Nonstationary dressed states and effects of decay in nonadiabatic crossing of decaying levels

The rigorous equations for a nonadiabatic coupling of the amplitudes of decaying discrete states dressed by a continuum are derived by means of the complex spectral decomposition method developed by the Brussels-Austin group. The limitations of the previously used phenomenological equations are shown within the scope of the time-dependent N-level Friedrichs-Fano model. The novel nonadiabatic effects owing to the decay of discrete levels into a continuum are found: 1. (i) nonunitary nonadiabaticity caused from unitary one,2. (ii) nonadiabaticity via time dependent coupling with a reservoir, and3. (iii) additional cross-decay due to nonadiabaticity. Reasonable generalization of Berryʹs phase for decaying eigenstates and regeneration of driven decaying states via coherent mixing with reservoir are discussed. General results are applied to the quasienergy-state dynamics of a three-level molecule driven by DC and AC fields and to the non-steady Born-Oppenheimer approach of molecules electronically excited to decaying states. Also, a “resonance” approximation leading to the true non-Hermitian Hamiltonian, similar to the phenomenological one (used in quantum optics in the stationary case) and applicable to the nonstationary case, is formulated explicitly.