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Imaging of OAM-entangled photon pairs in the Bessel-Gauss basis with full index control

Zeferino Ibarra-Borja, Roberto Ramírez-Alarcón, Carlos Sevilla-Gutiérrez, Héctor Cruz-Ramírez, Alfred B. U’Ren

Published Mar 1, 2021• 3 citations
Publisher

Abstract

In this paper, we directly image the orbital angular momentum (OAM) correlations, expressed in the Bessel-Gauss (BG) basis, present in quantum-entangled photon pairs produced by the process of spontaneous parametric downconversion (SPDC). We use a spatial light modulator that displays an appropriate phase mask, followed by coupling into a single-mode fiber, so as to project the signal, or heralding, photon onto a BG mode, and verify that the idler, or heralded, photon is projected non-locally as expected. In contrast with similar experiments relying on Laguerre-Gauss (LG) modes, our current experiment permits, firstly, full index control (allowing the experimenter to define both the azimuthal index ℓ s and the continuous radial index k rs , also referred to as scaling parameter). Importantly, while not resolving the radial index leaves the heralded single photon in a statistical mixture of all available radial modes, the ability to determine both indices allows us to herald single photons in a particular BG mode, described by a quantum-mechanically pure state. Our use of BG modes permits, secondly, the spatially-resolved detection of the heralded single photon, both in the near and far fields, with a time-gated intensified CCD camera, making it possible to experimentally determine both the radial and azimuthal indices of the heralded single photon. Thirdly, the fact that for BG modes the radial index (scaling parameter) is continuous makes it possible to use the scaling parameter as a continuous adjustment in quantum state engineering, for precise mode matching, or for the selection of photon-pair properties such as the spiral bandwidth, as we experimentally demonstrate. We believe that our work opens up interesting new possibilities in the field of quantum communications based on the spatial degree of freedom of photon pairs.

