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arXiv:0705.4038

Single-photon interferometry with orbital angular momentum circumvents standard wave-particle duality

Kolar, M., Tomáš Opatrný, Gershon Kurizki

Published May 28, 2007• 0 citations
arXivHTMLPDF

Abstract

A polarized photon with well-defined orbital angular momentum that emerges from a Mach-Zehnder interferometer (MZI) is shown to circumvent wave-particle duality. Its polarization-resolved detection probability forms a non-sinusoidal interferometric pattern. For certain phase differences between the MZI arms, this pattern yields both reliable which-path information and high phase-sensitivity.

DOI
10.48550/arxiv.0705.4038

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A polarized photon with well-defined orbital angular momentum that emerges from a Mach-Zehnder interferometer (MZI) is shown to circumvent wave-particle duality. Its polarization-resolved detection probability forms a non-sinusoidal interferometric pattern. For certain phase differences between the MZI arms, this pattern yields both reliable which-path information and high phase-sensitivity.
The quantum eraser effect exemplifies the distinctive properties of quantum mechanics that challenge classical intuition and reveal the wave-particle duality of light.Whether the photon exhibits particle-like or wave-like behavior depends on whether the path information is discernible.In this paper, we propose a novel quantum eraser scheme that utilizes photonic phase structures as the which-way indicator.This scheme is implemented using a Mach-Zehnder interferometer (MZI), where one arm is configured with orbital angular momentum (OAM) to establish predetermined which-way information.Consequently, at the output ports of the MZI, the photon displays particle-like characteristics when the which-way information is retained.However, the introduction of an additional spiral phase plate (SPP) to eliminate the phase structure from the output photon of the MZI unveils distinct interference patterns.This result enhances our understanding of the quantum erasure effect.
We examine two setups that reveal different operational implications of path-phase complementarity for single photons in a Mach-Zehnder interferometer (MZI). In both setups, the which-way (WW) information is recorded in the polarization state of the photon serving as a "flying which-way detector". In the "predictive" variant, using a {\em fixed} initial state, one obtains duality relation between the probability to correctly predict the outcome of either a which-way (WW) or which-phase (WP) measurement (equivalent to the conventional path-distinguishibility-visibility). In this setup, only one or the other (WW or WP) prediction has operational meaning in a single experiment. In the second, "retrodictive" protocol, the initial state is secretly selected {\em for each photon} by one party, Alice, among a set of initial states which may differ in the amplitudes and phases of the photon in each arm of the MZI. The goal of the other party, Bob, is to retrodict the initial state by measurements on the photon. Here, a similar duality relation between WP and WW probabilities, governs their {\em simultaneous} guesses in {\em each experimental run}.
Abstract. We examine two setups that reveal different operational implications of path-phase complementarity for single photons in a Mach-Zehnder interferometer (MZI). In both setups, the which-way (WW) information is recorded in the polarization state of the photon serving as a “flying which-way detector”. In the “predictive” variant, using a fixed initial state, one obtains duality relation between the probability to correctly predict the outcome of either a which-way (WW) or which-phase (WP) measurement (equivalent to the conventional path-distinguishibility-visibility). In this setup, only one or the other (WW or WP) prediction has operational meaning in a single experiment. In the second, “retrodictive ” protocol, the initial state is secretly selected for each photon by one party, Alice, among a set of initial states which may differ in the amplitudes and phases of the photon in each arm of the MZI. The goal of the other party, Bob, is to retrodict the initial state by measurements on the photon. Here, a similar duality relation between WP and WW probabilities, governs their simultaneous guesses in each experimental run.
The chapter discusses the Mach–Zehnder interferometer (MZI), which uses beam splitters in combination with mirrors to place a photon into a superposition of paths. In a final beam splitter, the two paths may be recombined to interfere, showing wave behavior. If the final beam splitter is removed, the photon is definitely in one path or the other, showing particle behavior. The polarization of light allows additional applications—one can use a polarizing beam splitter to separate and reconstitute the wave functions of a photon polarized at an angle. In a delayed-choice experiment, one decides which kind of experiment one is to do, particle or wave, after the photon has already entered the arms of the MZI. The chapter discusses a version of this that puts the MZI and a second-detector photon in an entangled state of particle and wave results.
The Mach-Zehnder Interferometer (MZI) is used to illustrate the long-standing wave-particle duality problem. How can the photon divide at the first beam splitter and yet terminate on either arm with its undiminished energy? Why is which-way (welcher weg) information incompatible with wave interference? How do we explain Wheeler’s delayed choice experiment? The position adopted is that the photon has two identities, one supporting particle features and the other wave features. There is photon kinetic energy that never splits (on half-silvered mirrors) or diffracts (in pinholes or slits). Then there is photon probability waves that do diffract and can reinforce or cancel. Interpretations of these two identities are suggested.