Localization of ultracold atoms in incommensurate spin-orbit-coupling and Zeeman lattices

Abstract

We consider a particle governed by a one-dimensional Hamiltonian in which artificial periodic spin-orbit coupling and Zeeman lattice have incommensurate periods. Using best rational approximations to such quasiperiodic Hamiltonian, the problem is reduced to description of spinor states in a superlattice. In the absence of a constant Zeeman splitting, the system acquires an additional symmetry, which hinders the localization. However, if the lattices are deep enough, then localized states can appear even for Zeeman field with zero or small mean value. Spatial distribution of localized modes is nearly uniform and is directly related to the topological properties of the effective superlattice: center-of-mass coordinates of modes are determined by Zak phases computed from the superlattice band structure. The best rational approximations feature the `memory' effect: each rational approximation holds the information about the energies and spatial distribution of the modes obtained under preceding, less accurate approximations. Dispersion of low-energy initial wavepackets is characterized by the law $\propto t^{\beta }$ with $\beta$ varying between $1/2$ at the initial stage and $1$ at longer, but still finite-time, evolution. The dynamics of initial wavepackets, exciting mainly localized modes, manifests quantum revivals.

10 pages, 6 figures; accepted for Phys. Rev. A

References in corpus (9)

• Tunable Spin-Orbit Coupling via Strong Driving in Ultracold Atom Systems
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Bose-Einstein Condensates in Spin-Orbit Coupled Optical Lattices: Flat Bands and Superfluidity
• Bloch Oscillations in Optical and Zeeman Lattices in the Presence of Spin-Orbit Coupling
• Localization of a spin-orbit coupled Bose-Einstein condensate in a bichromatic optical lattice
• Localization problem of the quasiperiodic system with the spin orbit interaction
• Dynamic localization in optical and Zeeman lattices in the presence of spin-orbit coupling
• Macroscopic random Paschen-Back effect in ultracold atomic gases
• Self-duality of One-dimensional Quasicrystals with Spin-Orbit Interaction

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• Stabilizing period-doubled density waves by spin-orbit coupling in Bose-Einstein condensates in optical lattices
• Duality breaking, mobility edges, and the connection between topological Aubry-André and quantum Hall insulators in atomic wires with fermions
• Band-edge superfluid of Bose-Einstein condensates in the spin-orbit-coupled Zeeman lattice
• Multistable localized states in highly photonic polariton rings with a quasiperiodic modulation
• Quantized transport of solitons in Bose-Einstein condensates driven by spin-orbit coupling