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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

A modified Mach-Zehnder experiment to test the applicability of quantum theory to single-particle experiments

Kristel F. L. Michielsen, Th. Lippert, M. Richter, B. Barbara, Seiji Miyashita, Hans A. De Raedt

Published Sep 8, 2011• 1 citation
Publisher

Abstract

We propose a modified single-particle Mach-Zehnder interferometer experiment in which the path length of one arm may change (randomly or systematically) according to the value of an external two-valued variable x, for each passage of a particle through the interferometer. Quantum theory predicts an interference pattern that is independent of the sequence of the values of x. On the other hand, corpuscular models that reproduce the results of quantum optics experiments carried out up to this date show a reduced visibility and a shift of the interference pattern depending on the details of the sequence of the values of x. The key question to be answered in a real laboratory experiment is: Which interference pattern is observed? Despite the general believe that quantum theory might be used to describe all single particle experiments, this is an interesting question to be answered since in the proposed experiment the experimental conditions not only continuously change but they might also have causal effects on the passage of the photons through the interferometer. The proposed experiment can be used to determine to what extent quantum theory provides a description of observed events beyond the usual statistical level.

DOI
10.1117/12.887643

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We propose a modified single-particle Mach-Zehnder interferometer experiment in which the path length of one arm may change (randomly or systematically) according to the value of an external two-valued variable x, for each passage of a particle through the interferometer. Quantum theory predicts an interference pattern that is independent of the sequence of the values of x. On the other hand, corpuscular models that reproduce the results of quantum optics experiments carried out up to this date show a reduced visibility and a shift of the interference pattern depending on the details of the sequence of the values of x. The key question to be answered in a real laboratory experiment is: Which interference pattern is observed? Despite the general believe that quantum theory might be used to describe all single particle experiments, this is an interesting question to be answered since in the proposed experiment the experimental conditions not only continuously change but they might also have causal effects on the passage of the photons through the interferometer. The proposed experiment can be used to determine to what extent quantum theory provides a description of observed events beyond the usual statistical level.
We analyze a single-particle Mach-Zehnder interferometer experiment in which the path length of one arm may change (randomly or systematically) according to the value of an external two-valued variable xxx, for each passage of a particle through the interferometer. Quantum theory predicts an interference pattern that is independent of the sequence of the values of xxx. On the other hand, corpuscular models that reproduce the results of quantum optics experiments carried out up to this date show a reduced visibility and a shift of the interference pattern depending on the details of the sequence of the values of xxx. The proposed experiment will show that: (1) it can be described by quantum theory, and thus not by the current corpuscular models, or (2) it cannot be described by quantum theory but can be described by the corpuscular models or variations thereof, or (3) it can neither be described by quantum theory nor by corpuscular models. Therefore, the proposed experiment can be used to determine to what extent quantum theory provides a description of observed events beyond the usual statistical level.
Classical wisdom of wave–particle duality regulates that a quantum object shows either the particle or wave nature but never both. Consequently, it would be impossible to observe simultaneously the complete wave and particle nature of the quantum object. Mathematically the principle requests that the interference visibility V and which-path distinguishability D satisfy an orthodox limit of V 2 + D 2 ≤ 1 . The present work reports a new wave–particle duality test experiment using single photons in a modified Mach–Zehnder interferometer to demonstrate the possibility of breaking the limit. The key element of the interferometer is a weakly scattering total internal reflection prism surface, which exhibits a pronounced single-photon interference with a visibility of up to 0.97 and simultaneously provides a path distinguishability of 0.83. Apparently, the result of V 2 + D 2 ≈ 1.63 exceeds the orthodox limit set by the classical principle of wave–particle duality for single photons. We expect that more delicate experiments in the future should be able to demonstrate the ultimate limit of V 2 + D 2 ≈ 2 and shed new light on the foundations of contemporary quantum mechanics.
The phenomenon of interference lies at the heart of quantum physics, and is responsible for many of the unusual aspects of quantum behaviour that deviate from our everyday expectations. Though classical physics allows for waves (e.g. of sound) to interfere, quantum theory allows for interference effects also to affect single particles. One device that demonstrates this experimentally is the Mach-Zehnder interferometer: here a single particle (e.g. a photon) travels down one of two possible paths, and quantum interference between the two paths affects the final position where the particle arrives. In this article, I propose a mechanism to musically demonstrate quantum single-particle interference: the musical Mach-Zehnder interferometer. This new quantum musical instrument makes use of two independently operated electronic keyboards, whose outputs are interfered according to the rules of the Mach-Zehnder interferometer. I discuss the musical possibilities this instrument enables, and outline a method to construct it via software simulation.
A re-visitation of the well known free space Mach Zehnder interferometer is here reported. Coexistence between one-photon and two-photons interference from collinear color entangled photon pairs is investigated. This is seen to arise from an arbitrarily small unbalance in the arm transmittance. The tuning of such asymmetry is reflected in dramatic changes in the coincidence detection, revealing beatings between one particle and two particle interference patterns. Our configuration explores new physics of the real Mach Zehnder interferometer especially useful for quantum optics on a chip, where the guiding geometry forces photons to travel in the same spatial mode.
A corpuscular simulation model of optical phenomena that does not require the knowledge of the solution of a wave equation of the whole system and reproduces the results of Maxwell's theory by generating detection events one-by-one is discussed. The event-based corpuscular model gives a unified description of multiple-beam fringes of a plane parallel plate and single-photon Mach-Zehnder interferometer, Wheeler's delayed choice, photon tunneling, quantum eraser, two-beam interference, Einstein-Podolsky-Rosen-Bohm and Hanbury Brown-Twiss experiments. The approach is illustrated by application to a recent proposal for a quantum-controlled delayed choice experiment, demonstrating that also this thought experiment can be understood in terms of particle processes only.
A distinct method to show a quantum object behaving both as wave and as particle is proposed and described in some detail. We make a systematic analysis using the elementary methodology of quantum mechanics upon Young's two-slit interferometer and the Mach—Zehnder two-arm interferometer with the focus placed on how to measure the interference pattern (wave nature) and the which-way information (particle nature) of quantum objects. We design several schemes to simultaneously acquire the which-way information for an individual quantum object and the high-contrast interference pattern for an ensemble of these quantum objects by placing two sets of measurement instruments that are well separated in space and whose perturbation of each other is negligibly small within the interferometer at the same time. Yet, improper arrangement and cooperation of these two sets of measurement instruments in the interferometer would lead to failure of simultaneous observation of wave and particle behaviors. The internal freedoms of quantum objects could be harnessed to probe both the which-way information and the interference pattern for the center-of-mass motion. That quantum objects can behave beyond the wave—particle duality and the complementarity principle would stimulate new conceptual examination and exploration of quantum theory at a deeper level.