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Journal of the Optical Society of America B

Testing of laser-dressed atomic states

Miodrag D. Janjusevic, Yukap Hahn

Published Apr 1, 1990• 7 citations
Publisher

Abstract

A simple procedure of dressing the atomic states distorted in the presence of a potential, bound or continuum, by a laser field is discussed, and the validity of the developed dressing procedure is tested by evaluating the harmonic generation and multiphoton ionization processes for a one-dimensional model potential of the form V(x) = −(1 + x2)−1/2. The results are compared with the exact one-dimensional model calculations of Eberly et al. for the same processes [ Phys. Rev. Lett.62, 881 ( 1989)]. Several other dressed-state wave functions proposed by other authors are also tested.

DOI
10.1364/josab.7.000592

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A simple procedure of dressing the atomic states distorted in the presence of a potential, bound or continuum, by a laser field is discussed, and the validity of the developed dressing procedure is tested by evaluating the harmonic generation and multiphoton ionization processes for a one-dimensional model potential of the form V(x) = −(1 + x2)−1/2. The results are compared with the exact one-dimensional model calculations of Eberly et al. for the same processes [ Phys. Rev. Lett.62, 881 ( 1989)]. Several other dressed-state wave functions proposed by other authors are also tested.
A simple, "exactly solvable" atomic model will be presented that helps to discuss some of the interesting features of multiphoton ionization of atoms. The electromagnetic field is treated non-perturbatively, it can be strong. The atomic electrons are assumed to be non-interacting (Hartree model). They are bound in a harmonic oscillator potential (one- or three-dimensional). At the ionization energy, the potential is cut off and the free electron has no Coulomb attraction. The Schrodinger equation has exact analytic solutions valid in the inner or outer regions. If the field is turned on adiabatically, the exact solution can be found by matching these solutions at the boundary; both of their value and the normal derivative at all times. Thus the machine calculation reduces to repeated application of fast Fourier transforms and to the solution of linear equations (unfortunately a lot of them).
The dual Dyson series [M. Frasca, Phys. Rev. A 585858 3439 (1998)] is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In fact, both the Dyson series and its dual, by renormalization-group methods to remove secular terms from the perturbation series, give the opportunity for a full study of the solution of the Schr\"odinger equation in different ranges of the parameters of the given Hamiltonian. In view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom-field interaction, showing that these are just the leading order of the dual Dyson series when the Hamiltonian is expressed in the interaction picture. In order to best exploit the method, a study is accomplished of the well-known Jaynes-Cummings model in the rotating-wave approximation, whose exact solution is known, comparing the perturbative solutions obtained by the Dyson series and its dual with the same approximations obtained by Taylor expanding the exact solution. Finally, a full perturbative study of high-order harmonic generation is given, obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even if the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spectrum it is necessary to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the energy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines.
We present the results of non-perturbative, R -matrix Floquet calculations of laser-induced continuum structures (LICS) in helium. We consider the case in which a Nd:YAG laser is used to embed the 1s4s Rydberg state in the continuum. The resulting modification of the photoionization rate of the 1s2s state is then calculated. This LICS has been studied recently by Halfmann et al (1998 Phys. Rev. A 58 R46) and good agreement with their experimental and theoretical findings is obtained. We also investigate the effects of incoherent channels due to higher-order multiphoton processes and LICS involving the 1s4d state. The validity of the simple two-level models that are frequently used for modelling LICS is tested by comparing these results with R -matrix Floquet calculations.