Sorting photons of different rotational Doppler shifts (RDS) by orbital angular momentum of single-photon with spin-orbit-RDS entanglement

We demonstrate that single photons from a rotating q- plate exhibit an entanglement in three degrees of freedom of spin, orbital angular momentum, and the rotational Doppler shift ( RDS) due to the nonconservation of total spin and orbital angular momenta. We find that the rotational Doppler shift Delta omega = Omega(Delta s+Delta l), where s, l and Omega are quantum numbers of spin, orbital angular momentum, and rotating velocity of the q-plate, respectively. Of interest is that the rotational Doppler shift directly reflects the rotational symmetry of q-plates and can be also expressed as Delta omega = Omega n, where n = 2(q-1) denotes the fold number of rotational symmetry. Besides, based on this single-photon spin-orbit-RDS entanglement, we propose an experimental scheme to sort photons of different frequency shifts according to individual orbital angular momentum. (C) 2008 Optical Society of America.