@article{13648, author = {Chengyi Luo and Haoqing Zhang and Chitose Maruko and Eliot Bohr and Anjun Chu and Ana Rey and James Thompson}, title = {Realization of three- and four-body interactions between momentum states in a cavity}, abstract = {Spin Hamiltonians in condensed matter and quantum sensing typically utilize pairwise or two-body interactions between constituents in the material or ensemble. However, there is growing interest in exploring more general n-body interactions for n \textgreater 2. In this study, we realized an effective n = 3-body Hamiltonian interaction using an ensemble of laser-cooled atoms in a high-finesse optical cavity with the pseudospin 1/2 encoded by two atomic momentum states. We applied two dressing tones that induce the atoms to exchange photons via the cavity to realize a virtual six-photon process; lower-order interactions destructively interfered. We also observed signatures of a n = 4-body interaction mediated by a virtual eight-photon process. Our approach may be extensible to three-body interactions in multilevel systems or to even higher-order interactions.}, year = {2025}, journal = {Science}, volume = {390}, number = {6776}, pages = {925-929}, month = {nov}, url = {https://www.science.org/doi/10.1126/science.adv0990}, doi = {10.1126/science.adv0990}, note = {Publisher: American Association for the Advancement of Science}, }