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By A. Schuster, J. Nicholson

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In Sect. 2, using these formulas we describe the absorption and emission processes of the light due to the electron (atom) systems, and understand the origin of the spontaneous emissions from excited atoms. Concerning stimulated emission we will discuss it in connection with laser oscillation in Chap. 4. In Sect. 3, we investigate how the natural width of the absorption or emission spectrum is characteristic of the spontaneous emission process. In Sect. 4 we find that the spontaneous emission is not characteristic of an atom and can be controlled artificially by controlling the geometrical structure of the radiation field.

It is also possible to describe the spontaneous emission in the framework of the semiclassical theory. However, using the idea of the photon that is deduced from quantization of the electromagnetic field, we deeply understand not only the spontaneous emission but also the relation between the absorption and stimulated emission. Moreover, we can straightforwardly calculate the Einstein A and B coefficients on the basis of quantum theory. Consider the optical transition due to the perturbation H(1) from the initial state Ψi = |a |n1 , n2 , .

7. This method has advantages such that it reduces the size of the equipment by using solid state devices; it is possible to generate a strong photon flux; and it is also possible to squeeze the photon-number fluctuation in a broad frequency range with high efficiency. In order to describe the photon-number squeezed state in quantum optics, the photon number operator n ˆ and the phase operators Sˆ and Cˆ are introduced as the following: ˆ, n ˆ=a ˆ† a 1 Sˆ = [(ˆ n + 1)−1/2 a ˆ−a ˆ† (ˆ n + 1)−1/2 ], 2i 1 Cˆ = [(ˆ n + 1)−1/2 a ˆ+a ˆ† (ˆ n + 1)−1/2 ].

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