Swallowtail band structure of the superfluid Fermi gas in an optical lattice

Nonlinear Landau-Zener-Stückelberg-Majorana tunneling and interferometry of extended Bose-Hubbard flux ladders

The nonlinear Landau-Zener-Stückelberg-Majorana (LZSM) tunneling dynamics and interferometry of an extended Bose-Hubbard flux ladder are studied. Based on the mean-field theory, the dispersion relation of the system is given, and it is found that loop structures periodically appear in the band structure and the nonlinear LZSM interference occurs naturally without Floquet engineering, which can be effectively modulated by atomic interactions. The nonlinear energy bands and the unique chirality feature of the flux ladder system can be identified through the dynamics of nonlinear Landau-Zener tunneling. Remarkably, the critical position of the noise in the interference pattern can be employed to identify the loop structure in the energy band, establishing an effective link between the nonlinear loop structure and LZSM interferometry. The position, intensity, symmetry, and width of interference patterns strongly depend on the magnetic field, atomic interactions, rung-to-leg coupling ratio, and energy bias, which provides an effective way to measure these parameters using the nonlinear LZSM interferometry. This paper further expands the dynamics of flux ladder systems to complex interaction regions and has potential applications in the precise measurement of related nonlinear systems.

Asymmetric Loop Spectra and Unbroken Phase Protection due to Nonlinearities in PT-Symmetric Periodic Potentials

We demonstrate that the interplay between a nonlinearity and PT symmetry in a periodic potential results in peculiar features of nonlinear periodic solutions. These include thresholdless symmetry breaking and asymmetric (multi-)loop structures of the nonlinear Bloch spectrum, persistence of unbroken PT symmetry even after the gap is closed, nonmonotonic dependence of the PT phase transition on the defocusing nonlinearity, and enhanced stability of the nonlinear states corresponding to the loop structures. The asymmetry and the loop structure of the spectrum are explained within the framework of a two-mode approximation and an effective potential theory and are validated numerically.