-way double-slit experiments with perfect detectors, it is assumed that having a second detector at the slits is redundant because it will not change the interference pattern. We, however, show that if higher-order or nonclassical paths are accounted for, the presence of the second detector will have an effect on the interference pattern. Accounting for these nonclassical paths also means that the Sorkin parameter in triple-slit experiments is only an approximate measure of Born-rule violation. Using the difference between single and double which-way detectors, we give an alternative parameter which is an exact measure of Born-rule violation.

DOI
10.1103/physreva.95.042129

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In which-way double-slit experiments with perfect detectors, it is assumed that having a second detector at the slits is redundant because it will not change the interference pattern. We, however, show that if higher-order or nonclassical paths are accounted for, the presence of the second detector will have an effect on the interference pattern. Accounting for these nonclassical paths also means that the Sorkin parameter in triple-slit experiments is only an approximate measure of Born-rule violation. Using the difference between single and double which-way detectors, we give an alternative parameter which is an exact measure of Born-rule violation.
In the the double-slit experiment, nonclassical paths are Feynman paths that go through both slits. Prior work with atom cavities as which-way detectors in the double-slit experiment has shown these paths to be experimentally inaccessible. In this paper, we show how such a setup can indeed detect nonclassical paths with 1% probability if one considers a different type of nonclassical path than previously investigated. We also show how this setup can be used to erase and restore the coherence of the nonclassical paths. Finally, we also show how atom cavities may be used to implement a exact measure of Born-rule violation [Quach, Which-way double-slit experiments and Born-rule violation, Phys. Rev. A 95, 042129 (2017)], which up until now has only been a formal construct.
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.
This paper is based on work published in [1]. It describes a triple slit experiment using single photons that has been used to provide a bound on one of the most fundamental axioms of quantum mechanics i.e. Born’s rule for probabilities [2]. In spite of being one of the most successful theories which describes various natural phenomena, quantum mechanics has enough intricacies and “weirdness” associated with it which makes many physicists believe that it may not be the final theory and hints towards the possibility of more generalized versions. Quantum interference as shown by a double slit diffraction experiment only occurs from pairs of paths. Even in multi‐slit versions, interference can only occur between pairs of possibilities and increasing the number of slits does not increase the complexity of the theory that still remains second‐order. However, more generalized versions of quantum mechanics may allow for multi‐path i.e. higher than second order interference. This experiment also provides a bound on the magnitude of such higher order interference. We have been able to bound the magnitude of three‐path interference to less than 10−2 of the expected two‐path interference, thus ruling out third and higher order interference and providing a bound on the accuracy of Born’s rule.
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.
Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born's rule--one of the axioms of quantum mechanics--could be violated. Born's rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons and bounded the magnitude of three-path interference to less than 10(-2) of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born's rule. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.
We propose a simple model to study the Gouy phase effect in the triple-slit experiment in which we consider a nonclassical path. The Gouy phase differs for classical and nonclassical paths as it depends on the propagation time. In this case the Gouy phase difference changes the Sorkin parameter $\ensuremath{\kappa}$ used to estimate the nonclassical path contribution in a nontrivial way, shedding some light on the implementation of experiments to detect nonclassical path contributions.