Two-dimensional Bloch oscillations: A Lie-algebraic approach

Abstract

A Lie-algebraic approach successfully used to describe one-dimensional Bloch oscillations in a tight-binding approximation is extended to two dimensions. This extension has the same algebraic structure as the one-dimensional case while the dynamics shows a much richer behaviour. The Bloch oscillations are discussed using analytical expressions for expectation values and widths of the operators of the algebra. It is shown under which conditions the oscillations survive in two dimensions and the centre of mass of a wave packet shows a Lissajous like motion. In contrast to the one-dimensional case, a wavepacket shows systematic dispersion that depends on the direction of the field and the dispersion relation of the field free system.

2 figures are included

References in corpus (3)

• Localization Effects in ac-driven Tight-Binding Lattices
• An algebraic solution of driven single band tight binding dynamics
• Atomic motion in tilted optical lattices

Cited by in corpus (8)

• Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices
• Discrete diffraction and shape-invariant beams in optical waveguide arrays
• Quantum transport and localization in biased periodic structures under bi- and polychromatic driving
• Wavepacket dynamics on Chern band lattices in a trap
• Bloch dynamics in inversion symmetry broken monolayer phosphorene
• Topological dynamics of adiabatic cat states
• Lissajous dynamics of a quantum particle in a tilted two-dimensional discrete lattice
• Bloch-Landau-Zener Oscillations in Moiré Lattices