Nonreciprocal and long-range three-body interactions in Bose-Einstein condensates induced by optical feedback

We propose generating long-range and nonreciprocal three-body interactions in quantum gases via optical feedback. By placing a quasi-two-dimensional Bose-Einstein condensate (BEC) in front of two reflecting mirrors and illuminating it with dichromatic laser beams, these driving optical fields traverse the BEC twice, thereby inducing a feedback effect on the atoms. We demonstrate that this optical feedback gives rise to an effective three-body atom-atom interaction with remarkable long-range and nonreciprocal properties. Due to its long-range nature, this three-body interaction can cause unique spatial symmetry-breaking behaviors in the BEC, resulting in various stable stationary states as well as unexpected diffusive collapse. Notably, a distinct ring state emerges through a purely self-organizing process. Furthermore, by analyzing the real-time dynamics of the BEC, we show that the nonreciprocal nature of this interaction can lead to intriguing self-acceleration of the condensate, seemingly violating Newton's law of motion. Additionally, our scheme offers a highly controllable setting, where pairwise two-body interactions can be tuned to vanish. This flexibility provides a promising route for exploring exotic physics associated with multi-body interactions.