Orbital angular momentum correlations of entangled paired photons

Abstract

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.

Azimuthal entanglement and multichannel Schmidt-type decomposition of noncollinear biphotons

“…Alternatively, the wave vectors k 1,2 ⊥ can be characterized by their absolute values ρ 1,2 = | k 1,2 ⊥ | and angles with respect to the x-axis (azimuthal angles), α 1,2 . This parametrization of transverse wave vectors k 1,2 ⊥ is widely used in the analysis based on the concept of the Orbital Angular Momentum of photons (OAM) [4][5][6][7]. Parametrization used in the present work slightly differs from that used in the OAM analysis.…”

Optical vortex generation by volume holographic elements with embedded phase singularity: Effects of misalignments

“…Besides, the properties of the OV-beams obtained under conditions of HE misalignment can be profitably exploited. For the OV-beams generated with thin HEs, this has been demonstrated for metrological and astronomical applications [9][10][11][12][13], as well as for discriminating different OV-beams in systems of information transfer and processing [14][15][16][38][39][40][41]. All of these points make it highly relevant to study in detail the role and significance of the diffracted-beam distortions appearing due to nonideal arrangement of the incident beam and the HE the with EPS.…”

Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

“…are coupled with promising applications. In particular, they concern capturing and manipulation of microparticles [7][8][9], measurement of small displacements and improved resolution of neighboring astronomical objects [10][11][12][13][14][15], encoding and processing information [16][17][18][19][20][21][22][23][24] (including analyses of quantum entanglement and verification of the Bell inequalities [19][20][21][22][23][24]). Both generation and analysis of the OV beams can be suitably performed with assistance of computer-generated holograms (CGH) whose special feature is the groove bifurcation ("fork" structure, see Fig.…”

“…, encoding and processing information [16][17][18][19][20][21][22][23][24] (including analyses of quantum entanglement and verification of the Bell inequalities [19][20][21][22][23][24]). Both generation and analysis of the OV beams can be suitably performed with assistance of computer-generated holograms (CGH) whose special feature is the groove bifurcation ("fork" structure, see Fig.…”