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Quantum Electronics

Quasienergy spectrum of a two-level atom in the field of high-intensity modulated radiation

Michael Z. Smirnov

Published Sep 30, 1995• 1 citation
Publisher

Abstract

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.

DOI
10.1070/qe1995v025n09abeh000491

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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.
Using techniques of complex analysis in an algebraic approach, we solve the wave equation for a two-level atom interacting with a monochromatic light field exactly. A closed-form expression for the quasienergies is obtained, which shows that the Bloch-Siegert shift is always finite, regardless of whether the original or the shifted level spacing is an integral multiple of the driving frequency $\ensuremath{\omega}$. We also find that the wave functions, though finite when the original level spacing is an integral multiple of $\ensuremath{\omega}$, become divergent when the intensity-dependent shifted energy spacing is an integral multiple of the photon energy. This result provides an ab initio theoretical explanation for the occurrence of the Freeman resonances observed in above-threshold ionization experiments.
We report our results on measurement of the total fluorescent power radiated by two-level atoms excited by a 100% amplitude modulated or bichromatic laser field. For the case of single-frequency excitation, it is well known that the total fluorescent power monotonically saturates as the intensity of the field is increased. This occurs because the inversion of the atoms approaches zero at high field strengths. In contrast, when the field is bichromatic the total fluorescent power displays resonant peaks as the strength of the driving field is increased. This occurs because there is enhanced absorption when the modulation frequency coincides with the Rabi freqeuncy or one of its subharmonics.
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.
The Hill method is used in an analysis of the Schrodinger equation for a quatum system subjected to a time-periodic nonmonochromatic field. An algebraic equation is obtained and its degree in respect of exp(iET), where E is the quasienergy and T is the period of the external field, is equal to the number of levels. The coefficients of this equation are expanded in powers of the intensity parameter into a series with a factorial convergence even when one of the field frequencies is in exact resonance with one of the transitions. The Fourier components of the density matrix are expressed in terms of quasienergy considered as a function of the parameters of the problem and this gives approximate expressions outside the perturbation theory framework. Various results are obtained for a two-level system and, in particular, a formula is derived for the description of the natural lifetime of a quasienergy state.