Spontaneous emission from cylindrical atomic cloud: Collective eigenstates and non-local effects

Abstract

We consider collective emission of a single photon stored in a cloud of N two-level atoms (with energy ћω) confined inside an infinite cylinder and discuss eigenstates of this system, their decay rates and collective frequency shifts. We found that states with wave number k z ≥ ω/ c do not decay and analogous to guiding modes in dielectric waveguides. Evolution of such states is qualitatively different in local (Markovian) and non-local regimes. We found that in the Markovian regime there is no photon emission. In contrast, non-local (memory) effects result in emission and reabsorption of the photon so that probability to find atoms excited oscillates with a collective Rabi frequency. Cross-over between local and non-local behavior can be observed by increasing radius of the cylinder or wave number k z of the excited atomic state. Similar behavior can also be observed in slab geometry and tested in synchrotron experiments on collective excitation of solid-state samples by increasing thickness of the nuclear layer.