Spontaneous and stimulated emission from atoms in a free one-dimensional space is considered from the quantum-mechanical point of view. The resolvent method is used to calculate the field density matrix, average electric field, and electromagnetic field energy density for a spontaneously emitting atom. For an atom emitting in the field of another atom, calculations are made of the electric field of the spontaneous and stimulated radiation. It is shown how the coherence length and coherence time of the spontaneous radiation increase. The application of these results in laser theory to explain the formation of a radiation mode structure and consequent appearance of coherent radiation is discussed.
Spontaneous and stimulated emission from atoms in a free one-dimensional space is considered from the quantum-mechanical point of view. The resolvent method is used to calculate the field density matrix, average electric field, and electromagnetic field energy density for a spontaneously emitting atom. For an atom emitting in the field of another atom, calculations are made of the electric field of the spontaneous and stimulated radiation. It is shown how the coherence length and coherence time of the spontaneous radiation increase. The application of these results in laser theory to explain the formation of a radiation mode structure and consequent appearance of coherent radiation is discussed.
Coherence properties of the single-mode electromagnetic radiation emitted by a system of identical two-level atoms which is initially in the superradiant state are determined approximately. The approximation is valid only for short times when the state of the atomic system does not differ appreciably from the superradiant state. The electromagnetic field radiated spontaneously possesses full coherence in the sense of Glauber's definition, its density operator having the form of that for the ideal laser radiation. This coherence disappears when, because of external radiation, stimulated and spontaneous emission both take place.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.
The basic phenomena of interaction between atoms and e.m. fields can be discussed in some detail without the need of a detailed model of the atom. Absorption and stimulated emission of radiation can be explained satisfactorily by the theory, where a classical electromagnetic wave provides a time-dependent perturbation to the energy of the atomic electrons. Laser radiation appears to a very good approximation to be a classical travelling wave of well-defined amplitude and phase. The radiation produced by a continuous laser is a good approximation to a coherent state. For conventional sources of radiation, the interaction energy is small compared with the energy an electron possesses by virtue of the attraction to the atomic nucleus, so perturbation theory produces quite acceptable results. The quantum mechanical analogy to the distortion of the classical charge cloud is given by the writing down of a general state function for the system, Ψ.
The coherence and directional properties of stimulated and spontaneous emission can be understood without a knowledge of quantum electrodynamics. This paper presents a semiclassical description of the interaction between a free atom and a weak optical field under conditions of either a stimulated emission or a stimulated absorption resonance. It is shown that, under certain conditions, the stimulated or spontaneous radiation fields emitted from a sample of atoms will propagate in the same direction as the incident beam, will be coherent with the incident beam, and will have the correct phase to provide amplification or attenuation.
The wave side of wave–photon duality, describing light as an electromagnetic field (EMF), is used in this article. The EMF of spontaneous light emission (SE) of a laser-excited atom is calculated from first principles for the first time. This calculation is done using the simple method of atomic quantum electrodynamics. The EMF of SE is also calculated for three types of polyatomic light sources excited by a laser. It is shown that light radiated by such sources can be coherent, which explains recent experiments on SE of laser-excited atoms. Small sources of SE can be superradiant, which also conforms to experiment. Thus, SE is shown not to be a random event itself. Random properties of natural light are simply explained as a result of thermal excitation randomness without additional hypotheses. The EMF of SE is described by simple complex functions, but not real ones.
A model of radiation by multi-atoms is discussed. System A, composed of N atoms with two energy levels, is coupled with a single-mode radiation B. A and B are in turn coupled with two thermal reservoirs D and C respectively, and we also assume that all atoms which are located within a wave length of the radiation field have the same phase. Then under the approximation of long wave, rotating wave and mean fields, by introducing Markov approximation after using the method of density matrix, we have derived the of equations motion for systems A and B respectively. These equations are concerning with the following processes: the spontaneous emission of single atom, the absorption and induced emission stimulated by thermal radiation, the induced emission of N atoms stimulated by single mode coherent state radiation as well as the coherent spontaneous emission of this multi-atoms system. The latter two processes are actually the two kinds of superradiance originated from Dicke model and had been investigated previonsly. We have analysed these five processes by numerical calculations. Besides, the influence of these processes upon the evolution of atomic system attaining thermal equilibrium and the increase of entropy is also discussed. It is pointed out that the correlations inside a multi-atoms system would not be destroyed by coherent spontaneous emission, in contrast with the incoherent one which leads to the change of entropy in atomic system. However, only when the entropy of the two reservoirs has been taken into account, will it be possible to demonstrate the mono-tonic increase in total entropy.