Figure 1. Floquet spectrum of a two-site Hubbard model.

(a) Floquet spectrum for U=10 and ω=6 as a function of Floquet amplitude . Thin dashed lines indicate the spectrum without driving. The exchange interaction (J_ex) is extracted from the difference between the lowest singlet (E_S) and triplet (E_T) levels. The result is shown in b for the same U=10 and two different frequencies above (ω=16, blue solid line) and below (ω=6, red dashed line) the Mott gap. For large driving strength , a reversal of J_ex is possible. In addition, thin blue dotted (ω=16) and thin red dash dotted (ω=6) lines indicate the modification of J_ex as obtained within second-order perturbation theory. (c) Illustration of the modification of J_ex in the Floquet picture. Red wavy lines indicate the virtual absorption and emission of an arbitrary number n of photons with frequency ω. This induces a coupling to excited states in different Floquet sectors displaced by an energy U±nω.