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Optics Letters

On the distinguishability of downconverted modes with orbital angular momentum

Geraldo Alexandre Barbosa

Published Sep 11, 2008• 1 citation
Publisher

Abstract

Assuming two quantum states of spontaneous parametric downconversion carrying orbital angular momentum, one may ask the question what is the minimum probability of error in identifying between two of these biphoton states by an arbitrary physical measurement over the biphoton state generated. While correctly chosen geometries may lead to perfect distinguishability of modes, it is worth noticing that experimental subtleties may lead to a poor mode distinguishability. We discuss the case where a restricted range instead of the needed range of wave vectors is collected by the experimental setup. These considerations may be useful for some applications, e.g., cryptography.

DOI
10.1364/ol.33.002119

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Assuming two quantum states of spontaneous parametric downconversion carrying orbital angular momentum, one may ask the question what is the minimum probability of error in identifying between two of these biphoton states by an arbitrary physical measurement over the biphoton state generated. While correctly chosen geometries may lead to perfect distinguishability of modes, it is worth noticing that experimental subtleties may lead to a poor mode distinguishability. We discuss the case where a restricted range instead of the needed range of wave vectors is collected by the experimental setup. These considerations may be useful for some applications, e.g., cryptography.
Identification of light modes usually requires careful considerations of the collecting geometry. This is particularly true for states carrying orbital angular-momentum modes from spontaneous parametric down-conversion due to the entanglement of the signal and idler fields. A detailed understanding of the generated modes in a general case allows the design of efficient detection setups. This is true for distinct cases, e.g., when multiple samplings are performed by repeated state generation or in single-photon cryptography or quantum computation, where a photon state is generated within a short-time window and a single measurement is performed. Aspects of nonorthogonality of signal and idler modes and effects of restrictions on the collecting geometry are discussed in this work.
The generation of paired photons entangled in orbital angular momentum (OAM), provides a new degree of freedom that is increasingly being used as a source of quantum states. Elucidation of the OAM spectrum of OAM spectrum of the generated photons is of paramount importance, since quantum information applications require the ability to generate arbitrary entangled states with the appropriate OAM correlations. Here we discuss the OAM spectrum of the photon generated via SPDC in two complementary scenarios. On one hand, we should consider the whole geometry of the nonlinear process, taking into account azimuthal variations of the nonlinear coefficient or the phase matching conditions. On the other hand, all relevant experiments reported to date detect only a small section of the full down-conversion cone. In this scenario, the measured OAM correlations depend of the emission angle of the photons and the strength of the Poynting vector walk-off. We will present experiments in SPDC where this dependence is clearly revealed.