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Journal of Physics B Atomic Molecular and Optical Physics

Highly selective excitations of a three-level atomic system by zero- and nonzero-delayed lasers

A. S. Choe, Jongmin Lee

Published Dec 28, 1997• 3 citations
Publisher

Abstract

Highly selective excitations, which occur in a three-level system under the conditions of zero- and nonzero-delayed lasers, are examined. The detuning ranges which reach half inversion and their dependences on the laser conditions are obtained numerically using the Bloch equation. It is found that in the optimal detuning method which uses the zero-delayed lasers, the range is independent of the Rabi frequency and the detuning, but in the adiabatic passage which uses the nonzero-delayed lasers, the range is dependent on the Rabi frequency and the time delay. The inversion methods show strong dependences on the pulse length. It turns out that the optimal detuning method which has the narrow range is more appropriate to obtain highly selective excitation than the adiabatic passage. The mechanisms of population inversion and the decay effects between the methods are compared.

DOI
10.1088/0953-4075/30/24/027

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Highly selective excitations, which occur in a three-level system under the conditions of zero- and nonzero-delayed lasers, are examined. The detuning ranges which reach half inversion and their dependences on the laser conditions are obtained numerically using the Bloch equation. It is found that in the optimal detuning method which uses the zero-delayed lasers, the range is independent of the Rabi frequency and the detuning, but in the adiabatic passage which uses the nonzero-delayed lasers, the range is dependent on the Rabi frequency and the time delay. The inversion methods show strong dependences on the pulse length. It turns out that the optimal detuning method which has the narrow range is more appropriate to obtain highly selective excitation than the adiabatic passage. The mechanisms of population inversion and the decay effects between the methods are compared.
A precessing vector model has been developed for the geometrical interpretation of the adiabatic following and the optimal detuning methods, which play a decisive role in coherent population transfer in a three-level system. In our model, the Bloch vector defined by a population inversion and two-photon coherence components precesses about the torque vector consisting of an effective Rabi frequency and detuning components. The Bloch vector traces out different routes depending on combinations of the time delay of two laser pulses and detunings from the resonant frequencies. For the extreme cases where the optimal detuning with zero delay and the optimal delay with zero detunings are taken, our vector model with analytical solutions is compared with numerical solutions.
In a three-level atom interacting with nondelayed laser pulses, the inversion dynamics is studied to examine the detunings of the laser frequencies. When two Rabi frequencies are unequal, we show the interesting fact that complete inversion occurs if chirping is used, which causes the effective detuning of a two-photon resonance line to be zero. Because fixed optimal detunings allow an easier experimental approach, it is useful to find a method for obtaining the optimal detunings for realistic ratios of two Rabi frequencies. Using these optimal detunings, the process turns out to be a diadiabatic transition from investigation of the eigenvector and Bloch vector motions, whose behaviours are compared with their behaviour in the case of complete inversion.
The population inversion in a three-level atomic system, interacting with two coherent laser pulses, occurs from the first level to the third level at the optimal detunings of the laser frequencies near the two-photon resonance. An examination is performed to see whether the energy density and time-delay of the photoionizing laser can significantly influence the ion yield for the case where the atom interacts with two coherent pulses and one photoionizing pulse incoherently coupled. The well-known three-colour, three-step, three-photon ionization scheme, which is available for the selective photoionization of 168Yb, is chosen for use in this research with the Bloch equation. It is revealed that the proper time-delay and energy density enable us to achieve higher efficiency for the selective photoionization of 168Yb, regardless of the Doppler-broadening, though the efficiency and selectivity of coherent excitation are prominently enhanced by applying the optimal detunings.
Population transfer in three-level atomic systems with high efficiency and selectivity is desirable for practical applications in laser spectroscopy, trace analysis, and isotope separation. The effective excitation method for achieving this population transfer in three-level atomic systems using coherent two-photon excitation with two optimally detuned counterpropagating pulsed lasers, initially investigated analytically assuming monochromatic lasers and Doppler-free systems, is studied numerically by solving the density matrix equations incorporating finite laser linewidth and effective Doppler width. A three-level Yb system is chosen for illustration of numerical results. The effects of laser linewidth and effective Doppler width on the values of optimal detunings and maximum third-level population are discussed.
The method of multiple scales is used to derive a solution of the damped optical Bloch equations of a two-level atomic system due to a strong pulsed field. The time dependence of the oscillations of the atomic inversion influenced by detuning and power broadening is found. The population inversion consists, in general, of three terms: a quasisteady term, quasisteady term that decays with time, and an oscillatory term that also decays with time. In the limit of constant fields, the solution of Torrey for damped systems and that of Rabi for undamped systems are recovered. For an adiabatic switching of the field, the solution for undamped systems reduces to that of Crisp in the adiabatic following limit. An equation describing the field envelope is derived for an arbitrary amount of detuning. At exact resonance, this equation reduces to a pendulum equation, in agreement with previous analyses.
A numerical analysis is presented of several potential pulsed-laser applications of adiabatic population inversion in atoms or molecules. A simple numerical method is demonstrated for evaluating adiabatic processes in multilevel systems for both swept-frequency and resonant, time-delayed pulses. Adiabatic inversion with time-delayed pulses is generalized to systems with any number of levels. The effect of Doppler broadening on time-delayed adiabatic pumping of a three-level system is investigated.