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arXiv:1403.4383 · Physica Scripta

Quantum properties of a which-way detector

J. S. Oliveira Filho, R. Rossi, Maria Carolina Nemes

Published Feb 5, 2015• 0 citations
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Abstract

We explore quantum properties of a which-way detector using three versions of an idealized two slit arrangement. First, we derive complementarity relations for the detector; second, we show how the ‘experiment’ may be altered in such a way that using a single-position measurement on the screen, we can obtain quantum erasure. Finally, we show how to construct a superposition of ‘wave’ and ‘particle’ components.

DOI
10.1088/0031-8949/90/3/035105

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We explore quantum properties of a which-way detector using three versions of an idealized two slit arrangement. First, we derive complementarity relations for the detector; second, we show how the ‘experiment’ may be altered in such a way that using a single-position measurement on the screen, we can obtain quantum erasure. Finally, we show how to construct a superposition of ‘wave’ and ‘particle’ components.
Recently, Mohrhoff [Am. J. Phys. 64, 1468–1475 (1996)] has analyzed a thought experiment of ours [Nature (London) 351, 111–116 (1991)] where a double-slit interferometer for atoms is supplemented by a pair of which-way detectors. Owing to the quantum nature of these detectors, the experimenter can choose between acquiring which-way knowledge and observing an interference pattern. The latter option makes use of a procedure called “quantum erasure.” Mohrhoff (along with other bright colleagues who have made similar statements) claims erroneously that the experimenter has to make this choice before the atom hits the screen. We readdress this issue here and demonstrate that our original assertion was correct: The experimenter can choose between which-way knowledge and quantum erasure at any time, even after the atom has left its mark on the screen.
In a typical double‐slit experiment, we seek for properties incompatible with Which Slit property, which can be detected without erasing the information about which slit each particle localized on the final screen passed through. It is found that these properties exist if the dimension of the Hilbert space describing the position of the particle is at least 4, but they can have a non‐trivial character only if such a dimension is at least 6. An ideal experiment realizing this non‐trivial detection without erasure is designed.
The quantum eraser involves a two-slit experiment in which an individual chooses, after the particles have passed through the slits, whether to do an interference experiment or a which-way experiment. If the experimenter chooses to erase the which-way information, the interference is restored. In one design, an excited atom enters one or the other cavity and emits a photon. By choosing to observe the photon’s position or to let it be absorbed by a detector atom, the investigator can pick the type of experiment to be done. The analysis uses the change-of-basis method, in which the form of wave function used depends on the experiment performed. A similar experiment can be performed by using polarizers at the slits and at the screen.
The principle of complementarity is one of the cornerstones of quantum theory. The aim of this study was to advance our understanding of complementarity by analyzing the role of delayed choice and quantum erasers in two-slit experiments, and by proposing experiments for verifying the analysis. The analysis is based on models consisting of measurable spaces and probability measures involved in the experiments. The main findings are as follows: (a) The complementarity principle manifests itself in such a way that wave and particle behaviors cannot be simultaneously observed almost surely with respect to any single, fixed measure. (b) Described by different measures, complementary properties can coexist in the same experimental setup. (c) Which-way information will not preclude or erase interference fringes. (d) Delayed choice and quantum erasers are irrelevant to testing complementarity. (e) It is possible for us to know through which slit each quantum object passed almost surely with respect to the measure corresponding to the slit while the interference pattern is intact. Based on the experiments analyzed, realizable experiments are proposed for verifying the above results.
The momentum changes caused by position measurements are a central feature of wave-particle duality. Here we investigate two cases - localization by a single slit, and which-way detection in the double-slit interference experiment - and examine in detail the associated momentum changes. Particular attention is given to the transfer of momentum between particle and detector, and the recoil of the measuring device. We find that single-slit diffraction relies on a form of `interaction-free' scattering, and that an ideal which-way measurement can be made without any back-reaction on the detector.