Vortex states and entanglement properties in multiphoton pair production

We investigate the multiphoton pair production in circularly polarized field via two level model. There appears obvious discrete ring structures in the momentum distribution of the created particles, in which the ring radius is mainly controlled by the number of the photons absorbed in the creation with the energy conservation and could also be modulated by the spin of the created pair. These multiphoton rings become narrower when both of the pair particles' spin are aligned with the direction of the field rotation, and become broader if both spin are antiparallel to that direction. This spin-modulation can be simply understood with the angular momentum conservation, as less orbital angular momentum from the absorbed photons would be transferred to the created particles if their spins are aligned with the field rotation. The orbital angular momentum of the created particles is manifested as the vortex structure in the phase of the momentum distribution, and valued as the topological charge of this phase vortex. We also study the spin entanglement between the created particles, and reveal that the entanglement becomes stronger with the increase of the particles' transverse momentum, and gets sharp peak in the transition between different multiphoton rings, where the topological charge of the phase vortex is changed.