Life-times of quantum resonances through the Geometrical Phase Propagator Approach

We employ the recently introduced Geometric Phase Propagator Approach (GPPA) (Diakonos et al., 2012) to develop an improved perturbative scheme for the calculation of life times in driven quantum systems. This incorporates a resummation of the contributions of virtual processes starting and ending at the same state in the considered time interval. The proposed procedure allows for a strict determination of the conditions leading to finite life times in a general driven quantum system by isolating the resummed terms in the perturbative expansion contributing to their generation. To illustrate how the derived conditions apply in practice, we consider the effect of driving in a system with purely discrete energy spectrum, as well as in a system for which the eigenvalue spectrum contains a continuous part. We show that in the first case, when the driving contains a dense set of frequencies acting as a noise to the system, the corresponding bound states acquire a finite life time. When the energy spectrum contains also a continuum set of eigenvalues then the bound states, due to the driving, couple to the continuum and become quasi-bound resonances. The benchmark of this change is the appearance of a Fano-type peak in the associated transmission profile. In both cases the corresponding life-time can be efficiently estimated within the reformulated GPPA approach.