Effective time-independent description of optical lattices with periodic driving

TL;DR

This paper derives an effective time-independent Hamiltonian for periodically driven optical lattices, enabling better understanding and control of quantum systems under strong periodic driving conditions.

Contribution

It provides a generalized method to obtain effective Hamiltonians for various driven optical lattice configurations, extending previous weak-driving results to strong-driving regimes.

Findings

Reproduces known tunneling rescaling in 1D lattices.

Generalizes 2D lattice modulation effects.

Extends interpretation of staggered magnetic fields to strong driving.

Abstract

For a periodically driven quantum system an effective time-independent Hamiltonian is derived with an eigen-energy spectrum, which in the regime of large driving frequencies approximates the quasi-energies of the corresponding Floquet Hamiltonian. The effective Hamiltonian is evaluated for the case of optical lattice models in the tight-binding regime subjected to strong periodic driving. Three scenarios are considered: a periodically shifted one-dimensional (1D) lattice, a two-dimensional (2D) square lattice with inversely phased temporal modulation of the well depths of adjacent lattice sites, and a 2D lattice subjected to an array of microscopic rotors commensurate with its plaquette structure. In case of the 1D scenario the rescaling of the tunneling energy, previously considered by Eckardt et al. in Phys. Rev. Lett. 95, 260404 (2005), is reproduced. The 2D lattice with well depth modulation turns out as a generalization of the 1D case. In the 2D case with staggered rotation, the expression previously found in the case of weak driving by Lim et al. in Phys. Rev. Lett. 100, 130402 (2008) is generalized, such that its interpretation in terms of an artificial staggered magnetic field can be extended into the regime of strong driving.