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DIRECT OBSERVATION OF ORBITAL ANGULAR MOMENTUM CONSERVATION IN COLLINEAR TYPE-I SPDC

Carlos Andres Sevilla Gutierrez

Published Nov 1, 2018• 0 citations
OpenAlex

Abstract

"We implement a direct measurement of the spatial modes distribution generated in a collinear type I spontaneous parametric down-conversion (SPDC) process using a triggered intensified CCD camera. This type of experiments have been realized previously. However in those cases the measurement was an indirect one, where both photons were collected into one-pixel detectors. In this thesis, to the best or our knowledge, it is the first time that a direct two dimensional measurement of the spatial modes distribution is made. These are well described by Laguerre-Gaussian modes. In our experiments we could observe up to mode l=+/-10. By exploiting the capabilities of an ICCD camera, it is possible to visualize the orbital angular momentum (OAM) conservation of the unprocessed SPDC bi-photon state. This is performed by observing the diffraction pattern by a triangular aperture. We show the results using this method for modes l=+/-1,+/-2. This conservation of OAM leads to entanglement in OAM, since one photon carries the anti-correlated topological charge with respect to the other one. Therefore, they are conditioned to the state of the other photon."

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"We implement a direct measurement of the spatial modes distribution generated in a collinear type I spontaneous parametric down-conversion (SPDC) process using a triggered intensified CCD camera. This type of experiments have been realized previously. However in those cases the measurement was an indirect one, where both photons were collected into one-pixel detectors. In this thesis, to the best or our knowledge, it is the first time that a direct two dimensional measurement of the spatial modes distribution is made. These are well described by Laguerre-Gaussian modes. In our experiments we could observe up to mode l=+/-10. By exploiting the capabilities of an ICCD camera, it is possible to visualize the orbital angular momentum (OAM) conservation of the unprocessed SPDC bi-photon state. This is performed by observing the diffraction pattern by a triangular aperture. We show the results using this method for modes l=+/-1,+/-2. This conservation of OAM leads to entanglement in OAM, since one photon carries the anti-correlated topological charge with respect to the other one. Therefore, they are conditioned to the state of the other photon."
We present spatially-resolved observations of orbital angular momentum (OAM) conservation, via a Laguerre-Gauss (LG) basis decomposition, of spatially-entangled photon pairs produced in type-I collinear spontaneous parametric downconversion (SPDC). These results were obtained with a novel detection system for OAM-entangled photon pairs that combines a projective measurement for the signal photon to a specific value of the azimuthal index ls, with a spatially-resolved measurement for the idler photon using an intensified charge coupled (ICCD) camera. In combination with far-field diffraction of the idler photon through a triangular aperture, we are able to obtain: i) the spatial structure of the heralded idler photon, as governed by the user-selected topological charge of the signal photon; ii) the OAM spectrum; and iii) the topological charge (both magnitude and sign) for the heralded idler photon.
Orbital angular momentum (OAM)-entangled states produced by spontaneous parametric down-conversion (SPDC) are considered ideal for realizing high-dimensional entangled states, which have several advantages for quantum technologies. However, the limited sensitivity of current two-photon OAM detectors is a major roadblock not only for realizing such technologies but also for resolving foundational questions, such as OAM conservation in SPDC. The current theoretical understanding is that OAM is not conserved in Type-II SPDC but is conserved in Type-I. Experimentally, although non-conservation in TypeII has not been demonstrated, conservation in Type-I has been reported frequently and has become an underlying assumption for techniques generating high-dimensional OAM entangled states. In this work, we experimentally demonstrate a high-sensitivity two-photon OAM detector, using which, contrary to the current understanding, we report non-conservation of OAM in Type-I SPDC. We attribute this to a spatial walk-off effect and prove it using a framework free of standard phase-matching approximations.
We elucidate the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) in different non-collinear geometries. To date, most investigations addressed SPDC in nearly collinear phase-matching geometries, where the pump, the signal and idler photons propagate coaxially almost along the same direction. However, non-collinear geometries introduce a variety of new features. The OAM of the entangled photons strongly depend on the propagation direction of the photons. Here we show that locally paraxial measurements of the OAM conducted with entangled photons generated in non collinear geometries, they do not comply with the known selection rules for the spiral index of the pump, signal and idler mode functions (Mair et al., Nature 412, 313 (2001)). In particular, we find the orbital angular momentum of entangled pairs generated in purely transverse-emitting configurations, where the entangled photons counter-propagate perpendicularly to the direction of propagation of the pump beam. In transverse emitting configurations, the spatial shape of the down converted in one transverse dimensions strongly depends on the corresponding spatial shape of the input pump beam, while in the other transverse dimension, the shape is tailored by the longitudinal phase matching. The spatial walk-off of all interacting waves in the parametric process also determines the OAM content of the down-converted photons, and here its influence is also revealed.
Abstract We experimentally demonstrate the quantum entanglement in various spatial modes of the correlated photons generated via spontaneous parametric down-conversion in a type-II phase-matched periodically-poled KTP crystal. The two-fold coincidence measurement reveals the spatial entanglement between the photon pairs by projecting one of the correlated photons onto a Gaussian mode while scanning the spatial mode of its partner photon through selective projection (Gaussian, Laguerre–Gaussian (LG), Bessel-Gaussian (BG), and Airy–Gaussian (AG)) using a spatial light modulator (SLM). We also show the spatially resolved measurement of the non-conservation of orbital angular momentum via modal decomposition of the correlated photon in LG and BG bases.
Identifying conservation laws is central to every subfield of physics, as they illuminate the underlying symmetries and fundamental principles. A prime example can be found in quantum optics: the conservation of orbital angular momentum (OAM) during spontaneous parametric down-conversion (SPDC) enables the generation of a photon pair with entangled OAM. In this Letter, we report on the observation of OAM conservation in SPDC pumped on the single-photon level by a preceding SPDC process. We implement this cascaded down-conversion scheme in free space, without waveguide confinement, and thereby set the stage for experiments on the direct generation of multiphoton high-dimensional entanglement using all degrees of freedom of light.
The generation of paired photons entangled in the spatial degree of freedom, i.e., in orbital angular momentum, offers a convenient physical resource to investigate the nature of entanglement in a multidimensional Hilbert space with controllable dimensionality. The two main physical processes that generate pairs of photons which show correlations in orbital angular momentum are (a) spontaneous parametric down-conversion (SPDC), and (b) Raman transitions induced in atomic ensembles. One question naturally arises: what kinds of correlations exist between the orbital angular momentum of the generated photons? The answer might be different if we consider the whole quantum state of the generated photons, i.e., all possible directions where the pairs of photons can be emitted, or if we consider only a small section of the full set of directions.