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Conference on Lasers and Electro-Optics

Theory of bound-free transitions: extension of the pole approximation

Abraham G. Kofman

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given. We have developed a general theory of single-photon bound-free transitions, which takes into account all the states of the quantum system of interest and treats the rotating- and counterrotating-wave terms on equal footing. With the help of the smoothed-dynamics approximation (SDA), which holds until the laser field is much weaker than the intramolecular field, a closed analytical result for the Laplace transform of the initial-state amplitude has been obtained. To perform the inverse Laplace transform, the pole approximation, extended to obtain higher-order corrections, has been employed.

DOI
10.1109/iqec.1998.680142

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Summary form only given. We have developed a general theory of single-photon bound-free transitions, which takes into account all the states of the quantum system of interest and treats the rotating- and counterrotating-wave terms on equal footing. With the help of the smoothed-dynamics approximation (SDA), which holds until the laser field is much weaker than the intramolecular field, a closed analytical result for the Laplace transform of the initial-state amplitude has been obtained. To perform the inverse Laplace transform, the pole approximation, extended to obtain higher-order corrections, has been employed.
A theory of single-photon ionization, detachment, and dissociation of quantum systems (atom, molecule, ion, etc) is presented. A unified treatment of excitation from the ground and excited states is performed, via a consideration of the rotating- and counter-rotating-wave terms on equal footing. The familiar pole approximation (PA) is extended to obtain higher-order corrections, which allows one to establish the PA validity conditions and provide a unified description of the cases of above- and below-threshold excitation. As a specific example, photodetachment of negative ions is considered. An exact long-time solution is obtained for the general case. A familiar model of photodetachment is used to validate the present PA formalism. The latter has allowed us to derive the PA validity condition, which holds for all values of the parameters, involving quite different situations. The applicability of the existing versions of the rotating-wave approximation has been checked.
The author solves the Schrodinger equation in terms of continued fractions for a system exhibiting light-induced bound-free transitions over an energy gap, without making the rotating-wave approximation. He describes the evolution of the bound state and the photoelectron spectrum by investigating the analytic properties of the Fourier transforms of the probability amplitudes. The main consequence of non-RWA transitions is a Bloch-Siegert shift of the continuum threshold, which may be comparable to RWA dynamic level shifts. At high intensities the counter-rotating wave also influences the evolution of the bound state, and gives rise to multiphoton transitions competing with RWA multiphoton transitions with an odd number of photons, but these effects are probably hard to isolate experimentally.
A general analytical result has been obtained for the calculation of higher-order corrections to the momentum-translation approximation. Explicit analytical results are given for the calculation of higher-order corrections for bound-bound and bound-free transitions for hydrogenic atoms. Numerical results are given for 1S1S1S to 2S2S2S transitions in hydrogen.
A non-relativistic quantum theory of matter-photon interaction is formulated, within the framework of the dipole approximation, by employing a canonical transformation to diago­ nalize the A' term plus the free photon Hamiltonian. The matter-photon interaction is there­ by expressed rigorously in a renormalized A·p form. Using this form for the Dicke model of two-level atoms interacting with a single-mode radiation field, we examine a possibility of the occurrence of stationary coherent states which could arise for a photon and atomic polarization as the ground state of the system, deducing a condition for such coherent states. The condition, expressed as an inequality which imposes a stable nontrivial Bloch angle of the uniform atomic polarization, is identical with that for the occurrence of a second order phase transition, and indicates that the non-existence of a second order phase transition pointed out by Rza2ewski et al. io; in fact a consequence of the present treatment of the A'­ term renormalization. However, a fulfillment of the condition is recovered, if exchange­ type atom-atom interaction is taken into account in the matter system. We also present a method to construct an effective Hamiltonian of atom-atom interaction which is equivalent to the above Dicke model in the thermodynamic limit.
An approximation method is developed which yields very simple and general analytical results for electromagnetic bound-bound or bound-free transitions for any arbitrarily high order of interaction with the electromagnetic field. The approximation is perturbative in the sense that transition probabilities are proportional to the field intensity raised to the power NNN, where NNN is the order of the interaction. Limiting values of electromagnetic field strength are given within which the approximation is valid. These limits depend upon the binding potential which produces the bound states. A feature of the results is that they show the onset of high-order dominance effects which can occur at high-field intensities.
I have obtained a general analytic result for calculating any higher-order correction to the transition amplitude for NNN-photon absorption by writing the time-dependent perturbation theory in the SSS-matrix form. In obtaining this result, I have made use of the concept of average energy as has been defined by Bebb and Gold. A formal expression has been obtained for the upper bound of the higher-order correction and the results are discussed for the case of the hydrogen atom.