Adiabatic evolution of an irreversible two level system

The adiabatic dynamics of a two level atom with spontaneous decay is studied. The existence of a complex adiabatic phase shift is established: The real part being the usual Berry’s phase. A closed‐form expression for this phase and the adiabatic transition amplitudes is obtained. Incorporation of a finite preparation time for the initial state yields a new asymptotic form for the adiabatic transition amplitudes which is significantly different from the standard Landau–Zener–Dykhne formula.