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In this paper we study up to which extent we can apply adiabatic controlstrategies to a quantum control model obtained by rotating wave approximation.In particular, we show that, under suitable assumptions on the asymptoticregime between the parameters characterizing the rotating wave and theadiabatic approximations, the induced flow converges to the one obtained byconsidering the two approximations separately and by combining them formally incascade. As a consequence, we propose explicit control laws which can be usedto induce desired populations transfers, robustly with respect to parameterdispersions in the controlled Hamiltonian.

Effective adiabatic control of a decoupled Hamiltonian obtained by rotating wave approximation