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Register a new userThree-Slit Ghost Interference and Nonlocal Duality
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Authors
Mohd Asad Siddiqui
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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.
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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.
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.
The ghost interference observed for entangled photons is theoretically analyzed using wave-packet dynamics. It is shown that ghost interference is a combined effect of virtual double-slit creation due to entanglement, and quantum erasure of which-path information for the interfering photon. For the case where the two photons are of different color, it is shown that fringe width of the interfering photon depends not only on its own wavelength, but also on the wavelength of the other photon which it is entangled with.
The two-photon ghost interference experiment, generalized to the case of massive particles, is theoretically analyzed. It is argued that the experiment is intimately connected to a double-slit interference experiment where, the which-path information exists. The reason for not observing first order interference behind the double-slit, is clarified.It is shown that the underlying mechanism for the appearance of ghost interference is, the more familiar, quantum erasure.
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