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Journal of Physics B Atomic and Molecular Physics

Interaction of a three-level system with two strong fields

Ludmila S. Kancheva, D. I. Pushkarov

Published Jan 28, 1980• 7 citations
Publisher

Abstract

General expressions for the steady-state population distribution and complex susceptibilities of a three-level system interacting with two strong near-resonant electromagnetic fields are obtained using a density-matrix formalism. A complete treatment of the steady-state population distribution established in the three-level system, under the action of two strong fields with arbitrary resonance detunings is presented. The criterion for maximal populations of the exciting levels, as well as conditions in which the population of the exciting levels exceeds the population of the ground state are found. The modification of the absorption and emission lines with increasing intensity of the second (probe) field is considered. The emphasis in the present treatment, as distinct from Panock and Temkin (see IEEE J. Quantum Electron., vol.QE-13, p.476 (1977)) is on the consideration of the arbitrary distribution of the equilibrium populations of the system which exhibits a number of interesting features which have not been previously discussed.

DOI
10.1088/0022-3700/13/2/028

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arXiv:quant-ph/9907002•Jul 1, 1999•0 citations
General expressions for the steady-state population distribution and complex susceptibilities of a three-level system interacting with two strong near-resonant electromagnetic fields are obtained using a density-matrix formalism. A complete treatment of the steady-state population distribution established in the three-level system, under the action of two strong fields with arbitrary resonance detunings is presented. The criterion for maximal populations of the exciting levels, as well as conditions in which the population of the exciting levels exceeds the population of the ground state are found. The modification of the absorption and emission lines with increasing intensity of the second (probe) field is considered. The emphasis in the present treatment, as distinct from Panock and Temkin (see IEEE J. Quantum Electron., vol.QE-13, p.476 (1977)) is on the consideration of the arbitrary distribution of the equilibrium populations of the system which exhibits a number of interesting features which have not been previously discussed.
A stationary distribution of populations in a three-level quantum system interacting with three intense monochromatic fields resonant to two allowed and one forbidden transition is determined for three possible configurations of the considered system. The obtained algebraic expressions for populations of levels are exact within the frameworks of RWA and dependent on the phases of fields even in the limit of strong field intensities. The latter circumstance causes the absorption line profile to be noisy due to random phase modulation of fields. The sets of parameters of the system and field are founded at which the populations of all the levels are equal to 1/3 also with the regions where a resonance-like dependence of level populations on the difference of field phases takes place.
A complete and detailed treatment of a three-level atom interacting with two near-resonant monochromatic fields is presented. It is assumed that the only damping mechanism is radiative damping, and that the atoms all have the same resonance frequencies, as is the case in an atomic beam. Detailed analytic solutions as well as numerical examples are determined from quantum-electrodynamic equations of motion. In addition, approximation techniques are presented which allow one to get accurate quantitative predictions for strong applied fields from simple rate-equation-like arguments. Absorption and emission spectra are determined, as are the transient and steady-state response of the atom. Two of the more interesting predictions are an emission spectrum containing up to seven components and a prediction of steady-state populations larger than 0.5 in the second excited state.
For pt.II see ibid., vol.9, p.1221 (1976). Discusses the steady-state response of a three-level atom in two-photon absorption. The applied laser fields can have arbitrary intensities (within the rotating-wave approximation (RWA)). A general expression is derived for the population excited on the uppermost energy level. Two special cases which allow a trivial Doppler averaging are treated in detail. For an off-resonant intermediate state the two-photon spectrum is a simple Lorentzian showing a power shift and modest cross power broadening. The same features are retained when several off-resonance intermediate levels are assumed. For very strong laser fields the Doppler shifts can be neglected in the first approximation. The corresponding spectra are analysed.
The rate of absorption and emission of radiation is calculated for two laser fields interacting with a homogeneously broadened, three-level molecular system. The time-dependent Schrödinger equation is used in the density matrix formalism and the laser fields are treated classically. The laser fields, at frequencies ωpand ωs, are off resonance by δpand δs, respectively, such that|\delta_{p}|, |\delta_{s}| \ll \omega_{p}, \omega_{s}. Analytic expressions are derived for the imaginary part of the electric susceptibility,\chi"(\omega_{p})and\chi"(\omega_{s}). The present work differs from previous calculations in that the laser fields may have arbitrary values of field strength and each field may be on or off resonance. A discussion is presented of the properties of the solutions for\chi"(\omega_{p})and\chi"(\omega_{s}), for both strong and weak laser fields, based on computer evaluation of the general analytic expressions. It is shown that the solutions may be divided into single-photon and two-photon, or Raman, contributions. Conditions for optimizingdI(\omega_{s})/dzand the photon conversion efficiency are derived. These results may be applied to analyzing the pulsed, optically pumped submillimeter laser and to studying two-photon absorption in a gas.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations