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American Journal of Physics

A simple experiment for discussion of quantum interference and which-way measurement

Mark B. Schneider, Indhira A. LaPuma

Published Mar 1, 2002• 50 citations
Publisher

Abstract

We have developed a which-way experiment using visible light that is completely analogous to a recent experiment involving which-way measurement in atom interference. This simple experiment, easily accessible to undergraduate students and the resources of undergraduate departments, facilitates the examination of the key elements of which-way measurement, quantum erasure, and related mysteries of quantum measurement. The experiment utilizes a Mach–Zehnder interferometer, and visually demonstrates the loss of interference fringes when a which-way measurement is imposed, and the restoration of that pattern when the which-way information is destroyed. This device is also sensitive enough to observe interference fringes arising from single photons. We present a simple analysis of the interference appropriate for the coherent classical field limit and the single photon limit at a level accessible to undergraduates. We also briefly mention related issues on the nature of the photon.

DOI
10.1119/1.1450558

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We have developed a which-way experiment using visible light that is completely analogous to a recent experiment involving which-way measurement in atom interference. This simple experiment, easily accessible to undergraduate students and the resources of undergraduate departments, facilitates the examination of the key elements of which-way measurement, quantum erasure, and related mysteries of quantum measurement. The experiment utilizes a Mach–Zehnder interferometer, and visually demonstrates the loss of interference fringes when a which-way measurement is imposed, and the restoration of that pattern when the which-way information is destroyed. This device is also sensitive enough to observe interference fringes arising from single photons. We present a simple analysis of the interference appropriate for the coherent classical field limit and the single photon limit at a level accessible to undergraduates. We also briefly mention related issues on the nature of the photon.
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.
We describe a series of experiments used in a sophomore-level quantum physics course that are designed to provide students with a hands-on introduction to quantum mechanics. By measuring correlations, we demonstrate that a helium-neon laser produces results consistent with a classical model of light. We then demonstrate that a light source derived from a spontaneous parametric down-conversion process produces results that can only be described using a quantum theory of light, thus providing a (nearly) single-photon source. These single photons are then sent into a Mach–Zehnder interferometer, and interference fringes are observed whenever the path of the photons cannot be determined. These experiments are investigated theoretically using straightforward quantum-mechanical calculations.
Over the past several decades, single photon-based path interference in double-slit experiment has been well demonstrated for the particle nature of photons satisfying complementarity theory, where the quantum mechanical interpretation of the single photon interference fringe is given by Born rule for complex amplitudes in measurements. Unlike most conventional methods using entangled photon pairs, here, a classical coherent light source is directly applied for the proof of the same self-interference phenomenon. Instead of double slits, we use a Mach-Zehnder interferometer as usual, where the resulting self-interference fringe of coherent single photons is exactly the same as that of the coherent photon ensemble of the laser, demonstrating that the classical coherence based on the wave nature is rooted in the single photon self-interference. This unexpected result seems to contradict our common understanding of decoherence phenomena caused by multi-wave interference among bandwidth distributed photons in coherence optics.
Young's double slit experiment has often been used to illustrate the concept of complementarity in quantum mechanics. If information can in principle be obtained about the path of the photon, then the visibility of the interference fringes is reduced or even destroyed. This Gedanken experiment discussed by Bohr and Einstein can be realized when the slit is replaced by individual atoms sensitive to the transferred recoil momentum of a photon which "passes through the slit". Early pioneering experiments were done with trapped ions and atom pairs created via photo-dissociation. Recently, it became possible to perform interference experiments with single neutral atoms cooled to the absolute ground state of a harmonic oscillator potential. The slits are now single atoms representing a two-level system, and the excitation in the harmonic oscillator potential is the which-way marker. In this note, we analyze and generalize two recent experiments performed with single atoms and emphasize the different ways they record which-way information.
Recently, A. Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] performed a much-discussed experiment in which which-way information was obtained from the light in a nested Mach-Zehnder interferometer by weak measurement. The presented analysis using the two-state vector formalism drew the conclusions that the photons followed disconnected paths. We analyze this experiment using standard quantum optical methods and arrive at analytical expressions that match the experimental results without the need for such disconnected photon paths. We also propose a simple amendment to the experiment capable of displaying new phenomena, highlighting the advantages of our description.