What is wrong with the projection operator method? removal of inconsistencies and a new self-consistent method for non-Markovian treatment of atom-field interactions

Abstract

s knowledge, that the application of the projection-operator method leads to the violation of a consistency condition if the so-called Born approximation is employed. Namely, the violation of this consistency condition causes the appearence of negative probabilities in the non-Markovian master equation and thus makes the applicability of the projection-operator method questionable. Further, it is shown that an additional Markov approximation re-establishes the applicability of the method. Moreover, a new self-consistent projection-operator method for treating non-Markovian time evolution in the case of interactions between atoms and field (reservoir) is developed. Finally, in the appendix it is shown that, if the usual non-self-consistent projection-operator method in the Born approximation is applied to the case of spontaneous emission from a two-level hydrogen atom, a negative probability for finding the atom in the excited state emerges. PACS 42.50 -Quantum optics. PACS 05.30 -Quantum statistical mechanics.