Periodic jumps in binary lattices with a static force

We investigate the dynamics of a particle in a binary lattice with staggered on-site energies. An additional static force is introduced which further adjusts the on-site energies. The binary lattice appears to be unrelated to the semiclassical Rabi model, which describes a periodically driven two-level system. However, in a certain parity subspace, the Floquet Hamiltonian of the semiclassical Rabi model can be exactly mapped to that of the binary lattice. These connections provide a different perspective for analyzing lattice systems. At resonance, namely that the mismatch of on-site energies between adjacent sites is nearly multiple of the strength of the static force, the level anticrossing occurs. This phenomenon is closely related to the Bloch-Siegert shift in the semiclassical Rabi model. At the $n$th order resonance, an initially localized particle exhibits periodic jumps between site $0$ and site $(2n+1)$, rather than continuous hopping between adjacent sites. The binary lattice with a static force serves as a bridge linking condensed matter physics and quantum optics, due to its connection with the semiclassical Rabi model.