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Journal of Hunan University of Science and Engineering

The Energy-level Configuration of Jaynes-Cummings Model in An External Field

Fei Zeng

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

We study a atomic system coupled to a quantum field and an external classical field at the same time. The interaction betwere the atom and the external field is regarded as a perturbation. Using perturbation theory to solve the energy-level configuration of this quantum system, where the first-order are zero, and the second-order are proportionate to the second power of the coupling constant betwere the atom and the external field.

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We study a atomic system coupled to a quantum field and an external classical field at the same time. The interaction betwere the atom and the external field is regarded as a perturbation. Using perturbation theory to solve the energy-level configuration of this quantum system, where the first-order are zero, and the second-order are proportionate to the second power of the coupling constant betwere the atom and the external field.
We studied a very simple model of the interaction between radiation and matter, named Jaynes-Cummings model. Matter is represented by an atom, treated as a two level system, which interacts with one single mode of the electromagnetic field. We looked at the problem in two different ways: first, treating both systems as quantum and later, considering the field as classical and the atom as quantum. In particular,we concentrate in obtaining the population inversion in both cases. In the context of semiclassical theory, we still used two distinct approachs: one, taking into account the field reaction of the atom and, the other, ignoring any effect of the atom onto the field. We verified that the first gives a more realistic description than the second because it accounts for spontaneous emission by the atom. We still included the environment on the description of both quantum and classical dynamics.
Chapter 17 begins by approaching the general problem of a quantum system subject to a time-dependent perturbation. We then apply perturbation theory to the interaction of atomic matter with the radiation field and derive the most important radiative corrections. Atomic transitions – both induced and spontaneous – are discussed in detail, with some important applications. The formal introduction of field quantization allows us to make contact with quantum electrodynamics and quantum optics and discuss the Jaynes–Cummings model. Stochastic electrodynamics, in which the matter–field interaction is not a perturbation but is present ab initio, is used to explain atomic stability and its breakdown leading to radiative transitions. In the same spirit, the quantization of the field is physically justified by deriving the conventionally postulated field operators and their basic commutators. The chapter ends with a brief introduction to second quantization, an elegant and powerful formalism for describing and analyzing quantum many-body systems.