Bloch dynamics in lattices with long range hoppings
arXiv:1411.2784 · doi:10.1103/PhysRevA.91.023606
Abstract
We study a discrete Schrödinger equation with arbitrary long range hopping terms under the influence of an external force. The impact of long range hoppings on the single particle Bloch dynamics in the lattice is investigated. A closed expression for the propagator is given, based on which we analyze the dynamics of initially Gaussian wave packets. Our findings capture the anharmonic oscillations recently observed in zigzag lattices and furthermore provide a detailed quantitative description of the crossover between center of mass Bloch oscillations for wide wave packets and left-right symmetric width oscillations for narrow single site excitations. The analytical results are shown to be in agreement with numerical simulations. A helix lattice setup for ultracold atoms is proposed where such hopping terms to far neighbors can be experimentally tuned to sizable values.
arXiv comment13 pages, 7 figures
References in corpus (26)
- Feshbach Resonances in Ultracold Gases
- The physics of dipolar bosonic quantum gases
- Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
- Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber
- Light propagation and localization in modulated photonic lattices and waveguides
- Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at micrometer scale
- A new determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattic
- Atom interferometry with trapped Fermi gases
- Exponential decay properties of Wannier functions and related quantities
- Simulation of interacting fermions with entanglement renormalization
- Localization Effects in ac-driven Tight-Binding Lattices
- Ultra-cold bosons in zig-zag optical lattices
- Nanofiber-based optical trapping of cold neutral atoms
- Application of compressed sensing to the simulation of atomic systems
- Nanofiber-Based Double-Helix Dipole Trap for Cold Neutral Atoms
- Lattice with a Twist : Helical Waveguides for Ultracold Matter
- Classical scattering of charged particles confined on an inhomogeneous helix
- Effective Long-Range Interactions in Confined Curved Dimensions
- Hardcore bosons in a zig-zag optical superlattice
- Ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping
- Formation of classical crystals of dipolar particles in a helical geometry
- Quantum Phase Transition between (Luttinger) Liquid and Gas of Cold Molecules
- Diffusion in infinite and semi-infinite lattices with long-range coupling
- Optimally localized Wannier functions for quasi one-dimensional nonperiodic insulators
- Dipoles on a Two-leg Ladder
- Destruction of Long-range Order by Quenching the Hopping Range in One Dimension
Cited by in corpus (15)
- Strong-field Phenomena in Periodic Systems
- Transient dynamics of a one-dimensional Holstein polaron under the influence of an external electric field
- Bloch oscillations in non-Hermitian lattices with trajectories in complex plane
- Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays
- Chaos-Assisted Long-Range Tunneling for Quantum Simulation
- Topological phase transitions of Thouless charge pumping realized in helical organic molecules with long-range hoppings
- Modulational instability and localized breather modes in the discrete nonlinear Schrödinger equation with helicoidal hopping
- Quantum few-body bound states of dipolar particles in a helical geometry
- Quantum single-particle properties in a one-dimensional curved space
- Many-body localization in a quantum gas with long-range interactions and linear external potential
- Bloch dynamics in inversion symmetry broken monolayer phosphorene
- Sub- and supercritical defect scattering in Schrödinger chains with higher-order hopping
- Driven toroidal helix as a generalization of Kapitzas pendulum
- Generalized Bloch oscillations of ultracold lattice atoms subject to higher-order gradients
- Localization Properties of a Disordered Helical Chain