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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Off-Resonance Behavior Of Atomic Interaction With Cavity Fields Of Arbitrary Detunings

D. L. Lin, Xiao-shen Li

Published Jan 1, 1987• 0 citations
Publisher

Abstract

The Jaynes-Cummings (JC) model has been studied extensively because of its simple and realistic representation of the dipole interaction between an atom and the quantized radiation field. It exhibits, without perturbative expansions or statistical decorrelations, many quantum mechanical effects in the case of strong or weak interaction, long or short time regime, on or off the resonance. The model is extended to a three-level atom for the investigation of physical phenomena associated with two-photon processes.

DOI
10.1117/12.967188

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The Jaynes-Cummings (JC) model has been studied extensively because of its simple and realistic representation of the dipole interaction between an atom and the quantized radiation field. It exhibits, without perturbative expansions or statistical decorrelations, many quantum mechanical effects in the case of strong or weak interaction, long or short time regime, on or off the resonance. The model is extended to a three-level atom for the investigation of physical phenomena associated with two-photon processes.
In this thesis we present a theoretical analysis of some of the implications of the quantum nature of the electromagnetic field.In particular, we are interested in how atomic dynamics are modified by coupling to a quantized radiation field.In chapter two we review the Jaynes-Cummings model of atom-field interactions.This model consists of a single two-level atom coupled to a single mode of the radiation field.The evolution of the atom depends upon the initial quantum state of the field mode.Chapter three is a review of the quantum theory of dissipation.In chapter four we examine the properties of the thermofield states of the two-mode, quantized radiation fields.We investigate the use of these states as a representation of single mode thermal states.The thermo field representation is used to describe interactions involving thermal averages and in an analysis of two-mode squeezing in parametric amplifiers.Chapters five to seven are concerned with the Rydberg atom maser.In chapter five we review some of the properties of Rydberg atoms in cavities and consider the validity of the Jaynes-Cummings model as a description of the maser.In chapter six we discuss the modification of the atomic dynamics when more than one atom is present in the cavity.We show how the collective atomic inversion is influenced by many-atom effects, as well as the photon statistical effects present in the single atom Jaynes-CHAPTER
We extend the standard Jaynes-Cummings model to include transient effects due to a modulation of the atom-field coupling. The exact solution for such a generalized model is found in terms of Bessel functions for the atom-cavity mode interaction modulated by the exponential function. This function is incorporated into the basic Hamiltonian phenomenologically for modelling the processes of adiabatic switching on or switching off the interaction of a two-level atom (at rest) with a quantized mode. The dynamical behaviour of the atomic inversion for such processes is plotted and compared with the atomic dynamics for the standard model. If we take into account that, in micromaser experiments, Rydberg atoms move through a cavity with a spatially inhomogenous field, we deal with the Jaynes-Cummings model with a spatial modulation the form of which is defined by the mode-shape function depending, in turn, on the geometrical form of resonator. In the cases of a rectangular and a spherical cavity the analytical solutions for atomic inversion are found in the explicit form in the weak-coupling limit. We consider in detail the time evolution of the atomic inversion while the atom passes through a rectangular cavity. Contrary to the standard model the initial inversion can be exactly restored during the atomic transit depending on the relation between the detuning, the atomic velocity and the number of half-wavelengths of the chosen mode. The numerical solutions of the basic equations are also obtained and plotted for rectangular and spherical resonators.
Jaynes–Cummings (JC) models are by far the most widely used to study the dynamics of two-level systems, such as atoms or molecules under suitable conditions, coupled to quantized electromagnetic fields. Nowadays, analytical solutions of JC models are more useful than ever for understanding and controlling radiation-matter interactions relevant to quantum information processing, quantum computing, and other quantum technologies. This study presents the analysis and generalization of a method for the solution of the dynamical problem in the time-independent JC model (Carbonaro et al., 1979) that enables an exact description of the atom-field dynamics in the resonant time-dependent JC model and in a nontrivial class of off-resonance time-dependent JC models. Our analysis produces the ready-to-use forms of the evolution operator in the resonant and non-resonant cases, which are then used to derive the evolution of the atomic population inversion for some types of atom-field coupling. The central idea behind the proposed approach offers opportunities for its extension to other time-dependent cases and its generalization to JC-related models.
An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.