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We employ the recently introduced Geometric Phase Propagator Approach (GPPA)[Phys. Rev. A85, 062110 (2012)] to develop an improved perturbative scheme forthe calculation of life times in driven quantum systems. This incorporates aresummation of the contributions of virtual processes starting and ending atthe same state in the considered time interval. The proposed procedure allowsfor a strict determination of the conditions leading to finite life times in ageneral driven quantum system by isolating the resummed terms in theperturbative expansion contributing to their generation. To illustrate how thederived conditions apply in practice, we consider the effect of driving in asystem with purely discrete energy spectrum, as well as in a system for whichthe eigenvalue spectrum contains a continuous part. We show that in the firstcase, when the driving contains a dense set of frequencies acting as a noise tothe system, the corresponding bound states acquire a finite life time. When theenergy spectrum contains also a continuum set of eigenvalues then the boundstates, due to the driving, couple to the continuum and become quasi-boundresonances. The benchmark of this change is the appearance of a Fano-type peakin the associated transmission profile. In both cases the correspondinglife-time can be efficiently estimated within the reformulated GPPA approach.

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