AI Article Synopsis
- - Changes in energy levels usually happen smoothly without creating complex patterns, but bifurcations can result in interesting phenomena like loops or swallowtail shapes in the energy spectrum.
- - A basic quantum Hamiltonian that displays swallowtails involves two states with their energy dependent on how the populations are distributed between them, and this can be tested using ultracold atoms in an optical lattice.
- - Experiments show that self-trapping and unusual tunneling behaviors, which indicate the presence of swallowtail structures, were observed, confirming that this setup is effective for studying advanced topics like Josephson junctions and superfluidity.
Article Abstract
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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