Quantum versus classical control of tunneling

Coherent tunneling can be suppressed or enhanced by exciting a vibrational mode coupled to the tunneling coordinate. The localization in a two-level system (TLS) driven by a periodic force is obtained as a semiclassical limit for such a mode. We derive and test a semiclassical quantization rule that relates the quasienergies of a classically driven TLS with the energy splittings in the model of a TLS coupled to a quantum oscillator. The dissipative stabilization of a quasilocalized state and the possibility of localization by a quasiperiodic force are analyzed from this perspective.