Single-step shaping of the orbital angular momentum spectrum of light

Conflict-free collective stochastic decision making by orbital angular momentum of photons through quantum interference

In recent cross-disciplinary studies involving both optics and computing, single-photon-based decision-making has been demonstrated by utilizing the wave-particle duality of light to solve multi-armed bandit problems. Furthermore, entangled-photon-based decision-making has managed to solve a competitive multi-armed bandit problem in such a way that conflicts of decisions among players are avoided while ensuring equality. However, as these studies are based on the polarization of light, the number of available choices is limited to two, corresponding to two orthogonal polarization states. Here we propose a scalable principle to solve competitive decision-making situations by using the orbital angular momentum of photons based on its high dimensionality, which theoretically allows an unlimited number of arms. Moreover, by extending the Hong-Ou-Mandel effect to more than two states, we theoretically establish an experimental configuration able to generate multi-photon states with orbital angular momentum and conditions that provide conflict-free selections at every turn. We numerically examine total rewards regarding three-armed bandit problems, for which the proposed strategy accomplishes almost the theoretical maximum, which is greater than a conventional mixed strategy intending to realize Nash equilibrium. This is thanks to the quantum interference effect that achieves no-conflict selections, even in the exploring phase to find the best arms.

Optical vortex beams with a symmetric and almost symmetric OAM spectrum

We show both theoretically and numerically that if an optical vortex beam has a symmetric or almost symmetric angular harmonics spectrum [orbital angular momentum (OAM) spectrum], then the order of the central harmonic in the OAM spectrum equals the normalized-to-power OAM of the beam. This means that an optical vortex beam with a symmetric OAM spectrum has the same topological charge and the normalized-to-power OAM has an optical vortex with only one central angular harmonic. For light fields with a symmetric OAM spectrum, we give a general expression in the form of a series. We also study two examples of form-invariant (structurally stable) vortex beams with their topological charges being infinite, while the normalized-to-power OAM is approximately equal to the topological charge of the central angular harmonic, contributing the most to the OAM of the entire beam.