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International Journal of Modern Physics B

HAMILTONIAN FORMULATION FOR THE THEORY OF MULTIPHOTON PROCESSES IN ATOMS BASED ON THE FIRST PRINCIPLES

A. A. Bakasov

Published Jul 1, 1989• 0 citations
Publisher

Abstract

A Hamiltonian is derived on the basis of the first principles of quantum electrodynamics. The Hamiltonian is seen to describe two- and multiphoton processes. A problem of consequent derivation and microscopic substantiation of models of multiphoton processes widely used in quantum optics is solved. The first correction to the Pauli equation is obtained. The constant of interaction of a two-level atom with two photons is given in an explicit form. A method of calculating interaction constants for multilevel atoms with multiphoton transitions is presented. Other results obtained on the basis of the developed approach are announced.

DOI
10.1142/s0217979289000750

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A Hamiltonian is derived on the basis of the first principles of quantum electrodynamics. The Hamiltonian is seen to describe two- and multiphoton processes. A problem of consequent derivation and microscopic substantiation of models of multiphoton processes widely used in quantum optics is solved. The first correction to the Pauli equation is obtained. The constant of interaction of a two-level atom with two photons is given in an explicit form. A method of calculating interaction constants for multilevel atoms with multiphoton transitions is presented. Other results obtained on the basis of the developed approach are announced.
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A treatment of nonlinear optical phenomena beginning with a microscopically correct Hamiltonian containing the Bose operators of the light field and the Fermi operators for the optically active electrons in the medium is presented. Using techniques recently developed, a nonperturbative solution to the Schrodinger equation is possible. No linearization or semiclassical approximations are introduced. Two photon emission and absorption including both the degenerate and nondegenerate cases are considered. Parametric amplification and frequency conversion are investigated as examples of multiphoton processes. Atomic cooperation is shown to enhance the above phenomena. A formal treatment of a model illustrating super and subradiance is included.
We present a formalism that enables the analytic calculation of the interaction of a spin-half particle with a polychromatic electromagnetic field. This powerful new approach provides a clear physical picture even for cases with highly degenerate energy levels, which are complicated to interpret in the standard dressed-atom picture. Typically semi-classical methods are used for such problems (leading to equations that are solved by Floquet theory). Our formalism is derived from quantum electrodynamics and thus is more widely applicable. In particular it makes accessible the intermediate regime between quantum and semi-classical dynamics. We give examples of the application to multi-frequency multi-photon processes in strong fields by deriving the Hamiltonians of such systems, and also to the dynamics of weak fields at long times for which semi-classical methods are insufficient.
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.
We often hear at seminars and presentations ‘Show me the Hamiltonian of your problem and I will tell you what problem you are talking about’. Therefore, to understand what quantum optics is about, we start from the description of a standard Hamiltonian of the problems considered in quantum optics. We illustrate the method of derivation of the explicit form of the Hamiltonian for a simple system that is composed of two subsystems that interact (communicate) with each other. As we shall see, the explicit form of the Hamiltonian is essential to explicitly calculate energy levels of a given combined system and the temporal evolution of an arbitrary operator representing the system.