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arXiv:2006.09496 · Physical Review Letters

Testing Higher-Order Quantum Interference with Many-Particle States

Marc-Oliver Pleinert, Alfredo Rueda, Eric Lutz, Joachim von Zanthier

Published May 10, 2021• 32 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.126.190401

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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.
The double-slit experiment is the most direct demonstration of interference between individual quantum objects. Since similar experiments with single particles and more slits produce interference fringes reducible to a combination of double-slit patterns, it is usually argued that quantum interference occurs between pairs of trajectories, compactly denoted as second-order interference. Here we show that quantum mechanics in fact allows for interference of arbitrarily high order. This occurs naturally when one considers multiple quantum objects interacting in the presence of a nonlinearity, both of which are required to observe higher-order interference. We make this clear by treating a generalized multislit interferometer using second quantization. We then present explicit experimentally relevant examples both with photons interacting in nonlinear media and an interfering Bose-Einstein condensate with particle-particle interactions. These examples are all perfectly described by quantum theory, and yet exhibit higher-order interference based on multiple particles interacting nonlinearly.
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.
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.
The double-slit experiment is the most direct demonstration of interference between individual quantum objects. Since similar experiments with more slits produce interference fringes reducible to a combination of double-slit patterns it is usually argued that quantum interference occurs between pairs of trajectories, compactly denoted as second-order interference. Here we show that quantum mechanics in fact allows for interference of arbitrarily high order. This occurs naturally when one considers multiple quantum objects interacting in the presence of a nonlinearity. We make this clear by treating a generalised M-slit interferometer using second-quantisation. We then present explicit experimentally-relevant examples both with photons interacting in nonlinear media and an interfering Bose-Einstein condensate with particle-particle interactions. These examples are all perfectly described by quantum theory, and yet exhibit higher-order interference.
Quantum mechanics predicts that for single quanta interference is limited to pairs of events. It can therefore be categorized as "second-order interference theory''. In this thesis, we wish to explore possibility of "higher-order interference'', exemplified by generalizations of Young’s double slit experiment to three and more paths. We show in the thesis that it is possible to create higher-order interference using non-linear processes within second quantization formalism and it is present in some extensions of quantum mechanics. We also discuss operational advantages of utilizing higher-order interference and propose precise experiment with atoms to bound its presence.
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.