Stroboscopic versus non-stroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

Abstract

We study the stroboscopic and non-stroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian. We show that the former produces the evolution expected in the high-frequency limit only for observables which commute with the operator to which the driving protocol couples. On the contrary, non-stroboscopic dynamics is capable of capturing the evolution governed by the Floquet Hamiltonian of any observable associated with the effective high-frequency model. We provide exact numerical simulations for the dynamics of the density operator following a quantum cyclotron orbit on a $2\times 2$ plaquette, as well as the chiral current operator flowing along the legs of a $2\times 20$ ladder. The exact evolution is compared with its stroboscopic and non-stroboscopic counterparts, including finite-frequency corrections.

9 pages, 8 figures

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• Unconventional fermionic pairing states in a monochromatically tilted optical lattice
• Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence
• Floquet analysis of extended Rabi models based on high-frequency expansion
• Optical Conductivity Signatures of Floquet Electronic Phases
• Dynamical preparation of an atomic condensate in a Hofstadter band
• Laser assisted tunneling in a Tonks-Girardeau gas
• Effective (Floquet) Lindblad generators from spectral unwinding
• Topological Phase Diagram of Optimally Shaken Honeycomb Lattices: A Dual Perspective from Stroboscopic and Non-Stroboscopic Floquet Hamiltonians
• Optical control of electrons in a Floquet topological insulator
• Generalized pulse design in Floquet engineering: Application to interacting spin systems