Floquet Condition for Quantum Adiabaticity

Quantum adiabaticity is characterized by the evolution of a quantum system that remains close to an instantaneous eigenstate of a time-varying Hamiltonian, precluding transitions between eigenstates. Employing Floquet formalism, we rigorously establish two sufficient conditions that ensure quantum adiabaticity in periodically driven systems, applicable for time evolution of arbitrary length. Distinct from traditional conditions, the Floquet-based conditions are tight for certain specific parameter regimes, dispense with supplementary constraints, and suggest the possibility of adiabaticity at high frequencies. We provide three illustrative examples that compare and contrast the Floquet conditions with traditional ones.
Comment: 11 pages, 2 figures