Superradiant and Subradiant Behavior of the Overdamped Many-Atom Micromaser Vasily V. Temnov, Mikhail I. Kolobov and Fritz Haake Summary. We present the quantum treatment of an overdamped many-atom mi- cromaser. Our model accounts for excited atoms entering the cavity but does not allow them to exit. The limit of overdamped Rabi-oscillations is assumed. We give a temporally coarse-grained description which smoothens over entrance events and compare it with a ”microscopic” treatment accounting for each of the entrances and the evolution between them. We find an interesting nonstationary behavior of the micromaser radiation: a sequence of superradiant pulses which converges to a subradiant stationary regime. In a micromaser [1] or microlaser [2] an atomic beam passing through the cavity usually has such a low atomic density that only a few atoms at a time interact with a single cavity mode. Collective atomic interaction with the cavity mode is interrupted by arrivals of new atoms and their escapes from the cavity. The question arises as to whether collective atomic behavior can persist in such a situation. It was shown recently [3] by means of Monte-Carlo simulations that two different types of collective behavior are possible in the overdamped many- atom micromaser: superradiance and subradiance [4]. In [3] collective dy- namics of superradiance for the density matrix of intracavity atoms [5], in- terrupted by entrances and escapes, was simulated numerically. Analytical treatment of such a model is extremely difficult because one has to follow the 2 N × 2 N atomic density matrix for large and possibly varying N . In the present paper we discuss another model of the overdamped many-atom mi- cromaser. The difference to [3] is that atoms, once entered into the cavity, are not allowed to escape from it. This assumption greatly simplifies the problem and allows for an analytical treatment. The scheme of our micromaser is shown in Fig. 1. The atoms first pass through a velocity selector and then a pump field which excites them into the upper level |e〉. After that they enter the cavity and remain there. The upper atomic level |e〉 and the lower level |g〉 constitute the masing transi- tion resonantly coupled to the single cavity mode. The collective atom-field interaction is interrupted by entrances of new excited atoms, to be referred as ”kicks”. These kicks change both the interaction Hamiltonian and the joint atom⊕field density matrix because the number of atoms inside the cavity grows by one after each kick. The dynamics between the kicks is described H.J. Carmichael, R.J. Glauber, M.O. Scully (Eds.): LNP 561, pp. 261–270, 2001. c  Springer-Verlag Berlin Heidelberg 2001