Dimers and discrete breathers in Bose-Einstein condensates in a quasi-periodic potential

Abstract

A quasi-one-dimensional Bose-Einstein condensate loaded into a quasi-periodic potential created by two sub-lattices of comparable amplitudes and incommensurate periods is considered. Although the conventional tight-binding approximation is not applicable in this setting, the description can still be reduced to a discrete model that accounts for the modes below the mobility edge. In the respective discrete lattice, where no linear hopping exists, solutions and their dynamics are governed solely by nonlinear interactions. Families of nonlinear modes, including those with no linear limit, are described with a special focus on dimers, which correspond to breather solutions of the Gross-Pitaevskii equation with a quasi-periodic potential. The breathers are found to be stable for negative scattering lengths. Localization and stable propagation of breathers are also observed for positive scattering lengths at relatively weak and moderate nonlinearities.

7 pages, 5 figures

References in corpus (8)

• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Optical soliton formation controlled by angle twisting in photonic moiré lattices
• Atomic Bose-Einstein condensate in a twisted-bilayer optical lattice
• Atomtronic circuits: from many-body physics to quantum technologies
• Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials
• Gap solitons in quasiperiodic optical lattices
• Localization of ultracold atoms in incommensurate spin-orbit-coupling and Zeeman lattices
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Cited by in corpus (6)

• Observation of nonlinear topological corner states originating from different spectral charges
• Observation of Light Localization at the Edges of Quasicrystal Waveguide Arrays
• Formation of nonlinear modes in one-dimensional quasiperiodic lattices with a mobility edge
• Families of localized modes of Bose-Einstein condensates enabled by incommensurate optical lattice and photon-atom interactions
• Towards the complete description of stationary states of a Bose-Einstein condensate in a one-dimensional quasiperiodic lattice: A coding approach
• Bloch-Landau-Zener Oscillations in Moiré Lattices