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Register a new userThree-Slit Interference: A Duality Relation
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The issue of interference and which-way information is addressed in the context of 3-slit interference experiments. A new path distinguishability ${mathcal D_Q}$ is introduced, based on Unambiguous Quantum State Discrimination (UQSD). An inequality connecting the interference visibility and path distinguishability, ${mathcal V} + {2{mathcal D_Q}over 3- {mathcal D_Q}} le 1$, is derived which puts a bound on how much fringe visibility and which-way information can be simultaneously obtained. It is argued that this bound is tight. For 2-slit interference, we derive a new duality relation which reduces to Englerts duality relation and Greenberger-Yasins duality relation, in different limits.
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A three-slit ghost interference experiment with entangled photons is theoretically analyzed using wave-packet dynamics. A non-local duality relation is derived which connects the path distinguishability of one photon to the interference visibility of the other.
It is well known that in a two-slit interference experiment, if the information, on which of the two paths the particle followed, is stored in a quantum path detector, the interference is destroyed. However, in a setup where this path information is erased, the interference can reappear. Such a setup is known as a quantum eraser. A generalization of quantum eraser to a three-slit interference is theoretically analyzed. It is shown that three complementary interference patterns can arise out of the quantum erasing process.
The validity of the superposition principle and of Borns rule are well-accepted tenants of quantum mechanics. Surprisingly, it has recently been predicted that the intensity pattern formed in a three-slit experiment is seemingly in contradiction with the predictions of the most conventional form of the superposition principle when exotic looped trajectories are taken into account. However, the probability of observing such paths is typically very small and thus rendering them extremely difficult to measure. In this work, we confirm the validity of Borns rule and present the first experimental observation of these exotic trajectories as additional paths for the light by directly measuring their contribution to the formation of optical interference fringes. We accomplish this by enhancing the electromagnetic near-fields in the vicinity of the slits through the excitation of surface plasmons. This process effectively increases the probability of occurrence of these exotic trajectories, demonstrating that they are related to the near-field component of the photons wavefunction.
In classical optics, Youngs double-slit experiment with colored coherent light gives rise to individual interference fringes for each light frequency, referring to single-photon interference. However, two-photon double-slit interference has been widely studied only for wavelength-degenerate biphoton, known as subwavelength quantum lithography. In this work, we report double-slit interference experiments with two-color biphoton. Different from the degenerate case, the experimental results depend on the measurement methods. From a two-axis coincidence measurement pattern we can extract complete interference information about two colors. The conceptual model provides an intuitional picture of the in-phase and out-of-phase photon correlations and a complete quantum understanding about the which-path information of two colored photons.
Some recent works have introduced a quantum twist to the concept of complementarity, exemplified by a setup in which the which-way detector is in a superposition of being present and absent. It has been argued that such experiments allow measurement of particle-like and wave-like behavior at the same time. Here we derive an inequality which puts a bound on the visibility of interference and the amount of which-way information that one can obtain, in the context of such modified experiments. As the wave-aspect can only be revealed by an ensemble of detections, we argue that in such experiments, a single detection can contribute only to one subensemble, corresponding to either wave-aspect or particle aspect. This way, each detected particle behaves either as particle or as wave, never both, and Bohrs complementarity is fully respected.
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