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Physical Review A

High-precision quasienergies for a driven two-level atom at the two-photon preresonance

Dong‐Sheng Guo, J. T. Wang, Yong-Shi Wu

Published Feb 4, 2008• 3 citations
Publisher

Abstract

A computation with unprecedented precision is presented for quasienergies of a two-level atom in a monochromatic radiation on the basis of a recently obtained exact expression [D.-S. Guo et al., Phys. Rev. A 73, 023419 (2006)]. We start with the proof of an expression theorem. With this theorem the quasienergies for any two-level atom can be expressed in terms of the quasienergies for only those with the original energy spacing (per field photon energy) being an integer (preresonances). Then we carry out a numerical evaluation of the quasienergies at the two-photon preresonance, which involves computing an infinite determinant, up to the 18th power of the coupling strength. The theoretical prediction presents an experimental challenge for high-precision tests of quantum mechanics and could be exploited for precise calibration of high laser intensities.

DOI
10.1103/physreva.77.025401

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A computation with unprecedented precision is presented for quasienergies of a two-level atom in a monochromatic radiation on the basis of a recently obtained exact expression [D.-S. Guo et al., Phys. Rev. A 73, 023419 (2006)]. We start with the proof of an expression theorem. With this theorem the quasienergies for any two-level atom can be expressed in terms of the quasienergies for only those with the original energy spacing (per field photon energy) being an integer (preresonances). Then we carry out a numerical evaluation of the quasienergies at the two-photon preresonance, which involves computing an infinite determinant, up to the 18th power of the coupling strength. The theoretical prediction presents an experimental challenge for high-precision tests of quantum mechanics and could be exploited for precise calibration of high laser intensities.
An asymptotic method is proposed for the determination of quasienergy levels of an atom in the field of modulated optical radiation. A comparison of the asymptotic and exact solutions is used to show that the range of validity of the new method is considerably wider than those of the known asymptotic methods. An analysis is made of the shifts of the quasienergy levels of an atom under the influence of bichromatic radiation and of a periodic pulse sequence. A modulation method is proposed for the attainment of Doppler-free resonances in gases.
Analytical expressions for the quasienergies and corresponding semiclassical dressed states are obtained for a two-level quantum system driven by a nonresonant and/or strong laser field in a coherent state. These expressions are of first order in a proper perturbative expansion, and already contain all the relevant physical information on the dynamical and spectroscopic properties displayed by these systems under such particular conditions. The influence of the laser field parameters on transition frequencies, selection rules, and line intensities is easily understood in terms of the quasienergy-level diagram and the allowed transitions between the different semiclassical dressed states.
Analytical expressions for the semiclassical dressed states and corresponding quasienergies are obtained for a two-level quantum system driven by a non-resonant and/or strong laser field in a coherent state. These expressions are of first order in a proper perturbative expansion, and already contain all the relevant physical information on the dynamical and spectroscopic properties displayed by these systems under such particular conditions. The influence of the laser field parameters on transition frequencies, selection rules and line intensities can be easily understood in terms of the quasienergy-level diagram and the allowed transitions between the different semiclassical dressed states.
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].