Floquet Engineering of Lie Algebraic Quantum Systems
arXiv:2103.15923 · doi:10.1103/PhysRevB.105.L020301
Abstract
We propose a `Floquet engineering' formalism to systematically design a periodic driving protocol in order to stroboscopically realize the desired system starting from a given static Hamiltonian. The formalism is applicable to quantum systems which have an underlying closed Lie-algebraic structure, for example, solid-state systems with noninteracting particles moving on a lattice or its variant described by the ultra-cold atoms moving on an optical lattice. Unlike previous attempts at Floquet engineering, our method produces the desired Floquet Hamiltonian at any driving frequency and is not restricted to the fast or slow driving regimes. The approach is based on Wei-Norman ansatz, which was originally proposed to construct a time-evolution operator for any arbitrary driving. Here, we apply this ansatz to the micro-motion dynamics, defined within one period of the driving, and obtain the driving protocol by fixing the gauge of the micro-motion. To illustrate our idea, we use a two-band system or the systems consisting of two sub-lattices as a testbed. Particularly, we focus on engineering the cross-stitched lattice model that has been a paradigmatic flat-band model.
5 (Main Text) + 11 (Supplementary) pages, 3 figures. Accepted in Physical Review B Letters
References in corpus (6)
- Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
- Flat Bands Under Correlated Perturbations
- Analytically solvable driven time-dependent two-level quantum systems
- Electric-Field-Induced Resistive Switching in a Family of Mott Insulators : towards Non-Volatile Mott-RRAM Memories
- Effective Floquet Hamiltonian in the low-frequency regime
- Floquet engineering of twisted double bilayer graphene