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In this paper we propose a scheme to model the phonon analog of opticalelements, including a polarizing beam splitter, a half- wave plate, and aquarter- wave plate, as well as an implementation of CNOT and Pauli gates, byusing two atoms confined in a 2D plane. The internal states of the atoms aretaken to be Rydberg circular states. Using this model we can manipulate themotional state of the atom, with possible applications in optomechanicalintegrated circuits for quantum information processing and quantum simulation.Towards this aim, we study the interaction of two trapped atoms with twocircularly polarized Laguerre-Gaussian beams, in such a way that the beamsilluminate selectively only one of the atoms.

physical review. a/physical review, a

Modeling the atomtronic analog of an optical polarizing beam splitter, a  half-wave plate, and a quarter-wave plate for phonons of the motional state  of two trapped atom