Typically, energy levels change without bifurcating in response to a change of a control parameter. Bifurcations can lead to loops or swallowtails in the energy spectrum. The simplest quantum Hamiltonian that supports swallowtails is a nonlinear $2\times 2$ Hamiltonian with nonzero off-diagonal elements and diagonal elements that depend on the population difference of the two states. This work implements such a Hamiltonian experimentally using ultracold atoms in a moving one-dimensional optical lattice. Self-trapping and nonexponential tunneling probabilities, a hallmark signature of band structures that support swallowtails, are observed. The good agreement between theory and experiment validates the optical lattice system as a powerful platform to study, e.g., Josephson junction physics and superfluidity in ring-shaped geometries.

中文翻译：

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由于均值场燕尾引起的非指数隧穿

通常，响应于控制参数的改变，能量水平改变而不会分叉。分叉会导致能谱中的回路或燕尾状。支持燕尾的最简单的量子哈密顿量是非线性的$2\times 2$具有非零非对角线元素和对角线元素的哈密顿量，这取决于两个州的​​人口差异。这项工作使用超冷原子在移动的一维光学晶格中实验性地实现了这种哈密顿量。观察到自陷和非指数隧穿概率是支持燕尾的能带结构的标志。理论和实验之间的良好一致性验证了光学晶格系统是研究诸如约瑟夫森结物理和环形几何中的超流动性的强大平台。