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arXiv:1408.6192 · The European Physical Journal D

Complementarity, quantum erasure and delayed choice with modified Mach-Zehnder interferometers

Stefan Ataman

Published Oct 1, 2014• 3 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2014-50483-9

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We discuss complementarity and uncertainty in a gedanken Which-Way (Welcher-Weg) experiment in a Mach-Zehnder interferometer. Although a Welcher-Weg measurement can be performed with only a negligible amount of momentum change in the detector itself, the change in the interference pattern must correspond to a change in the momentum distribution of the particle. Entanglement between the Mach-Zehnder interferometer and the Welcher-Weg measurement introduces orthogonality that disables the interference of the particle, but simultaneously, it also generates a momentum transfer between the particle and other parts of the whole entangled system (including macroscopic parts). This analysis can be related to the Delayed Choice interpretation. We show where the momentum change takes place and we conclude that entanglement is the key to understand how complementarity (i.e. Which Way versus interference) and the position-momentum uncertainty relation are interwoven.
Ever since the proposal of delayed choice quantum erasure and subsequent realization in the experiment by Kim et al., the interpretation and implications of delayed-choice experiments have remained a subject of intense foundational debate. This paper resolves the apparent paradox attached to the experiment using standard quantum mechanics. Using an extended Mach-Zehnder interferometer which captures every operational feature of the original experiment, we show that choosing between which-path and erasure detectors is simply a choice of measurement bases, which does not rewrite a photon's past. Furthermore, by mapping the experiment to a two-way Stern-Gerlach framework, we prove that quantum erasure is an expected result of measuring entangled states, not a physical anomaly. Ultimately, through a pedagogical game, we illustrate that the illusion of retrocausality arises from asking illegitimate questions, and that a forward-in-time description is entirely sufficient to explain the logic.
We report an experimental test of quantum complementarity with single-photon pulses sent into a Mach-Zehnder interferometer with an output beam splitter of adjustable reflection coefficient R. In addition, the experiment is realized in Wheeler's delayed-choice regime. Each randomly set value of R allows us to observe interference with visibility V and to obtain incomplete which-path information characterized by the distinguishability parameter D. Measured values of V and D are found to fulfill the complementarity relation V2+D2 < or =1.