The Semiclassical Description of Spontaneous Decay

Alan V. Durrant

A semiclassical radiation theory is developed in which the spontaneous emission field of a two-level atom is a quantum entity represented by atomic operators acting in the Hilbert space of the atomic states. The theory is applied to an investigation of the coherence properties of spontaneous emission. It is found that incoherent and coherent components can be identified in the emission field, the former dominating in the early stages of the decay from the excited state and the latter dominating in the later stages or in the emission from a weakly excited atom. The single-atom coherence properties are shown to lead to well-known superradiance phenomena in the spontaneous emission from an assembly of similar atoms. The paper does not use the theory of quantum electrodynamics; it builds on knowledge at the undergraduate level of classical radiation theory and the quantum mechanics of atoms.

Walter Meissner

Sun Kyung Lee, Hai-Woong Lee

We investigate the time evolution of atomic population in a two-level atom driven by a monochromatic radiation field, taking spontaneous emission into account. The Rabi oscillation exhibits amplitude damping in time caused by spontaneous emission. We show that the semiclassical master equation leads in general to an overestimation of the damping rate and that a correct quantitative description of the damped Rabi oscillation can thus be obtained only with a full quantum mechanical theory.

H. J. Korsch

Péter Horák, Helmut Ritsch

We extend an earlier semiclassical model to describe the dissipative motion of N atoms coupled to M modes inside a coherently driven high-finesse cavity. The description includes momentum diffusion via spontaneous emission and cavity decay. Simple analytical formulas for the steady-state temperature and the cooling-time for a single atom are derived and show surprisingly good agreement with direct stochastic simulations of the semiclassical equations for N atoms with properly scaled parameters. A thorough comparison with standard free-space Doppler cooling is performed and yields a lower temperature and a cooling-time enhancement by a factor of M times the square of the ratio of the atom-field coupling constant to the cavity decay rate. Finally, it is shown that laser cooling with negligible spontaneous emission should indeed be possible, especially for relatively light particles in a strongly coupled field configuration.