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arXiv:quant-ph/0608073

Comment on a paper by Lapaire and Sipe

Morton H. Rubin

Published Aug 8, 2006• 1 citation
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Abstract

In a recent paper [quant-ph/0607008] Lapaire and Sipe argue that one can discuss interference experiments using entangled photons in terms of single photon wave functions. Furthermore, they argue that contrary to the claim of the authors of the postponed compensation experiment [2], the single photon wave functions overlap on the beam splitter when interference is observed. In this comment, we show that the claim in [2] is correct and we argue that the idea of single photon wave functions in entangled states is misleading.

DOI
10.48550/arxiv.quant-ph/0608073

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In a recent paper [quant-ph/0607008] Lapaire and Sipe argue that one can discuss interference experiments using entangled photons in terms of single photon wave functions. Furthermore, they argue that contrary to the claim of the authors of the postponed compensation experiment [2], the single photon wave functions overlap on the beam splitter when interference is observed. In this comment, we show that the claim in [2] is correct and we argue that the idea of single photon wave functions in entangled states is misleading.
We report on a ``postponed compensation'' experiment in which the observed two-photon entangled state interference cannot be pictured in terms of the overlap of the two individual photon wave packets of a parametric down-conversion pair on a beam splitter. In the sense of a quantum eraser, the distinguishability of the different two-photon Feynman amplitudes leading to a coincidence detection is removed by delaying the compensation until after the output of an unbalanced two-photon interferometer.
We present a general theory to describe two-photon interference, including a formal description of few photon intereference in terms of single-photon amplitudes. With this formalism, it is possible to describe both frequency entangled and separable two-photon interference in terms of single-photon wave functions. Using this description, we address issues related to the physical interpretation of two-photon interference experiments. We include a discussion on how few-photon interference can be interpreted as a bosonic exchange effect, and how this relates to traditional exchange effects with fermions.
Abstract The Mach–Zehnder interferometer experiment described earlier shows why and how quantum mechanics is different from classical mechanics. A photon sent through a beam splitter behaves like a particle when it is observed by only one of the two detectors. When two beam splitters are used, the photon “interferes with itself” and behaves like a wave. This is the so-called wave-particle duality of quantum mechanics which leads to quantum entanglement. This chapter discusses quantum superpositions when two or more particles are present. Understanding and analysing entanglement is one of the most interesting directions in the field of quantum information. First, a historical background of quantum entanglement is given, followed by a discussion on Bell's inequalities, separable states that do not violate Bell's inequalities, pure states that violate Bell's inequalities, mixed states that do not violate Bell's inequalities, and entanglement in second quantisation.
The production of maxima and minima by the superposition of two or more light signals provides fundamental support for the wave nature of light. This result is based on the study of wave interference phenomena which remains the only approach to explain the production of those maxima and minima. In a system that is prepared to work with only one photon at a time, any detector can signal only one or zero. In 1986, a rigorously controlled experiment was designed by Grangier, G. Roger, and A. Aspect, [Europhys Lett. 1(4), p. 173, 1986] that guaranteed a single-photon beam. The explanation of the experimental results implied the interference of the wave function of a single-photon with itself. Thus, the explanation of interference that is accepted for an ensemble of photons was assumed to be valid for a single photon. In this study, we prepare a Mach-Zehnder interferometer using the same type of beam splitters used by Grangier et al. to test the assumption mentioned above. Our results allow us to explain the results of Grangier et al. because of the interaction between light and the beam splitters. Our results also verify that their wave interpretation of the results is not valid. Here, we present the essential findings of the extensive experimental evidence that supports our ideas.
We report on two experiments using an atomic cascade as a light source, and a triggered detection scheme for the second photon of the cascade. The first experiment shows a strong anticorrelation between the triggered detections on both sides of a beam splitter. This result is in contradiction with any classical wave model of light, but in agreement with a quantum description involving single-photon states. The same source and detection scheme were used in a second experiment, where we have observed interferences with a visibility over 98%.