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Journal of Physics B Atomic and Molecular Physics

The thermodynamics of multiphoton processes

G. J. Pert

Published Sep 1, 1971• 0 citations
Publisher

Abstract

By considering the thermodynamic equilibrium of a radiation field with matter through multiphoton processes, generalized expressions equivalent to the Einstein and Milne relations for single photon interactions are derived. Mixed stimulated spontaneous effects are predicted with an integral intensity power law index less then n, the order of the process.

DOI
10.1088/0022-3700/4/9/016

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By considering the thermodynamic equilibrium of a radiation field with matter through multiphoton processes, generalized expressions equivalent to the Einstein and Milne relations for single photon interactions are derived. Mixed stimulated spontaneous effects are predicted with an integral intensity power law index less then n, the order of the process.
The non linear interaction between an intense laser radiation and atoms leads to ionization through the absorption of N photons from the laser radiation via laser-induced virtual states. The multiphoton ionization rate varies as a function of the laser intensity I as IN. We discuss the two most important effects which govern multiphoton ionization processes : resonance effects and laser-coherence effects. In a moderate laser intensity range (107 - 109 W cm-2) corresponding to the two, three or four-photon ionization of atoms, resonance effects play a dominant role while the photon statistics of the laser radiation are relatively unimportant. On the contrary, in the very high intensity range (1012 - 1013 W cm-2) required to observe large Nth - order ionization processes, coherence effects play a dominant role through N! enhancement in the N-photon ionization rate, while resonance effects are completely damped due to the high laser intensity. We conclude by reviewing the possible applications of multiphoton absorption processes in other fields.
Partial table of contents: PART I: GENERAL CONCEPTS AND METHODS OF NONLINEAR OPTICS. Electromagnetic Fields. Classical Description. The Quantized Free Radiation Field. Interaction Between Radiation and Matter. Semiclassical Description of Nonlinear Optics. Statistical and Coherence Properties of the Radiation Field and Their Measurement. Nonstationary Processes. PART II: EFFECTS AND PROCESSES OF NONLINEAR OPTICS. Nonlinear One--photon Processes in Lasers. Nonlinearities in Transient One--photon Processes. Nonlinearities and Qunatum Phenomena in Transient One--photon Processes. Multiphoton Absorption and Emission. Generation of Harmonics and Sum and Difference Frequencies. Parametric Amplification and Oscillation. Stimulated Raman Scattering. Optical Bistability. APPENDIX A: Compilation of Quantum--Theoretical Definitions and Relations. General References. Index.
Abstract Laser radiation is an intense coherent light field that is characterized by its high monochromatic brightness and high photon degeneracy. Thus, it is capable of generating various stimulated scattering effects and a series of multiphoton excitation-induced opto-physical and opto-chemical effects. There are two parallel theoretical regimes. The first regime is the semiclassical theory that treats light as a classical electromagnetic field described by Maxwell’s equations. The second regime is the quantum electrodynamic theory, which treats light as an assembly of photons obeying Bose–Einstein statistics. Both regimes can be complementarily adopted to describe the interaction of light radiation with matter.
The thermodynamic properties of a system of two-level atoms interacting with a quantized radiation field are investigated. We allow from the outset an infinite number of photon modes; we calculate the free-energy density in the thermodynamic limit exactly and rigorously. A second-order phase transition is evident from the expression for the free-energy density. We investigate it in detail by examining the distribution of the mean photon number density as a function of photon frequency. We use the Lieb-Berezin inequalities combined with the large-deviation principle.