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

中文翻译：

---

合成动量状态晶格中的非线性动力学

在过去的几十年里，原子、分子和光学系统中的模拟模拟范围已经大大扩展。最近，合成维度的想法——其中传输发生在由场驱动转换耦合的内部或运动状态跨越的空间中——在这种扩展中发挥了关键作用。虽然基于合成维度的方法导致单粒子哈密顿工程的快速发展，但大多数合成维度平台明显缺乏强相互作用效应。在这里，在耦合原子动量状态的晶格中，我们表明原子相互作用导致合成维度中动力学的巨大和质的变化。