# 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

## TL;DR

This paper proposes a scheme to emulate optical quantum elements and gates using the motional states of two Rydberg atoms in a 2D plane, enabling advanced quantum information processing.

## Contribution

It introduces a novel model for phonon analogs of optical components and quantum gates using trapped Rydberg atoms and Laguerre-Gaussian beams.

## Key findings

- Model successfully simulates polarizing beam splitter, wave plates, and quantum gates.
- Enables manipulation of atomic motional states for quantum computing.
- Potential applications in optomechanical quantum circuits.

## Abstract

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.