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Physical Review Letters

Measurement of the Spiral Spectrum of Entangled Two-Photon States

H. Di Lorenzo Pires, H. C. B. Florijn, Martin P. van Exter

Published Jan 15, 2010• 129 citations
Publisher

Abstract

We implement an interferometric method to measure the orbital angular momentum (OAM) spectrum of photon pairs generated by spontaneous parametric down-conversion. In contrast with previous experiments, which were all limited by the modal capacity of the detection system, our method operates on the entire down-conversion cone and reveals the complete distribution of the generated OAM. In this geometry, new features can be studied. We show that the phase-matching conditions can be used as a tool to enhance the azimuthal Schmidt number and to flatten the spectral profile, allowing the efficient production of high-quality multidimensional entangled states.

DOI
10.1103/physrevlett.104.020505

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We implement an interferometric method to measure the orbital angular momentum (OAM) spectrum of photon pairs generated by spontaneous parametric down-conversion. In contrast with previous experiments, which were all limited by the modal capacity of the detection system, our method operates on the entire down-conversion cone and reveals the complete distribution of the generated OAM. In this geometry, new features can be studied. We show that the phase-matching conditions can be used as a tool to enhance the azimuthal Schmidt number and to flatten the spectral profile, allowing the efficient production of high-quality multidimensional entangled states.
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.
Photon pairs entangled in high-dimensional orbital angular momentum (OAM) degrees of freedom (DOF) have been widely regarded as a possible source for improving the capacity of quantum information processing. The generation of a high-dimensional maximally entangled state in the OAM DOF is therefore much desired. In this work, we demonstrate a simple method to generate a broader and flatter OAM spectrum, i.e., a larger spiral bandwidth (SB), of entangled photon pairs generated through spontaneous parametric down-conversion by modifying the pump beam profile. By investigating both experimentally and theoretically, we find that an exponential pump profile that is roughly the inverse of the mode profiles of the single-mode fibers used for OAM detection will provide a much larger SB compared to a Gaussian-shaped pump.
The existing methods for measuring the orbital-angular-momentum (OAM) spectrum suffer from issues such as poor efficiency, strict interferometric stability requirements, and too much loss. Furthermore, most techniques inevitably discard part of the field and measure only a post-selected portion of the true spectrum. Here, we propose and demonstrate an interferometric technique for measuring the true OAM spectrum of optical fields in a single-shot manner. Our technique directly encodes the OAM-spectrum information in the azimuthal intensity profile of the output interferogram. In the absence of noise, the spectrum can be fully decoded using a single acquisition of the output interferogram, and, in the presence of noise, acquisition of two suitable interferograms is sufficient for the purpose. As an important application of our technique, we demonstrate measurements of the angular Schmidt spectrum of the entangled photons produced by parametric down-conversion and report a broad spectrum with the angular Schmidt number 82.1.
Any practical experiment utilizing the innate DDD-dimensional entanglement of the orbital angular momentum (OAM) of photons is subject to the generation capacity of the entangled photon source and the modal capacity of the detection system. We report an experimental spontaneous parametric-down-conversion system able to generate and detect tunable high-dimensional OAM entanglement. By tuning the phase matching, we demonstrate a factor of 2 increase on the half-width of the OAM-correlation spectrum, from 10 to 20. In terms of quantum mutual information capacity, this is an increase from 3.183.183.18 to 4.954.954.95 bits/photon. Furthermore, we measure correlations in the conjugate variable, angular position, and obtain concurrence values 0.960.960.96 and 0.900.900.90. The good entanglement measures in both OAM and angular position bases indicate bipartite, DDD-dimensional entanglement where DDD is tunable.
We derive an exact computationally-efficient formula for the angular Schmidt spectrum of orbital angular momentum (OAM) entangled states produced by parametric down-conversion (PDC). Our formula yields the true spectrum and does not suffer from convergence issues arising due to infinite summations, as has been the case with previously derived formulas. We use this formula to experimentally characterize the angular Schmidt spectrum of entangled photons produced by PDC with noncollinear phase matching. We report measurements of very broad angular Schmidt spectra, corresponding to the angular Schmidt numbers up to 229. Our work could have important implications for OAM-based quantum information applications.