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Physical Review A

Franson’s experiment using polarized photons

Luiz Carlos Ryff

Published Aug 1, 1993• 9 citations
Publisher

Abstract

A modified Franson's two-photon correlation experiment is discussed. It is shown that the interference in the coincidence detection rate is lost when it is possible to determine the path followed by one of the photons. The interference is recovered when this information is ``erased.'' The experiment is devised so that the polarization of one of the photons depends on the path followed in the interferometer. Although the path difference is greater than the coherence length, when the two paths are open the photon can be found in a polarization state represented by the superposition of the polarization states associated to the paths. This can be comprehended by considering the situation in which one of the photons is detected before the other can reach the interferometer. In this case, the second photon has to be described by two wave packets simultaneously.

DOI
10.1103/physreva.48.1020

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Zeitschrift für Naturforschung A•Feb 1, 2001•0 citations
A modified Franson's two-photon correlation experiment is discussed. It is shown that the interference in the coincidence detection rate is lost when it is possible to determine the path followed by one of the photons. The interference is recovered when this information is ``erased.'' The experiment is devised so that the polarization of one of the photons depends on the path followed in the interferometer. Although the path difference is greater than the coherence length, when the two paths are open the photon can be found in a polarization state represented by the superposition of the polarization states associated to the paths. This can be comprehended by considering the situation in which one of the photons is detected before the other can reach the interferometer. In this case, the second photon has to be described by two wave packets simultaneously.
A variant of a Franson's two-photon correlation experiment is discussed, in which the linear polarization state of one of the photons depends on the path followed in the interferometer. It is shown that although the path difference is greater than the coherence length, the photon can be found in a polarization state represented by the superposition of the polarization states associated to the paths when there is coincident detection. Since the photons, produced via parametric down-conversion, are fairly well localized in space and time, the situation in which one of the photons is detected before the other can reach the interferometer raises an intriguing point: it seems that in some cases the second photon would have to be described by two wave packets simultaneously. Unlike previous experiments, in which nonlocal effects were induced by means of polarizers of phase shifters, in the proposed experiment nonlocal effects can be induced by means of variable absorbers.
A two-photon correlation experiment of the kind that was proposed by Franson and has recently been carried out by two groups is analyzed. In this experiment two simultaneously produced photons are directed along two paths to two photodetectors without mixing. An unbalanced interferometer with delay time that is much longer than the coherence time of the light is inserted in each path. Yet the rate of two-photon detection by the two detectors in coincidence exhibits interference as the path difference is changed. The question of whether classical field theory can account for these observations is discussed. We show that no ergodic classical field is able to reproduce the experimental results, although a nonergodic field can give rise to interference through the artifice of generating an ensemble by initializing repeatedly.
We present two-photon interference experiments with polarization-entangled photon pairs in a polarization-based Franson-type interferometer. Although the two photons do not meet at a common beamsplitter, a phase-insensitive Hong-Ou-Mandel type two-photon interference peak and dip fringes are observed, resulting from the two-photon interference effect between two indistinguishable two-photon probability amplitudes leading to a coincidence detection. A spatial quantum beating fringe is also measured for nondegenerate photon pairs in the same interferometer, although the two-photon states have no frequency entanglement. When unentangled polarization-correlated photons are used as an input state, the polarization entanglement is successfully recovered through the interferometer via delayed compensation.
Models of a two-photon interference experiment proposed by Franson to study the Einstein-Podolsky-Rosen (EPR) effect are presented. The experiment considers a pair of photons correlated in time and in frequency, each of which is passed through an interferometer. When the path difference through the two interferometers is set so there is no first-order interference, Franson showed that second-order interference between the two photons could occur with 100% visibility. In this paper both quantum and classical models are considered and the importance of the coincidence time window and the effect of the frequency correlation are shown. Calculations are presented for all settings of the interferometers. The EPR effect arises from entangled states; a brief discussion is given of the nature of the entangled state for this type of experiment.
We have observed an effect known as a quantum eraser, using a setup similar to one previously employed to demonstrate a violation of Bell's inequalities. In this effect, an interfering system is first rendered incoherent by making the alternate Feynman paths which contribute to the overall process distinguishable; with our apparatus this is achieved by placing a half wave plate in one arm of a Hong-Ou-Mandel interferometer so as to rotate the polarization of the light in that arm by 90\ifmmode^\circ\else\textdegree\fi{}. This adds information to the system, in that polarization is a new parameter which serves to label the path of a given photon, even after a recombining beam splitter. The quantum ``eraser'' removes this information from the state vector, after the output port of the interferometer, but in time to cause interference effects to reappear upon coincidence detection. For this purpose, we use two polarizers in front of our detectors. We present experimental results showing how the degree of erasure (which determines the visibility of the interference) depends on the relative orientation of the polarizers, along with theoretical curves. In addition, we show how this procedure may do more than merely erase, in that the act of ``pasting together'' two previously distinguishable paths can introduce a new relative phase between them.
Abstract Let us consider a single particle in an interferometer. If one of the two possible paths is blocked and the particle is detected, we know that the particle has followed the path which is not blocked. This would be an interference-free "which-path" information experiment. However, we no longer have an interfe­rometer, since one path is blocked. An alternative is to interact with the particle, but this would change its momentum and as a consequence the interference fringes would disappear, as discussed by Feynman. We can also consider two particles entangled in direction. Knowing the path followed by one of the par­ticles, it is possible to know the path followed by the other. On the other hand, when this information is erased, interference can be observed. However, this is a two particle interference: no single particle inter­ference can be observed. Retrodiction experiments are also possible, but these are not conclusive. Here we propose a much less intuitive experiment in which, without blocking one path or directly interacting with the particle, it is possible to know the path which is being followed by the particle in the interferom­eter. According to quantum mechanics, this is sufficient to lose the single particle interference. The same idea can be used to test the local pilot wave interpretation, to test quantum nonlocality under new conditions, and to devise an interferometer for a two-photon wave packet. This last result strongly suggests that there must be some connection between the deBroglie wavelength of an N-particle wave packet and entanglement. Wavelength of an /V-particle Wave Packet.