Periodic excitations of bilinear quantum systems
For researchers in quantum control, this provides a rigorous theoretical foundation for a widely used approximation in infinite-dimensional systems, though it is an incremental extension of known finite-dimensional results.
The paper extends the Rotating Wave Approximation from finite to infinite dimensional quantum systems, providing explicit convergence estimates for population transfer using periodic control laws.
A well-known method of transferring the population of a quantum system from an eigenspace of the free Hamiltonian to another is to use a periodic control law with an angular frequency equal to the difference of the eigenvalues. For finite dimensional quantum systems, the classical theory of averaging provides a rigorous explanation of this experimentally validated result. This paper extends this finite dimensional result, known as the Rotating Wave Approximation, to infinite dimensional systems and provides explicit convergence estimates.