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.
13 pages, 7 figures
References in corpus (5)
- Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at micrometer scale
- Nanofiber-Based Double-Helix Dipole Trap for Cold Neutral Atoms
- Lattice with a Twist : Helical Waveguides for Ultracold Matter
- Quantum Phase Transition between (Luttinger) Liquid and Gas of Cold Molecules
- Optimally localized Wannier functions for quasi one-dimensional nonperiodic insulators