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Measuring higher-order interferences with a five-path interferometer

Thomas Kauten, Robert Keil, Thomas Kaufmann, Benedikt Pressl, Gregor Weihs

Published Aug 13, 2015• 0 citations
OpenAlex

Abstract

Within the established theoretical framework of quantum mechanics, interference always occurs between pairs of trajectories. Higher order interferences with multiple constituents are, however, excluded by Born's rule and can only exist in generalized probabilistic theories. Thus, high-precision experiments searching for such higher order interferences are a powerful method to test the validity of the Born rule and distinguish between quantum mechanics and more general theories. Here, we perform such a test in optical multi-path interferometers. Our results permit to rule out the existence of higher order interference terms to an extent which is more than four orders of magnitude smaller than the expected pairwise interference, refining previous bounds by two orders of magnitudes. This establishes the hitherto tightest constraints on generalized interference theories.

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Within the established theoretical framework of quantum mechanics, interference always occurs between pairs of trajectories. Higher order interferences with multiple constituents are, however, excluded by Born's rule and can only exist in generalized probabilistic theories. Thus, high-precision experiments searching for such higher order interferences are a powerful method to test the validity of the Born rule and distinguish between quantum mechanics and more general theories. Here, we perform such a test in optical multi-path interferometers. Our results permit to rule out the existence of higher order interference terms to an extent which is more than four orders of magnitude smaller than the expected pairwise interference, refining previous bounds by two orders of magnitudes. This establishes the hitherto tightest constraints on generalized interference theories.
Within the established theoretical framework of quantum mechanics, interference always occurs between pairs of paths through an interferometer.Higher order interferences with multiple constituents are excluded by Born's rule and can only exist in generalized probabilistic theories.Thus, high-precision experiments searching for such higher order interferences are a powerful method to distinguish between quantum mechanics and more general theories.Here, we perform such a test in an optical multi-path interferometer, which avoids crucial systematic errors, has access to the entire phase space and is more stable than previous experiments.Our results are in accordance with quantum mechanics and rule out the existence of higher order interference terms in optical interferometry to an extent that is more than four orders of magnitude smaller than the expected pairwise interference, refining previous bounds by two orders of magnitude.
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.
In this paper results of an improved version of an experiment was presented, which was proposed by Sorkin in 1994, and was experimentally implemented for the first time in 2010, with the goal of putting a bound on the potential magnitude of higher order interference terms. The work's experiment expands this to five paths, which not only allows us to measure 3rd and 4th order interference terms but also allows testing for the possibility of quantum mechanical wavefunctions based on quaternions or octonions rather than complex numbers.
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.
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.
Quantum theory permits interference between indistinguishable paths but, at the same time, restricts its order. Single-particle interference, for instance, is limited to the second order, that is, to pairs of single-particle paths. To date, all experimental efforts to search for higher-order interferences beyond those compatible with quantum mechanics have been based on such single-particle schemes. However, quantum physics is not bound to single-particle interference. We here experimentally study many-particle higher-order interference using a two-photon-five-slit setup. We observe nonzero two-particle interference up to fourth order, corresponding to the interference of two distinct two-particle paths. We further show that fifth-order interference is restricted to 10^{-3} in the intensity-correlation regime and to 10^{-2} in the photon-correlation regime, thus providing novel bounds on higher-order quantum interference.