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arXiv:1003.4566 · Physical Review A

Dipole spectrum structure of nonresonant nonpertubative driven two-level atoms

Antonio Picón, L. Roso, J. Mompart, O. Varela, V. Ahufinger, R. Corbalán, Luis Plaja

Published Mar 23, 2010• 14 citations
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Abstract

We analyze the dipole spectrum of a two-level atom excited by a nonresonant intense monochromatic field under the electric dipole approximation and beyond the rotating wave approximation. We show that the apparently complex spectral structure can be completely described by two families: harmonic frequencies of the driving field and field-induced nonlinear fluorescence. Our formulation of the problem provides quantitative laws for the most relevant spectral features: harmonic ratios and phases, nonperturbative Stark shift, and frequency limits of the harmonic plateau. In particular, we demonstrate the locking of the harmonic phases at the wings of the plateau opening the possibility of ultrashort pulse generation through harmonic filtering.

DOI
10.1103/physreva.81.033420

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We analyze the dipole spectrum of a two-level atom excited by a nonresonant intense monochromatic field under the electric dipole approximation and beyond the rotating wave approximation. We show that the apparently complex spectral structure can be completely described by two families: harmonic frequencies of the driving field and field-induced nonlinear fluorescence. Our formulation of the problem provides quantitative laws for the most relevant spectral features: harmonic ratios and phases, nonperturbative Stark shift, and frequency limits of the harmonic plateau. In particular, we demonstrate the locking of the harmonic phases at the wings of the plateau opening the possibility of ultrashort pulse generation through harmonic filtering.
Resonance-fluorescence power spectrum of two-level atoms driven by a strong monochromatic laser field is discussed, taking into account effects due to the dipole-dipole interaction between the atoms. For two atoms confined to a region smaller than the wavelength of the driving field, we predict significant deviations of the power spectrum from the single-atom case. The two-atom spectrum is nonsymmetric, the wing peaks are shifted from their Rabi-frequency positions, and additional maxima may appear.
The problem of a two-level atom interacting with a nonmonochromatic radiation pulse is studied both with and without the resonant approximation. Using the time-dependent perturbation theory, the analytical expressions for transition probability of the atom are obtained. It is shown how, depending on the value of the field strength, the atom's excitation probability can be obtained with the needed accuracy. It is shown that the upper level population of the atom exhibits oscillations which are absent in the resonant approximation. It is shown that absorption probability and dipole moment spectrum are governed by interference between the spectral components of a non- monochromatic radiation involved in nonlinear interaction process. Spectral distribution symmetry with respect to the resonance frequency being destroyed, the atom can be excited even if there is no resonant component in the pulse spectrum.
We show that a simple nonperturbative two-level model of an atom driven by a very strong periodic field, results in a rich picture of very high harmonic generation and related phenomena. It reproduces experimentally observed plateau, yields for the first time simple analytic formulas for the plateau cutoff frequency, critical driving intensity, and saturation, and predicts intensity-induced multi-resonances. One of the most fascinating phenomenon discovered recently in nonlinear interaction of light with atoms and ions, is very high-order (up to 135) odd harmonic generation (HHG) by intense (∼ 1013 W/cm2 and higher) optical laser radiation in rare gasses and some ions [1], The spectra of generated harmonics drasticly deviate from the perturbation theory predictions [2], In particular, intensity of harmonics, falling monotonically with their orders only up to a certain point, levels off forming a so-called “plateau", and falls monotonically again beyond it. Generally, harmonte generation depends on phase-matching conditions and nonlinear response of individual atoms. It has recently become clear however [3,4] that the major features of HHG, in particular the plateau, result mainly from general properties of atomic nonlinear response. The most direct and apparently successful way so far to approach the problem theoretically has been numerical simulation of the Schrödinger [2,5-7] (including an empiric rule [6]) for many-electron atoms using Hartry-Slater approximation. This approach requires, however, tremendous amount of calculations and involves many processes, making it difficult to gain simple insights. An interesting simplified model [8] based on 3-D delta-potential with a single (ground) level [9] produces results in integration form. The idea of retaining a single energy scale (ionization energy) brings one close to an even simpler system: a two-level model atom. A two-level model of HHG [10], however, due to various complications introduced into it, failed to generate simple results, whereas an analytic solution [11] holds for a virtually degenerate two-level model only (see below) which is unapplicable to the experimental conditions [1-4,7,9]; besides, no relaxation was considered in [10,11].
The problem of a two-level atom interacting with a non-monochromatic radiation pulse is studied in the resonant approximation for arbitrary detunings, and without the resonant approximation. By using the time-dependent theory of perturbation the analytical expressions for the transition probability and induced dipole moment of the atom are obtained. It is shown that the upper level population of the atom exhibits oscillations that are absent in the resonant approximation. The temporal shape of the pulse is shown to affect significantly the atomic transition probability. The behaviour of the transition probability and dipole moment spectrum for arbitrary pulse shapes, phases and detunings is investigated. The interference between the spectral components arising in nonlinear processes is shown to play a considerable role in the formation of a dipole moment spectrum.
The resonance fluorescence system of a coherently driven two-level atom in the presence of a broadband squeezed vacuum field whose central frequency is not in resonance with either the driving field frequency or the atomic transition frequency is analyzed. Solutions of the Bloch equations of the system are presented in terms of continued fractions for arbitrary strength of the coherent driving field. Numerical results are presented for the first-harmonic quadrature components of the absorption spectrum and the fluorescent intensity. The effects of the squeezed vacuum field detuning on the absorption spectrum result in hole burning or a dip structure in the weak-field case and two absorption–amplification peaks in the strong-field case. Results are sensitive to the relative phase of the squeezed vacuum.