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European Journal of Physics

Single photon quantum erasing: a demonstration experiment

Todorka L. Dimitrova, Antoine Weis

Published Apr 7, 2010• 22 citations
Publisher

Abstract

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.

DOI
10.1088/0143-0807/31/3/020

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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.
Single-photon interference is a beautiful manifestation of the wave–particle duality of light and the double-slit Gedankenexperiment is a standard lecture example for introducing quantum mechanical reality. Interference arises only if each photon can follow several (classical) paths from the source to the detector, and if one does not have the possibility to determine which specific path the photon has taken. Attaching a specific label to the photon traveling along a specific path destroys the interference. However, in some cases those labels can be erased from the photon between leaving the apparatus and being detected, by which interference can be restored, a phenomenon called quantum erasing. We present lecture demonstration experiments that illustrate the wave–particle duality of light and the phenomenon of quantum erasing. Both experiments are first shown with strong light and, in a second step, on a photon-by-photon basis. The smooth transition from the quantum to the classical case can be shown in real time by varying the incident light intensity.
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.
We have observed an effect known as a quantum eraser, using a setup similar to one previously employed to demonstrate a violation of Bell's inequalities. In this effect, an interfering system is first rendered incoherent by making the alternate Feynman paths which contribute to the overall process distinguishable; with our apparatus this is achieved by placing a half wave plate in one arm of a Hong-Ou-Mandel interferometer so as to rotate the polarization of the light in that arm by 90\ifmmode^\circ\else\textdegree\fi{}. This adds information to the system, in that polarization is a new parameter which serves to label the path of a given photon, even after a recombining beam splitter. The quantum ``eraser'' removes this information from the state vector, after the output port of the interferometer, but in time to cause interference effects to reappear upon coincidence detection. For this purpose, we use two polarizers in front of our detectors. We present experimental results showing how the degree of erasure (which determines the visibility of the interference) depends on the relative orientation of the polarizers, along with theoretical curves. In addition, we show how this procedure may do more than merely erase, in that the act of ``pasting together'' two previously distinguishable paths can introduce a new relative phase between them.
Abstract The delayed-choice quantum eraser has long been a subject of controversy, and has been looked at as being incomprehensible to having retro-causal effect in time. Here the delayed-choice quantum eraser is theoretically analyzed using standard quantum mechanics. Employing a Mach–Zehnder interferometer, instead of a conventional two-slit interference, brings in surprising clarity. Some common mistakes in interpreting the experiment are pointed out. It is demonstrated that in the delayed mode there is no which-way information present after the particle is registered on the screen or the final detectors, contrary to popular belief. However, it is shown that another kind of path information is present even after the particle is registered in the final detectors. The registered particle can be used to predict the results of certain yet to be made measurements on the which-way detector. This novel correlation can be tested in a careful experiment. It is consequently argued that there is no big mystery in the experiment, and no retro-causal effect whatsoever.
The notion of wave-particle duality may be quantified by the inequality V2+K2< 1,{V}^{2}{+K}^{2}<~1,V2+K2< 1, relating interference fringe visibility V, and path knowledge K. With a single-photon interferometer in which polarization is used to label the paths, we have investigated the relation for various situations, including pure, mixed, and partially mixed input states. A quantum-eraser scheme has been realized that recovers interference fringes even when no which way information is available to erase.
The quantum eraser effect exemplifies the distinctive properties of quantum mechanics that challenge classical intuition and reveal the wave-particle duality of light.Whether the photon exhibits particle-like or wave-like behavior depends on whether the path information is discernible.In this paper, we propose a novel quantum eraser scheme that utilizes photonic phase structures as the which-way indicator.This scheme is implemented using a Mach-Zehnder interferometer (MZI), where one arm is configured with orbital angular momentum (OAM) to establish predetermined which-way information.Consequently, at the output ports of the MZI, the photon displays particle-like characteristics when the which-way information is retained.However, the introduction of an additional spiral phase plate (SPP) to eliminate the phase structure from the output photon of the MZI unveils distinct interference patterns.This result enhances our understanding of the quantum erasure effect.