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Journal of Modern Optics

Information and Complementarity in a Proposed Which-path Experiment Using Photons

Michael G. Raymer, Shuangbo Yang

Published Jun 1, 1992• 10 citations
Publisher

Abstract

We propose a scheme to realize the famous two-slit gedanken experiment using photons. Measurements using optical parametric amplifiers (OPAs) are proposed to infer the probabilities that the input photon has taken a particular path in a Mach-Zehnder interferometer, without destroying the photon. Using information theory and Bayes' theorem, we find that the visibility of ensemble averaged interference fringes is inversely related to the which-path information that is made available by the OPAs. This is in agreement with the complementarity principle. A method is found to erase partially the which-path information before it is recorded; then by making conditional measurements the fringe visibility can be partially restored.

DOI
10.1080/713823533

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We propose a scheme to realize the famous two-slit gedanken experiment using photons. Measurements using optical parametric amplifiers (OPAs) are proposed to infer the probabilities that the input photon has taken a particular path in a Mach-Zehnder interferometer, without destroying the photon. Using information theory and Bayes' theorem, we find that the visibility of ensemble averaged interference fringes is inversely related to the which-path information that is made available by the OPAs. This is in agreement with the complementarity principle. A method is found to erase partially the which-path information before it is recorded; then by making conditional measurements the fringe visibility can be partially restored.
A scheme is proposed for experimentally achieving the famous two-slit gedanken experiment using photons. A particle’s quantum pathways can interfere to produce fringes in the probability for the particle to be found at some location. If the path taken by the particle is experimentally determined, the complementarity principle says that the fringes must disappear. To carry out this experiment with photons is difficult because normally the act of determining a photon’s location destroys it. We propose to overcome this by putting a type-II optical parametric amplifier (OPA) in each arm of a Mach-Zehnder interferometer and observing fringes at the output. An OPA responds to an input photon by increasing its probability to produce a pair of photons, one having polarization orthogonal to the input photon.
We study the fringe visibility and the which-path information (WPI) of a general Mach–Zehnder interferometer with an asymmetric beam splitter (BS). A minimum error measurement in the detector is used to extract the WPI. Both the fringe visibility V and the WPI Ipath are affected by the initial state of the photon and the second asymmetric BS. The condition in which the WPI takes the maximum is obtained. The complementarity relationship V 2 + I path 2 ≤ 1 is found, and the conditions for equality are also presented.
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.
Which-path information of a quantum particle in interferometers is the key to infer the past of the quantum particle. It has led to many extensive discussions, including discussions of quantum complementarity and the path-visibility relation. The basics of these discussions are the description, detection, and control of which-path information. In this paper, we focus on the investigation of multidimensional which-path information in a nested Mach-Zehnder interferometer. A general expression of which-path information is given and can be partially extracted by different detection methods. Further analysis shows that the which-path information can be controlled by the phase differences and beam-splitting ratios between the arms of the nested Mach-Zehnder interferometer. Moreover, an alternative which-path information elimination phenomenon has been predicted and demonstrated experimentally. Our work can help us to understand the physics of quantum particles, with potential applications for quantum information processing and quantum metrology.
We probe the principle of complementarity by performing a double-slit experiment based on entangled photons created by spontaneous parametric down-conversion from a pump mode in a TEM01-mode. Our setup brings out the need for a careful selection of the signal-idler photon pairs for our study of visibility and distinguishability. Indeed, when the signal photons interfering at the double-slit belong to this double-hump mode we obtain almost perfect visibility of the interference fringes and no "which-slit" information is available. However, when we break the symmetry between the two maxima of the mode by detecting the entangled idler photon, the paths through the slits become distinguishable and the visibility vanishes. It is the mode function of the photons selected by the detection system which decides if interference, or "which-slit" information is accessible in the experiment.