Few-body interactions in frozen Rydberg gases

The strong dipole-dipole coupling and the Stark tunability make Forster resonances an attractive tool for the implementation of quantum gates. In this direction a generalization to a N-body process would be a powerful instrument to implement multi-qubit gate and it will also path the way to the understanding of many-body physics. In this review, we give a general introduction on Forster resonances, also known as two-body FRET, giving an overview of the different application in quantum engineering and quantum simulation. Then we will describe an analogous process, the quasi-forbidden FRET, which is related to the Stark mixing due to the presence of an external electric field. We will then focus on its use in a peculiar four-body FRET. The second part of this review is focused on our study of few-body interactions in a cold gas of Cs Rydberg atoms. After a detailed description of a series of quasi-forbidden resonances detected in the proximity of an allowed two-body FRET we will show our most promising result: the observation of a three-body FRET. This process corresponds to a generalization of the usual two-body FRET, where a third atom serves as a relay for the energy transport. This relay also compensates for the energy mismatch which prevents a direct two-body FRET between the donor and the acceptor, but on the other side allowed a three-body process; for this reason, the three-body FRET observed is a "Borromean" process. It can be generalized for any quantum system displaying two-body FRET from quasi-degenerate levels. We also predict N-body FRET, based on the same interaction scheme. Three-body FRET thus promises important applications in the formation of macro-trimers, implementation of few-body quantum gates, few-body entanglement or heralded entanglement.