Cavity-mediated Interaction in a Bragg Interferometer (I): One-axis Twisting and Mössbauer-like Suppression of Doppler Dephasing

Laser-cooled atoms interacting via photon-mediated interactions are powerful platforms for quantum simulation and sensing. Here we realize for the first time momentum-exchange interactions in which pairs of atoms exchange their momentum states via 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 experimentally observed all-to-all Ising-like interaction in a Bragg matter-wave interferometer, which is useful for entanglement generation. An experimentally observable many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing with analogies 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.