Paradigmatic spin Hamiltonians in condensed matter and quantum sensing typically utilize pair-wise or 2-body interactions between constituents in the material or ensemble. However, there is growing interest in exploring more general
n-body interactions for
n>2, with examples including more efficient quantum gates or the realization of exotic many-body fracton states. Here we realize an effective
n=3-body Hamiltonian interaction using an ensemble of laser-cooled atoms in a high finesse optical cavity with the pseudo-spin 1/2 encoded by two atomic momentum states. To realize this interaction, we apply two dressing tones that coax the atoms to exchange photons via the cavity to realize a virtual 6-photon process, while the lower-order interactions destructively interfere. The resulting photon mediated interactions are not only
n>2-body but also all-to-all(-to-all) and therefore of great interest for fast entanglement generation and quantum simulation of exotic phases such as the long sought but not yet observed charge-Qe superconductors, with
Q=2n . The versatility of our experimental system can also allow for extending to 3-body interactions in multi-level systems or to higher-order interactions, such as the signature of a
n=4-body interaction mediated by a virtual eight photon process that we also observe.
Quantum simulation and sensing hold great promise for providing new insights into nature, from understanding complex interacting systems to searching for undiscovered physics. Large ensembles of laser-cooled atoms interacting via infinite-range photon mediated interactions are a powerful platform for both endeavours. Here, we realize for the first time momentum-exchange interactions in which atoms exchange their momentum states via collective emission and absorption of photons from a common cavity mode. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer, which is useful for entanglement generation. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing, akin to Mössbauer spectroscopy. The tunable momentum-exchange interaction provides a new capability for quantum interaction-enhanced matter-wave interferometry and for realizing exotic behaviors including simulations of superconductors and dynamical gauge fields.
The generation of high-performance nonclassical light remains a cornerstone of quantum technologies, yet faces a fundamental trade-off between emission purity and brightness. Here, we demonstrate that cavity-mediated many-body spin-exchange interactions provide a route to overcome this constraint by collectively amplifying spectral anharmonicity. In a cavity-coupled atomic array with a programmable relative phase
φ, the resulting interference-interaction mechanism reshapes the dressed-state manifold and enables deterministic switching between distinct quantum emission regimes. For
φ=0, constructive interference yields high-purity single-photon emission with antibunching improved by four orders of magnitude while preserving strong photon flux. Conversely, for
φ=π, destructive interference creates a dark single-photon manifold, resonantly activating two-photon processes to produce bright and pure photon-pair bundles. Our work establishes interference-engineered many-body interactions as a scalable mechanism for on-demand quantum light generation and open a new avenue for harnessing collective many-body physics in quantum photonics.
Large ensembles of laser-cooled atoms interacting through infinite-range photon-mediated interactions are powerful platforms for quantum simulation and sensing. Here we realize momentum-exchange interactions in which pairs of atoms exchange their momentum states by collective emission and absorption of photons from a common cavity mode, a process equivalent to a spin-exchange or XX collective Heisenberg interaction. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing in analogy to Mössbauer spectroscopy. The tunable momentum-exchange interaction expands the capabilities of quantum interaction-enhanced matter-wave interferometry and may enable the realization of exotic behaviors, including simulations of superconductors and dynamical gauge fields.
Ultracold atoms in an ultrahigh-finesse optical cavity are a powerful platform to produce spin squeezing since photon of cavity mode can induce nonlinear spin-spin interaction and thus generate a one-axis twisting Hamiltonian
HOAT=qJx2, whose corresponding maximal squeezing factor scales as
N−2/3, where
N is the atomic number. On the contrary, for the other two-axis twisting Hamiltonian
HTAT=q(Jx2−Jy2), the maximal squeezing factor scales as
N−1, approaching the Heisenberg limit. In this paper, inspired by recent experiments of cavity-assisted Raman transitions, we propose a scheme, in which an ensemble of ultracold six-level atoms interacts with two quantized cavity fields and two pairs of Raman lasers, to realize a tunable two-axis spin Hamiltonian
. For proper parameters, the above one- and two- axis twisting Hamiltonians are recovered, and the scaling of
N−1 of the maximal squeezing factor can occur naturally. On the other hand, in the two-axis twisting Hamiltonian, spin squeezing is usually reduced when increasing the effective atomic resonant frequency
ω0. Surprisingly, we find that by combined with the dimensionless parameter
χ(>−1), the effective atomic resonant frequency
ω0 can enhance spin squeezing largely. These results are benefit for achieving the required spin squeezing in experiments.