Physical Review Letters ( IF 8.385 ) Pub Date : 2020-11-20 , DOI: 10.1103/physrevlett.125.213401
Q. Guan; M. K. H. Ome; T. M. Bersano; S. Mossman; P. Engels; D. Blume

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 $2×2$ 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.

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