Nonlinear Dynamics in a Synthetic Momentum-State Lattice

The scope of analog simulation in atomic, molecular, and optical systems has expanded greatly over the past decades. Recently, idea synthetic dimensions -- which transport occurs a space spanned by internal or motional states coupled field-driven transitions played key role this expansion. While approaches based on have led to rapid advances single-particle Hamiltonian engineering, strong interaction effects been conspicuously absent from most platforms. Here, lattice atomic momentum states, we show that interactions result large qualitative changes dynamics dimension. We explore how interplay nonlinear coherent tunneling enriches one-band tight-binding model, giving rise macroscopic self-trapping phase-driven Josephson with nonsinusoidal current-phase relationship, can be viewed as stemming band structure arising interactions.