Transient Effects in Resonance Fluorescence and Spontaneous Emission by a System of Identical Atoms

Abstract

A simple theoretical model is formulated which describes dynamical features of the interaction of two-level atoms with a continuum of radiation oscillators. In particular, this paper is concerned with resonance scattering by single atoms in the presence of an external classical field, and spontaneous emission by a system of identical atoms. In the case of resonance scattering, the response of an atom to rapid changes of the amplitude of the external field is studied. The model for spontaneous emission by a system of atoms is based on the assumptions that all atoms have the same resonance frequency, and that the atoms are contained in a volume whose extension is small compared with the wavelength of the emitted radiation. The complete evolution of a system of m atoms is determined by a set of coupled first-order linear differential equations, and explicit solutions are presented for the values m = 1, 2, 3, 4, and 8. Pair correlations of the atoms and photon-number fluctuations are discussed. An approximation for resonance fluorescence by a system of atoms with a broad distribution of resonance frequencies is included in an Appendix.

A perturbative formalism for the spontaneous emission by excited systems

“…Up to this point, the same results should have been obtained by using method A, B, or C. In order to evaluate higher-order contributions to the eigenstates, still using the assumptions of Raiford [7] and Dillard and Robl [14] on the interaction between atoms and the photon field, methods A and B seem to be inadequate. Consequently only method C will be used here.…”

“…In the limit of an infinite L system, for which summations over the states of this system can be replaced by integrals, the operator given by equation (14) loses its hermitian nature. In fact, as will be shown in w 4, when the spectrum of the hamiltonian 3fa0 (L) is considered as continuous, the summation involved in equation (16), under some assumptions on the spectral density, becomes a sum of integrals of the same kind as the following one :…”

“…Furthermore, following Raiford [7] and Dillard and Robl [14], the interaction is restricted to a finite frequency range from to o-A to to o + A, where A < too and A~F. Finally, we have assumed as negligible the radiative energy shifts and, for simplicity, we have chosen the same sign for the imaginary part of the six nonvanishing elements of the matrix ~s (~).…”

Spontaneous emission by two three-level atoms

“…Figures 6 and 7 clearly tell us that the emission rates for initial states (1) and (2) are much different because of the difference between the two decay constants y, and yz. In state (1), there are two units of excitation stored in the atomic system, while in state (2) there is only one unit of excitation; this illustrates that decay constants strongly affect the strength of the emission rate. From Figs.…”

“…(2) is taken on the initial state of the whole system IV(0) &, which consists of the atomic and radiation-field states. %'e shall consider the initial radiation-field state to be the vacuum state.…”