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Time-Modulated Hamiltonian for Interpreting Delayed-Choice Experiments via Mach–Zehnder Interferometers |
| Zhi-Yuan Li1,2** |
1Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190
2College of Physics and Optoelectronics, South China University of Technology, Guangzhou 510641
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| Cite this article: |
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Zhi-Yuan Li 2016 Chin. Phys. Lett. 33 080302 |
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Abstract Many delayed-choice experiments based on Mach–Zehnder interferometers (MZI) have been considered and made to address the fundamental problem of wave-particle duality. Conventional wisdom long holds that by inserting or removing the second beam splitter (BS2) in a controllable way, microscopic particles (photons, electrons, etc.) transporting within the MZI can lie in the quantum superposition of the wave and particle state as $\psi =a_{\rm w} \psi _{\rm wave} +a_{\rm p} \psi _{\rm particle}$. Here we present an alternative interpretation to these delayed-choice experiments. We notice that as the BS2 is purely classical, the inserting and removing operation of the BS2 imposes a time-modulated Hamiltonian $H_{\bmod} (t)=a(t)H_{\rm in} +b(t)H_{\rm out}$, instead of a quantum superposition of $H_{\rm in}$ and $H_{\rm out}$ as $H=a_{\rm w} H_{\rm in} +a_{\rm p} H_{\rm out}$, to act upon the incident wave function. Solution of this quantum scattering problem, rather than the long held quantum eigen-problem yields a synchronically time-modulated output wave function as $\psi _{\bmod} (t)=a(t)\psi _{\rm wave} +b(t)\psi _{\rm particle}$, instead of the stationary quantum superposition state $\psi =a_{\rm w} \psi _{\rm wave} +a_{\rm p} \psi _{\rm particle}$. As a result, the probability of particle output from the MZI behaves as if they are in the superposition of the wave and particle state when many events over time accumulation are counted and averaged. We expect that these elementary but insightful analyses will shed a new light on exploring basic physics beyond the long-held wisdom of wave-particle duality and the principle of complementarity.
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Received: 06 March 2016
Published: 31 August 2016
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| PACS: |
03.65.Ta
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(Foundations of quantum mechanics; measurement theory)
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03.75.Dg
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(Atom and neutron interferometry)
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42.50.Xa
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(Optical tests of quantum theory)
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