TY - JOUR AU - Chengyi Luo AU - Haoqing Zhang AU - Chitose Maruko AU - Eliot Bohr AU - Anjun Chu AU - Ana Rey AU - James Thompson AB - 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. BT - Science DA - nov DO - 10.1126/science.adv0990 M1 - 6776 N1 - Publisher: American Association for the Advancement of Science N2 - 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. PY - 2025 SP - 925 EP - 929 T2 - Science TI - Realization of three- and four-body interactions between momentum states in a cavity UR - https://www.science.org/doi/10.1126/science.adv0990 VL - 390 ER -