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

We study the stroboscopic and nonstroboscopic 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, nonstroboscopic 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 number operator following a quantum cyclotron orbit on a 2 x 2 plaquette, as well as the chiral current operator flowing along the legs of a 2 x 20 ladder. The exact evolution is compared with its stroboscopic and nonstroboscopic counterparts, including finite-frequency corrections.