Anomalous dynamics in multilevel quantum decay

Abstract

A metastable quantum state coupled to a continuum undergoes an exponential decay in the Weisskopf-Wigner (Markovian) approximation. However, quantum theory strictly predicts deviations from an exponential decay law both at small and long time scales. In multilevel systems, even in the Markovian approximation strong deviations from an exponential decay can be observed in the intermediate time scale owing to interference of overlapping resonances. Such interference effects are simply described by an effective non-Hermitian Hamiltonian and are known to explain, for example, the existence of dark states and fractional decay. Here we show that the wide variety of anomalous behaviors observed in multilevel quantum decay are rooted in the non-normal nature of the effective non-Hermitian Hamiltonian, revealing strong similarities between anomalous quantum mechanical decay and non-normal dynamics found in hydrodynamic flows. Major signatures of non-normal dynamics include delayed decay, accelerated decay, and exponential-power-law decay at an exceptional point. Such signatures are exemplified by suggesting simple tight-binding lattice realizations of multilevel quantum decay, which could be emulated in integrated photonic experiments. Finally, it is shown that for noninteracting particles with fermionic statistics the usual exponential decay law is restored, i.e., all anomalous decay effects arising from single-particle non-normal dynamics are washed out.