# Quantum Nonlinear Optics without Photons

## TL;DR

This paper proposes a coherent, reversible atomic process mediated by virtual photons, enabling nonlinear interactions between atoms that could be used for quantum error correction and quantum device architectures.

## Contribution

It introduces a novel atomic nonlinear process analogous to nonlinear optics, utilizing virtual photon exchange for coherent, reversible excitation transfer between atoms.

## Key findings

- High probability of excitation transfer between atoms
- Feasibility with parameters from ultrastrong circuit QED
- Potential for quantum error correction via four-atom mixing

## Abstract

Spontaneous parametric down-conversion is a well-known process in quantum nonlinear optics in which a photon incident on a nonlinear crystal spontaneously splits into two photons. Here we propose an analogous physical process where one excited atom directly transfers its excitation to a pair of spatially-separated atoms with probability approaching one. The interaction is mediated by the exchange of virtual rather than real photons. This nonlinear atomic process is coherent and reversible, so the pair of excited atoms can transfer the excitation back to the first one: the atomic analogue of sum-frequency generation of light. The parameters used to investigate this process correspond to experimentally-demonstrated values in ultrastrong circuit quantum electrodynamics. This approach can be extended to realize other nonlinear inter-atomic processes, such as four-atom mixing, and is an attractive architecture for the realization of quantum devices on a chip. We show that four-qubit mixing can efficiently implement quantum repetition codes and, thus, can be used for error-correction codes.