@article{6e6667bf2bd542268f53290ebdd30304,

title = "The damped degenerate-level atom",

abstract = "Equations are derived for the time evolution of the reduced density operator for an (N + 1)-state atom which is damped by its coupling to a finite-temperature boson bath. General formal solutions are discussed in the limit of low temperature. Exact solutions are given for the decay of a p level in an electric field. The effects of a driving field and of transitions between the excited states on the equations are discussed. The application for the decay of elementary particles is mentioned.",

author = "Amnon Aharony",

note = "Funding Information: In this paper we investigate the damping of an (N + I)-state atom in interaction with a thermal bath of bosons. The states are divided into N nearly degenerate excited states and a ground state. The interaction with the bath induces transitions between the excited states and the ground state, combined with the creation or annihilation of bosons in the bath. Similar problems, motivated by studies of laser radiation, have been dealt by Louise11a nd Marburger [l] for a damped harmonic oscillator and by Mollow and Miller [2]-for a damped (nondegenerate) two-level atom at zero temperature. The case we present here, of a degeneratel evel, does not appear to have been treated in the literature. In Section 2 of this article we define the Hamiltonian of the problem, and obtain the master equation for the reduced density matrix describing the state of the atomic system [3]. In Section 3 we consider the limit of low temperatures in which the master equation may formally be exactly solved, the solution being a sum of oscillating exponentially decaying terms. In Section 4, special casesw ith exact solutions of the general problem are considered. Section 5 contains a discussion of a physical example of the interaction of an atom with an electric field. Sections 6-8 contain short discussionso n further possible extensions of the model to contain driving electric fields (in Section a), excitations among the excited states (in Sec- * Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, U. S. Air Force, under AFOSR grant number EOOAR-68-0010, through the European Office of Aerospace Research.",

year = "1971",

month = jan,

day = "1",

doi = "10.1016/0003-4916(71)90095-9",

language = "English",

volume = "62",

pages = "343--360",

journal = "Annals of Physics",

issn = "0003-4916",

publisher = "Academic Press Inc.",

number = "2",

}