Period doubling, two-color lattices, and the growth of swallowtails in Bose-Einstein condensates

TL;DR

This paper explores how two-color lattice potentials influence the band structure of Bose-Einstein condensates, revealing the formation and stability of swallowtail loops even at weak nonlinearities, with implications for experimental realizations.

Contribution

It introduces a novel understanding of swallowtail formation in BECs using a two-color lattice approach, supported by exact solutions for Kronig-Penney potentials.

Findings

Swallowtails form even at weak nonlinearity.

The physical properties are independent of lattice type.

Stability analysis relates to current experiments.

Abstract

The band structure of a Bose-Einstein condensate is studied for lattice traps of sinusoidal, Jacobi elliptic, and Kronig-Penney form. It is demonstrated that the physical properties of the system are independent of the choice of lattice. The Kronig-Penney potential, which admits a full exact solution in closed analytical form, is then used to understand in a novel way the swallowtails, or loops, that form in the band structure. Their appearance can be explained by adiabatically tuning a second lattice with half the period. Such a two-color lattice, which can be easily realized in experiments, has intriguing new physical properties. For instance, swallowtails appear even for weak nonlinearity, which is the experimental regime. We determine the stability properties of this system and relate them to current experiments.