Effective Hamiltonians for fastly driven tight-binding chains

Abstract

We consider a single particle tunnelling in a tight-binding model with nearest-neighbour couplings, in the presence of a periodic high-frequency force. An effective Hamiltonian for the particle is derived using an averaging method resembling classical canonical perturbation theory. Three cases are considered: uniform lattice with periodic and open boundary conditions, and lattice with a parabolic potential. We find that in the latter case, interplay of the potential and driving leads to appearence of the effective next-nearest neighbour couplings. In the uniform case with periodic boundary conditions the second- and third-order corrections to the averaged Hamiltonian are completely absent, while in the case with open boundary conditions they have a very simple form, found before in some particular cases by S.Longhi [Phys. Rev. B 77, 195326 (2008)]. These general results may found applications in designing effective Hamiltonian models in experiments with ultracold atoms in optical lattices, e.g. for simulating solid-state phenomena.

Presented on the seminar of Institut für Theoretische Physik I, Hamburg; comments are welcome

References in corpus (4)

• Coherent control of dressed matter waves
• Interaction-controlled transport of an ultracold Fermi gas
• Directed transport in a spatially periodic potential under periodic non-biased forcing
• Directed transport in a classical lattice with a high-frequency driving

Cited by in corpus (9)

• Effective Hamiltonians for fastly driven many-body lattice systems
• Laser-induced topological transitions in phosphorene with inversion symmetry
• Dynamical and Reversible Control of Topological Spin Textures
• Dynamical control of electron-phonon interactions with high-frequency light
• Method for finding the exact effective Hamiltonian of time driven quantum systems
• Efficient excitation of nonlinear phonons via chirped mid-infrared pulses: induced structural phase transitions
• Dynamically induced doublon repulsion in the Fermi-Hubbard model probed by a single-particle density of states
• Coexistence of $s$-wave superconductivity and phase separation in the half-filled extended Hubbard model with attractive interactions
• Floquet-Engineered Valley-Topotronics in Kekulé-Y Bond Textured Graphene Superlattice