  In this paper we propose a scheme to model the phonon analog of optical
elements, including a polarizing beam splitter, a half- wave plate, and a
quarter- wave plate, as well as an implementation of CNOT and Pauli gates, by
using two atoms confined in a 2D plane. The internal states of the atoms are
taken to be Rydberg circular states. Using this model we can manipulate the
motional state of the atom, with possible applications in optomechanical
integrated circuits for quantum information processing and quantum simulation.
Towards this aim, we study the interaction of two trapped atoms with two
circularly polarized Laguerre-Gaussian beams, in such a way that the beams
illuminate selectively only one of the atoms.
