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Three body resonant interactions between Rydberg atoms are considered inorder to perform few-body quantum gates. So far, the resonances found in cesiumor rubidium atoms relied on an adjacent two-body resonance which ceases toexist for principal quantum numbers above $n \simeq 40$. We have proposedrecently a new class of 3-body interaction resonances in alkali-metal Rydbergatoms [P. Cheinet \textit{et al.}, Quant. Elect. \textbf{50}, 213 (2020)],which circumvienes this limit. We investigate here the relative strengthbetween this new class of 3-body interaction resonance and quasi-forbidden2-body interaction resonances in rubidium and cesium Rydberg atoms. We thenidentify the best case scenario for detecting and using this 3-bodyinteraction.

Searching optimal conditions for quantum gates application with the new 3-body F\"orster resonances in Rb and Cs Rydberg atoms