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Muzikologija

The musical Mach-Zehnder interferometer

Andrew J. P. Garner

Published Jan 1, 2018• 1 citation
Publisher

Abstract

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.

DOI
10.2298/muz1824039g

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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.
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 show that a quantum particle subjected to a positive force in one path of a Mach-Zehnder interferometer and a null force in the other path may receive a negative average momentum transfer when it leaves the interferometer by a particular exit. In this scenario, an ensemble of particles may receive an average momentum in the opposite direction of the applied force due to quantum interference, a behavior with no classical analogue. We discuss some experimental schemes that could verify the effect with current technology, with electrons or neutrons in Mach-Zehnder interferometers in free space and with atoms from a Bose-Einstein condensate.
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.
In the conventional interpretation of quantum mechanics the interference of particles in a two-beam interferometer is closely related to the problem of which-way information. One of the mysteries of quantum mechanics relies on the assumption that the wavefunction of each photon propagates simultaneously along both classically allowed paths, and that interference arises as a consequence of the indistinguishability of those paths. Any attempt to obtain which-way information by putting individual labels on the photons in each pathway inevitably destroys interference. However, even in cases in which the photons carry which-way labels, it is possible to erase those labels after the particle has left the interferometer. The erasing process (partly or completely) destroys the which-way information, and thereby restores interference. This phenomenon is known as quantum erasing. Here we present a lecture demonstration experiment of quantum erasing based on a Mach–Zehnder interferometer operated with single photons.
Abstract A re-visitation of the well known free space Mach-Zehnder interferometer is reported here. The coexistence between one-photon and two-photons interference from collinear color entangled photon pairs is investigated. Thisarises 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. In particular, the role of the losses and of the intrinsic phase imperfectness of the lossy beamsplitter are explored in a single-port excited Mach-Zehnder interferometer. This configuration is especially useful for quantum optics on a chip, where the guiding geometry forces photons to travel in the same spatial mode.