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New Journal of Physics

Measuring the deviation from the superposition principle in interference experiments

G. Rengaraj, U. Prathwiraj, Surya Narayan Sahoo, R. Somashekhar, Urbasi Sinha

Published May 31, 2018• 34 citations
Publisher

Abstract

The Feynman path integral formalism has long been used for calculations of probability amplitudes. Over the last few years, it has been extensively used to theoretically demonstrate that the usual application of the superposition principle in slit based interference experiments is often incorrect. This has caveat in both optics and quantum mechanics where it is often naively assumed that the boundary condition represented by slits opened individually is same as them being opened together. The correction term comes from exotic sub-leading terms in the path integral which can be described by what are popularly called non-classical paths. In this work, we report an experiment where we have a controllable parameter that can be varied in its contribution such that the effect due to these non-classical paths, which we will refer to as sub-leading paths, can be increased or diminished at will. Thus, the reality of these sub-leading paths is brought forth in a classical experiment using microwaves, thereby proving that the boundary condition effect being investigated transcends the classical-quantum divide and that the Feynman path integral formalism is an overarching framework. We report the first measurement of a deviation (as big as 6%) from the superposition principle in the microwave domain using antennas as sources and detectors of the electromagnetic waves. We also show that our results can have potential applications in astronomy.

DOI
10.1088/1367-2630/aac92c

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The Feynman path integral formalism has long been used for calculations of probability amplitudes. Over the last few years, it has been extensively used to theoretically demonstrate that the usual application of the superposition principle in slit based interference experiments is often incorrect. This has caveat in both optics and quantum mechanics where it is often naively assumed that the boundary condition represented by slits opened individually is same as them being opened together. The correction term comes from exotic sub-leading terms in the path integral which can be described by what are popularly called non-classical paths. In this work, we report an experiment where we have a controllable parameter that can be varied in its contribution such that the effect due to these non-classical paths, which we will refer to as sub-leading paths, can be increased or diminished at will. Thus, the reality of these sub-leading paths is brought forth in a classical experiment using microwaves, thereby proving that the boundary condition effect being investigated transcends the classical-quantum divide and that the Feynman path integral formalism is an overarching framework. We report the first measurement of a deviation (as big as 6%) from the superposition principle in the microwave domain using antennas as sources and detectors of the electromagnetic waves. We also show that our results can have potential applications in astronomy.
The Feynman Path Integral formalism has long been used for calculations of probability amplitudes. Over the last few years, it has been extensively used to theoretically demonstrate that the usual application of the superposition principle in slit based interference experiments is often incorrect. This has caveat in both optics and quantum mechanics where it is often naively assumed that the boundary condition represented by slits opened individually is same as them being opened together. The correction term comes from exotic sub leading terms in the Path Integral which can be described by what are popularly called non-classical paths. In this work, we report an experiment where we have a controllable parameter that can be varied in its contribution such that the effect due to these non-classical paths can be increased or diminished at will. Thus, the reality of these non-classical paths is brought forth in a classical experiment using microwaves, thereby proving that the boundary condition effect being investigated transcends the classical-quantum divide. We report the first measurement of a deviation (as big as 6%6\%6%) from the superposition principle in the microwave domain using antennas as sources and detectors of the electromagnetic waves. We also show that our results can have potential applications in astronomy.
In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.
In a double slit interference experiment, the wave function at the screen with both slits open is not exactly the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well known text books in quantum mechanics implicitly and/or explicitly use this assumption, the wave function hypothesis, which is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from non-classical paths in interference experiments which provide a measurable deviation from the wave function hypothesis. A direct experimental demonstration for the existence of these non-classical paths is hard. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.
The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrödinger equation.
Superposition principle of wave function in multi-slit interference experiment has been widely accepted by many quantum mechanics textbooks, however the expression ψAB=ψA+ψB{ψ_{AB}} = {ψ_A} + {ψ_B}ψAB​=ψA​+ψB​ does not strictly hold. The non-classical paths in Feynman path integral provide an explanation to the multi-path interference effect, and can be used to quantitatively analyse the multi-slit interference effect. In this work, we apply quantities in Bohmian mechanics to the measurement of multi-order interference by analysing the contribution of non-classical paths to Bohmian velocity in electron's multi-slit interferometer. The result shows that the non-classical paths effect will cause a relative deviation of 10−310^{-3}10−3 in electron's Bohmian velocity, which is observable by doing weak measurement similar to previous work.
Interference experiments have been paramount in our understanding of quantum mechanics and are frequently the basis of testing the superposition principle in the framework of quantum theory. In recent years, several studies have challenged the nature of wave-function interference from the perspective of Born's rule---namely, the manifestation of so-called high-order interference terms in a superposition generated by diffraction of the wave functions. Here we present an experimental test of multipath interference in the diffraction of metastable helium atoms, with large-number counting statistics, comparable to photon-based experiments. We use a variation of the original triple-slit experiment and accurate single-event counting techniques to provide a new experimental bound of $2.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ on the statistical deviation from the commonly approximated null third-order interference term in Born's rule for matter waves. Our value is on the order of the maximal contribution predicted for multipath trajectories by Feynman path integrals.