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A triple slit test for quantum mechanics

Urbasi Sinha, Christophe Couteau, Fay Dowker B, Thomas D. Jennewein, Gregor Weihs, Raymond Laflamme

Published Jan 1, 2010• 1 citation
OpenAlex

Abstract

As one of the postulates of quantum mechanics, Born's rule tells us how to get probabilities for experimental outcomes from the complex wave function of the system. Its quadratic nature entails that interference occurs in pairs of paths. We present an experiment that sets out to test the correctness of Born's rule by testing for the presence or absence of genuine three-path interference. This is done using single photons and a three slit aperture.

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As one of the postulates of quantum mechanics, Born's rule tells us how to get probabilities for experimental outcomes from the complex wave function of the system. Its quadratic nature entails that interference occurs in pairs of paths. We present an experiment that sets out to test the correctness of Born's rule by testing for the presence or absence of genuine three-path interference. This is done using single photons and a three slit aperture.
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.
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.
The Born rule is at the foundation of quantum mechanics and transforms the classical understanding of probabilities by predicting that interference occurs between pairs of independent paths of a single object. One consequence of the Born rule is that three-way (or three-path) quantum interference does not exist. In order to test the consistency of the Born rule, we examine detection probabilities in three-path interference using an ensemble of spin-1/2 quantum registers in liquid state nuclear magnetic resonance. As a measure of the consistency, we evaluate the ratio of three-way interference to two-way interference. Our experiment bounded the ratio to the order of 10 −3 ± 10 −3 , and hence it is consistent with Born's rule.