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arXiv:1402.0370

Losses-based test of wave-particle duality with Mach-Zehnder interferometers

Yang Chen, Aiai Jia, Deng, Xue, Yuchi Zhang, Li, Gang, Shi-Yao Zhu, Tiancai Zhang

Published Feb 3, 2014• 0 citations
arXivHTMLPDF

Abstract

Wave-particle duality of photons with losses in the Mach-Zehnder interferometer (MZI) is investigated experimentally and theoretically. The experiment is done with the standard MZI with the beam splitter or the beam merger being continuously varied. The losses are deliberately introduced either inside the MZI (the two arms between the beam splitter and beam mergers) or outside the MZI (after the beam merger). It is proved that the unbalanced losses have great influence on the predictability $P$ (particle nature) and visibility $V$ (wave nature). For the former case the duality inequality holds while for the later the duality inequality is ``violated''. We get $P^2+V^2>1$. This ``violation'' could be eliminated in principle by switching the two paths and detectors and then averaging the results. The observed results can be exactly explained theoretically. The experiment is done with coherent beam, instead of single photons, and we have proved that they are exactly equivalent in duality experiment with MZI.

DOI
10.48550/arxiv.1402.0370

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Wave-particle duality of photons with losses in the Mach-Zehnder interferometer (MZI) is investigated experimentally and theoretically. The experiment is done with the standard MZI with the beam splitter or the beam merger being continuously varied. The losses are deliberately introduced either inside the MZI (the two arms between the beam splitter and beam mergers) or outside the MZI (after the beam merger). It is proved that the unbalanced losses have great influence on the predictability PPP (particle nature) and visibility VVV (wave nature). For the former case the duality inequality holds while for the later the duality inequality is violated''. We get $P^2+V^2>1$. This violation'' could be eliminated in principle by switching the two paths and detectors and then averaging the results. The observed results can be exactly explained theoretically. The experiment is done with coherent beam, instead of single photons, and we have proved that they are exactly equivalent in duality experiment with MZI.
We theoretically investigate the influence of losses on the wave-particle duality in a Mach-Zehnder interferometer. Balanced losses (equal loss on the two paths) have no effect on the visibility and predictability (also the duality relation), while unbalanced losses do have influence on them. If the unbalanced losses occur inside the interferometer, the losses have an effect on both the visibility and predictability, while the losses have no effect on the duality relation. If the unbalanced losses occur after the interferometer, the losses have no effect on the visibility, but do have an effect on the predictability (also the wave-particle duality), which can lead to a result that the duality relation exceeds 1, P2+V2>1{P}^{2}+{V}^{2}>1P2+V2>1. The influence of losses can be eliminated by exchanging the two detectors or the two inputs (one photon and the vacuum) of the interferometer and then averaging the two results. Consequently, we have the visibility, predictability, and duality relation ${P}^{2}+{V}^{2}\ensuremath{\le}1$ independent of the unbalanced losses. The obtained PPP and VVV for the unbalanced losses in the two paths do not represent the original predictability and visibility, and the result of PD2+VD2>1{P}_{D}^{2}+{V}_{D}^{2}>1PD2​+VD2​>1 does not mean the ``violation'' of the original duality.
\n\nThe Mach-Zehnder interferometer (MZI) is a regular yet simple instrument to test wave-particle duality. One key device in a standard MZI is the beam splitter 2 (BS2). Here we make a simple quantum mechanics analysis about the wave function evolution and find that the strong and exclusive interaction of BS2 with the incident microscopic particle beam (photons, electrons, etc.) is the fundamental reason why standard MZIs could not allow for the simultaneous observation of wave and particle properties of these particles. A weak-measurement (WM) MZI setup is then proposed, where BS2 is replaced with a deliberately designed highly transparent interference screen operating via either weak absorption or weak-scattering effect. Quantum-mechanical analysis on this WM-MZI shows that the overall power to make simultaneous observation of interference fringe (wave nature) and which-path information (particle nature) of microscopic particles can be significantly enhanced compared with the standard MZIs.\n
The Mach-Zehnder Interferometer (MZI) is used to illustrate the long-standing wave-particle duality problem. How can the photon divide at the first beam splitter and yet terminate on either arm with its undiminished energy? Why is which-way (welcher weg) information incompatible with wave interference? How do we explain Wheeler’s delayed choice experiment? The position adopted is that the photon has two identities, one supporting particle features and the other wave features. There is photon kinetic energy that never splits (on half-silvered mirrors) or diffracts (in pinholes or slits). Then there is photon probability waves that do diffract and can reinforce or cancel. Interpretations of these two identities are suggested.
Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave-particle properties of single photons (or single particles in general) showed that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with a Bell state. By doing so, we experimentally test the complementarity principle in a scenario in which the setting of the interferometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we establish the three-photon entangled state, i.e., the entanglement between a single photon and a two-photon Bell state, send the photon of interest SSS into a quantum Mach-Zehnder interferometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon CCC, which is entangled with a third photon AAA. Therefore, the individual quantum state of photon CCC is undefined, which implements the undefined settings of the MZI for photon SSS. This is realized by using three cascaded phase-stable interferometers for three photons. There is typically no well-defined setting of the MZI and thus the very formulation of the wave-particle objectivity from local hidden variable models becomes internally inconsistent.
We present a study of the relation between wave-particle duality and quantum uncertainty in a two-path interferometer and derive equalities and inequalities involving the visibility (representing wave-like behavior), the predictability (representing particle-like behavior), and their variances. We experimentally demonstrate that, for a single photon in a Mach-Zehnder interferometer, these quantities are related via an equation that connects both duality and uncertainty. This relation holds for the single-photon source prepared either in a pure state or a mixed state.
The chapter discusses the Mach–Zehnder interferometer (MZI), which uses beam splitters in combination with mirrors to place a photon into a superposition of paths. In a final beam splitter, the two paths may be recombined to interfere, showing wave behavior. If the final beam splitter is removed, the photon is definitely in one path or the other, showing particle behavior. The polarization of light allows additional applications—one can use a polarizing beam splitter to separate and reconstitute the wave functions of a photon polarized at an angle. In a delayed-choice experiment, one decides which kind of experiment one is to do, particle or wave, after the photon has already entered the arms of the MZI. The chapter discusses a version of this that puts the MZI and a second-detector photon in an entangled state of particle and wave results.