DOI
10.1364/osac.414790

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 14, 2005•0 citations
In this paper, we directly image the orbital angular momentum (OAM) correlations, expressed in the Bessel-Gauss (BG) basis, present in quantum-entangled photon pairs produced by the process of spontaneous parametric downconversion (SPDC). We use a spatial light modulator that displays an appropriate phase mask, followed by coupling into a single-mode fiber, so as to project the signal, or heralding, photon onto a BG mode, and verify that the idler, or heralded, photon is projected non-locally as expected. In contrast with similar experiments relying on Laguerre-Gauss (LG) modes, our current experiment permits, firstly, full index control (allowing the experimenter to define both the azimuthal index ℓ s and the continuous radial index k rs , also referred to as scaling parameter). Importantly, while not resolving the radial index leaves the heralded single photon in a statistical mixture of all available radial modes, the ability to determine both indices allows us to herald single photons in a particular BG mode, described by a quantum-mechanically pure state. Our use of BG modes permits, secondly, the spatially-resolved detection of the heralded single photon, both in the near and far fields, with a time-gated intensified CCD camera, making it possible to experimentally determine both the radial and azimuthal indices of the heralded single photon. Thirdly, the fact that for BG modes the radial index (scaling parameter) is continuous makes it possible to use the scaling parameter as a continuous adjustment in quantum state engineering, for precise mode matching, or for the selection of photon-pair properties such as the spiral bandwidth, as we experimentally demonstrate. We believe that our work opens up interesting new possibilities in the field of quantum communications based on the spatial degree of freedom of photon pairs.
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.
ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per photon; a highly desirable property for quantum information processes such as quantum communication, computation and teleportation. As the orbital angular momentum (OAM) modes of light span an infinite-dimensional Hilbert space, they have become frontrunners in achieving entanglement in higher dimensions. In light of this, we investigate the potential of OAM entanglement of photons by controlling the parameters in both the generation and measurement systems. We show the experimental procedures and apparatus involved in generating and measuring entangled photons in two-dimensions. We verify important quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle correlations, as well as a violation of a Bell-type inequality. By performing a full state tomography, we characterise our quantum state and show we have a pure, highly entangled quantum state. We demonstrate that this method can be extended to higher dimensions. The experimental techniques used to generate and measure OAM entanglement place an upper bound on the number of accessible OAM modes. As such, we investigate new methods in which to increase the spiral bandwidth of our generated quantum state. We alter the shape of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement in this basis. We show that this method allows the measured spiral bandwidth to be optimised by simply varying the continuous radial parameter of the BG modes. We demonstrate that BG modes can be entangled in higher dimensions compared with the commonly used helical modes by calculating and comparing the linear entropy and fidelity for both modes. We also show that quantum entanglement can be accurately simulated using classical light using back-projection, which allows the study of projective measurements and predicts the strength of the coincidence correlations in an entanglement experiment. Finally, we make use of each of the techniques to demonstrate the effect of a perturbation on OAM entanglement measured in the BG basis. We investigate the self-healing property of BG beams and show that the classical property is translated to the quantum regime. By calculating the concurrence, we see that measured entanglement recovers after encountering an obstruction.
The OAM or spiral bandwidth indicates the dimensionality of an entangled state that is produced by the spontaneous parametric down-conversion process. Normally this bandwidth is determined by modulating the signal and idler beams with helical phase functions with opposite azimuthal indices on the spatial light modulators in the signal and idler beams, respectively. We added an additional binary Bessel function to the helical phase, thereby specifying the radial dependence of the mode to be Bessel-Gaussian (BG) modes. This comes down to a post selection process, which is known to have the ability to increase entanglement. The result is a modification to the shape of the OAM spectrum, which leads to a higher dimensionality for the quantum states. We perform analytical calculations to show that the bandwidths obtained by measuring in the BG modal basis are larger than those for the LG modes. These theoretical predictions are confirmed by experimental measurements of the bandwidths for LG modes and for BG modes with different transverse scales.
We demonstrate that the combination of digital spiral imaging with high-dimensional orbital angular momentum (OAM) entanglement can be used for efficiently probing and identifying pure phase objects, where the probing light does not necessarily touch the object, via the experimental, non-local decomposition of non-integer pure phase vortices in OAM-entangled photon pairs. The entangled photons are generated by parametric downconversion and then measured with spatial light modulators and single-mode fibers. The fractional phase vortices are defined in the idler photons, while their corresponding spiral spectra are obtained non-locally by scanning the measured OAM states in the signal photons. We conceptually illustrate our results with the biphoton Klyshko picture and the effective dimensionality to demonstrate the high-dimensional nature of the associated quantum OAM channels. Our result is a proof of concept that quantum imaging techniques exploiting high-dimensional entanglement can potentially be used for remote sensing. Photon pairs entangled in their orbital angular momentum can reveal information about an object with a complex phase profile. Lixiang Chen and co-workers from China and Scotland used entangled photons to recover the spiral spectrum of an optical fractional phase vortex. First they used a beta barium borate crystal to generate a pair of signal and idler entangled photons through spontaneous parametric downconversion. They then split the beam into two arms, each containing a programmable spatial light modulator (SLM) that can imprint any desired phase profile onto an incident photon. By encoding a fractional phase vortex on the SLM of one arm, and scanning through different orbital angular momentum values on the SLM of the other arm, the team recovered the spiral spectra of the fractional phase vortex nonlocally.
In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number in this basis and show how this may be varied by control over the radial degree of freedom, a continuous parameter in Bessel-Gaussian modes. As a test we first implement a back-projection technique to classically predict, by experiment, the quantum correlations for Bessel-Gaussian modes produced by three holographic masks: a blazed axicon, a binary axicon, and a binary Bessel function. We then proceed to test the theory on the down-converted photons using the binary Bessel mask. We experimentally quantify the number of usable OAM modes and confirm the theoretical prediction of a flattening in the OAM spectrum and a concomitant increase in the OAM bandwidth. The results have implications for the control of dimensionality in quantum states.
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.