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arXiv:quant-ph/0106154

A quantum field theoretic description of the delayed choice experiment

R. Srikanth

Published Jun 27, 2001• 2 citations
arXivHTMLPDF

Abstract

Wheeler's delayed choice experiment, a well known manifestation of the complementarity principle, has proved somewhat difficult to physically interpret. We show that, restated in quantum field theoretic language, the experiment submits to a simple explanation: that wave- or particle-nature is imposed not at the slit plane but at the detector system. The intepretational difficulty conventionally encountered is due to the assumption of enforcement of complementarity at the former.

DOI
10.48550/arxiv.quant-ph/0106154

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Wheeler's delayed choice experiment, a well known manifestation of the complementarity principle, has proved somewhat difficult to physically interpret. We show that, restated in quantum field theoretic language, the experiment submits to a simple explanation: that wave- or particle-nature is imposed not at the slit plane but at the detector system. The intepretational difficulty conventionally encountered is due to the assumption of enforcement of complementarity at the former.
Abstract Quantum delayed-choice experiments are designed to probe the robustness of the complementarity principle. In this proceeding, we revisit the main ideas reported recently in Ref. [Commun. Phys. 5, 82 (2022)] concerning a setup (quantum-controlled reality experiment) that has the same final visibility as the quantum version of Wheeler’s delayed-choice arrangement. Besides the same final statistics, upon an operational criterion of physical realism, the authors claimed a different state of affairs for the wave-and-particle behavior in delayed-choice experiments. To this end, we put forward an analysis by employing the relative entropy of coherence to study how the local wave and particle coherences when the system is traveling inside the interferometer change accordingly to the final observed visibility.
It is well known that Wheeler proposed several delayed choice experiments in order to show the impossibility to speak of the way a quantum system behaves before being detected. In a double-slit experiment, when do photons decide to travel by one way or by two ways? Delayed choice experiments seem to indicate that, strangely, it is possible to change the decision of the photons until the very last moment before they are detected. This led Wheeler to his famous sentence: No elementary quantum phenomenon is a phenomenon until it is a registered phenomenon, brought to a close by an irreversible act of amplification. Nevertheless some authors wrote that backward in time effects were needed to explain these results. I will show that in delayed choice experiments involving only one particle, a simple explanation is possible without invoking any backward in time effect. Delayed choice experiments involving entangled particles such as the so called quantum eraser can also be explained without invoking any backward in time effect but I will argue that these experiments cannot be accounted for so simply because they rise the whole problem of knowing what a measurement and a collapse are. A previously presented interpretation, Convivial Solipsism, is a natural framework for giving a simple explanation of these delayed choice experiments with entangled particles. In this paper, I show how Convivial Solipsism helps clarifying the puzzling questions raised by the collapse of the wave function of entangled systems.
Wave-particle complementarity lies at the heart of quantum mechanics. To illustrate this mysterious feature, Wheeler proposed the delayed-choice experiment, where a quantum system manifests the wave- or particle-like attribute, depending on the experimental arrangement, which is made after the system has entered the interferometer. In recent quantum delayed-choice experiments, these two complementary behaviors were simultaneously observed with a quantum interferometer in a superposition of being closed and open. We suggest and implement a conceptually different quantum delayed-choice experiment by introducing a which-path detector (WPD) that can simultaneously record and neglect the system's path information, but where the interferometer itself is classical. Our experiment is realized with a superconducting circuit, where a cavity acts as the WPD for an interfering qubit. Using this setup, we implement the first twofold delayed-choice experiment, which demonstrates that the system's behavior depends not only on the measuring device's configuration that can be chosen even after the system has been detected but also on whether we a posteriori erase or mark the which-path information, the latter of which cannot be revealed by previous quantum delayed-choice experiments. Our results represent the first demonstration of both counterintuitive features with the same experimental setup, significantly extending the concept of quantum delayed-choice experiment.
A new `wave-particle non-dualistic interpretation' at the single-quantum level, existing within the quantum formalism, is presented by showing the Schr\odinger wave function as an `{\it instantaneous resonant spatial mode}' where a particle moves. For the first time, the position eigenstate of a particle is identified to be related to the absolute phase of the wave function in such a way that its position eigen values always lie on a classical trajectory, proving that the `time parameter' is common to both classical and quantum mechanics. It's brought into light that the quantum formalism demands a different kind of boundary conditions to be imposed to the wave function unlike classical formalism and hence naturally yields the Born rule as a limiting case of the relative frequency of detection. This derivation of the Born rule automatically resolves the measurement problem. Also, these boundary conditions immediately expound Bohr's principle of complementarity at a single quantum level. Further, the non-duality naturally contains the required physical mechanism to elucidate why the Copenhagen interpretation is experimentally so successful. The single-quantum phenomenon is then used to unambiguously explain what's really going on in the Young double-slit experiment as anticipated by Feynmann and the same is again used to provide a causal explanation of Wheeler's delayed-choice experiment.
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.