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.
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.
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.
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.
Orbital angular momentum (OAM) entanglement is investigated in the Bessel-Gaussian (BG) basis. Having a readily adjustable radial scale, BG modes provide an alternative basis for OAM entanglement over Laguerre-Gaussian modes. We show that the OAM bandwidth in terms of BG modes can be increased by selection of particular radial wavevectors and leads to a flattening of the spectrum, which allows for higher dimensionality in the entangled state. We demonstrate entanglement in terms of BG modes by performing a Bell-type experiment and showing a violation of the Clauser-Horne-Shimony-Holt inequality for the ℓ = ±1 subspace. In addition, we use quantum state tomography to indicate higher-dimensional entanglement in terms of BG modes.
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.
Bessel-Gaussian (BG) modes possess unique characteristics that have been exploited in the classical world and which may also offer advantages over other modes in the quantum regime. The easily adjustable radial scale of BG modes provides a more favourable basis of orbital angular momentum (OAM) entanglement over Laguerre- Gaussian (LG) modes, where the radial dependence is often ignored. We demonstrate high-dimensional entanglement with the BG modes and show a higher fidelity than the LG modes. We use the reconstruction property of BG modes to recover the degree of entanglement of our quantum state after encountering an obstruction. By moving the obstruction along the path of propagation of the entangled photon pairs, we quantitatively show a increase in the degree of entanglement as the obstruction was moved beyond that minimum distance.
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.