Simulating Non-Local Multibody Interactions in a One-Dimensional Ultracold Atomic Gas

Local quantum field theories are constructed using delta function interactions, such that elementary point particles only interact when in direct contact. The usual paradigm is that relativity requires local interactions between point particles, and quantum mechanical models involving long-range interaction potentials then arise as effective interactions. Here we explore a class of simple one-dimensional models with non-local, delta function, multibody interactions: a global interaction between two separated particle pairs, that only turns on when the two particles in each pair come in contact. The comparative simplicity of this model allows us to study analytically some fundamental features of non-local interactions without many of the obscuring complications that arise for familiar quantum mechanical long-range potentials. We show how this model can be realized within an ultracold atomic system, making possible the experimental creation of synthetic nonlocal delta function interactions. We further analyze that topologically non-trivial, few body and many-body states occur in the model.