Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement

Abstract

Any practical experiment utilising the innate D-dimensional entanglement of the orbital angular momentum (OAM) state space of photons is subject to the modal capacity of the detection system. We show that given such a constraint, the number of measured, entangled OAM modes in photon pairs generated by spontaneous parametric down-conversion (SPDC) can be maximised by tuning the phase-matching conditions in the SPDC process. We demonstrate a factor of 2 increase on the half-width of the OAM-correlation spectrum, from 10 to 20, the latter implying ≈ 50 -dimensional two-photon OAM entanglement. Exploiting correlations in the conjugate variable, angular position, we measure concurrence values 0.96 and 0.90 for two phase-matching conditions, indicating bipartite, D-dimensional entanglement where D is tuneable.PACS numbers: 03.65. Ud, 03.67.Bg, 03.67.Mn Much attention has been directed to the twodimensional state space of photon polarisation which provides both a conceptually and experimentally accessible playground [1][2][3]. D-dimensional two-photon entanglement, wherein each photon is a D-level quDit taking on any of D possible values, is an even more fertile playground. From a fundamental standpoint, higherdimensional entanglement implies stronger violations of locality [4,5] and is especially useful in the study of mutually unbiased bases in higher dimensions [6]. More relevant to practical applications, higher-dimensional entanglement provides higher information capacity [7,8] and increased security and robustness [8,9]. Experimentally, D-levels in photons can be achieved by using the temporal and spectral degrees of freedom [10], polarisation of more than one photon [11], transverse spatial profile [7], position and linear momentum [12], and angular position and orbital angular momentum [13].The entanglement of orbital angular momentum (OAM) in photons generated via spontaneous parametric down-conversion (SPDC) is firmly established theoretically and experimentally [14,15]. The interest in OAM stems from its discrete and theoretically infinitedimensional Hilbert space. Since the pioneering experiment of Zeilinger and co-workers ten years ago, OAM and it conjugate variable, angular position, has been steadily gaining ground as a mainstream variable in which to observe quantum correlations. Bell-type and Leggett inequalities have both been violated in twodimensional OAM subspaces analogous to the experiments done previously for polarisation [16,17]. The innate high-dimensional nature of OAM entanglement has been verified in an Einstein-Podolsky-Rosen (EPR) type experiment which measured both OAM and angular position [13]. A Bell-type inequality for higher dimensions has been recently violated using OAM states demonstrating experimental, two-photon, 11-dimensional entanglement [5]. The number of entangled OAM states that can be measured, i.e. the measurement spiral bandwidth depends on both the detection capability and the number of OAM states that is generated by the down-conversion process, i.e. the generation...

Two-photon optics of Bessel-Gaussian modes

“…Ideally, back-projection could be used as a simple technique to fully align the down-conversion system by reflecting the back-projected light off the crystal. However, typically the nonlinear crystal is cut in such a way that requires a slight additional vertical tilt to achieve the phase-matching conditions for collinear down-conversion [28]. This minute change to the crystal orientation is significant enough to misalign the back-projected beam (i.e., the reflected light does not couple into the other fiber).…”

Scattering of wave packets with phases

“…Using the detected non-plane-wave states with a definite set of quantum numbers, we imply that there exists an appropriate detector, which is sensitive to this set. For twisted photons, an OAM-sensitive "detector" may be thought of as a combination of a computer-generated hologram projecting the twisted state back onto the fundamental mode with = 0, a mono-mode fiber, and a "usual" detector -a setup routinely used in quantum optics with the parametric down-converted twisted photons (see, for example, [67,74]). For electrons and other massive vortex particles, an analogous registration scheme may also include a pair of appropriate holograms and a CCD camera.…”

High speed switching between arbitrary spatial light profiles

“…OAM modes are characterised by their azimuthally varying phase around a central vortex line. They offer a theoretically infinite dimensional state space, and the generation of large OAM values up to several hundred has been demonstrated [11][12][13].…”