Cooperative Effects in Spontaneous Emission

Abstract

We discuss the cooperative superradiant decay of N two-level atoms contained in a pencil-shaped volume. The Dicke “coherence brightening” - i.e. the emission of a hyperbolic secant pulse whose intensity is proportional to N² and whose time duration is inversely proportional to N - occurs instead of the usual exponential decay under the following conditions:

• i) the incoherent atomic decay, due to natural relaxation, is so slow that the individual atomic dipoles do not get out of phase with each other before the cooperative decay is over.

• ii) the length of the pencil-shaped volume is smaller than a critical “cooperation length” inversely proportional to the square root of N. This condition guarantees that they cannot feed themselves back into atomic excitation to any appreciable amount, and that the envelope of the emitted pulse is essentially constant over the length of the sample, so that all the atoms radiate as a single macroscopic dipole rather than seeing and producing different values of the field at different points. The emitted light pulse is found to have different statistical properties for an incoherently and a coherently prepared “superradiant” atomic initial state. The former case is characterized by large quantum fluctuations and strong atom-atom and atom-field correlations. In the latter case quantum fluctuations are small and the system behaves essentially classically. By also solving for a class of coherently prepared intermediate initial states we show that large quantum fluctuations occur only if the initial total occupancy of the excited state differs from the total number of atoms at most by a number of order unity.

This report is based on recent work done in collaboration with F. Haake and P. Schwendimann and published in Phys. Rev. A4, 302 (1971) and Phys. Rev. A4, 854 (1971).