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arXiv:1708.01408 · Physical Review A

Unambiguous path discrimination in a two-path interferometer

Yink Loong Len, Jibo Dai, Berthold‐Georg Englert, Leonid A. Krivitsky

Published Aug 7, 2018• 12 citations
arXivHTMLPDF

Abstract

When a photon is detected after passing through an interferometer one might wonder which path it took, and a meaningful answer can only be given if one has the means of monitoring the photon's whereabouts. We report the realization of a single-photon experiment for a two-path interferometer with path marking. In this experiment, the path of a photon (``signal'') through a Mach-Zehnder interferometer becomes known by unambiguous discrimination between the two paths. We encode the signal path in the polarization state of a partner photon (``idler'') whose polarization is examined by a three-outcome measurement: one outcome each for the two signal paths plus an inconclusive outcome. Our results agree fully with the theoretical predictions from a common-sense analysis of what can be said about the past of a quantum particle: The signals for which we get the inconclusive result have full interference strength, as their paths through the interferometer cannot be known; and every photon that emerges from the dark output port of the balanced interferometer has a known path.

DOI
10.1103/physreva.98.022110

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When a photon is detected after passing through an interferometer one might wonder which path it took, and a meaningful answer can only be given if one has the means of monitoring the photon's whereabouts. We report the realization of a single-photon experiment for a two-path interferometer with path marking. In this experiment, the path of a photon (signal'') through a Mach-Zehnder interferometer becomes known by unambiguous discrimination between the two paths. We encode the signal path in the polarization state of a partner photon (idler'') whose polarization is examined by a three-outcome measurement: one outcome each for the two signal paths plus an inconclusive outcome. Our results agree fully with the theoretical predictions from a common-sense analysis of what can be said about the past of a quantum particle: The signals for which we get the inconclusive result have full interference strength, as their paths through the interferometer cannot be known; and every photon that emerges from the dark output port of the balanced interferometer has a known path.
We analyze Vaidman's three-path interferometer with weak path marking [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and find that common sense yields correct statements about the particle's path through the interferometer. This disagrees with the original claim that the particles have discontinuous trajectories at odds with common sense. In our analysis, ``the particle's path'' has operational meaning as acquired by a path-discriminating measurement. For a quantum-mechanical experimental demonstration of the case, one should perform a single-photon version of the experiment by Danan et al. [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] with unambiguous path discrimination. We present a detailed proposal for such an experiment.
We prepared polarization-entangled photon pairs and sent one of the photons through a Mach-Zehnder interferometer. The apparatus was arranged so that when going through each arm of the interferometer the pairs were in a different Bell state. The distinguishability of the interferometer paths was determined by projecting the entangled state of the two photons with a polarizer placed in the path of the photon that does not go through the interferometer. As a consequence, actions on the remote photon determined nonlocally the visibility of the interference pattern. We present a full theoretical analysis and experimental results that confirm the theoretical predictions.
We present a three-path photon interferometer, theoretically investigate the behavior of the photon passing through it, and revisit the surprising experimental outcomes introduced by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)]. Our study shows that the ``discontinuous trajectory'' behavior of the photon results from the interference of the three propagation paths of the photon, which originate from the light source and end in the detector. If two of the three paths are adjusted in a destructive interference condition, there will be a zero probability domain in the overlap region of these two paths. However, these two paths can still individually interfere with the third path and contribute to the final output. In this condition, the discontinuous trajectory phenomenon appears. Our theory has a clear physical image and agrees with the experimental outcomes very well.
Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a "common sense" approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.
Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a ``common sense'' approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.
A pair of light quanta with different colors (155.9-nm difference in center wavelength) generated from parametric down-conversion was injected collinearly into one input port of a Mach-Zehnder interferometer. Coincidence interference behavior was studied over a wide range of optical path differences of the interferometer. A measurement of 75% interference visibility with oscillation of the pump frequency for a large optical path difference of the interferometer (43 cm) is the signature of a quantum two-photon entangled state, which reflects both particle and wave nature of the light quanta in one experiment.