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Physical Review A

Statistical broadening and population loss in strongly excited three-level systems

Jay R. Ackerhalt, Joseph H. Eberly, Bruce W. Shore

Published Jan 1, 1979• 41 citations
Publisher

Abstract

We study the effects of statistical broadening and population loss on the dynamics of strongly excited three-level quantum systems. The results of both analytic and numerical treatments of the three-level Schr\"odinger equation are displayed. In order to allow for statistical broadening, solutions are required for arbitrary detuning of the two very intense monochromatic lasers. The most efficient statistically averaged population depletion occurs when the Rabi frequency of the second transition is greater than that of the first.

DOI
10.1103/physreva.19.248

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We study the effects of statistical broadening and population loss on the dynamics of strongly excited three-level quantum systems. The results of both analytic and numerical treatments of the three-level Schr"odinger equation are displayed. In order to allow for statistical broadening, solutions are required for arbitrary detuning of the two very intense monochromatic lasers. The most efficient statistically averaged population depletion occurs when the Rabi frequency of the second transition is greater than that of the first.
By constructing a vector model we study the coherent dynamics of a special three-level quantum system--one with equal detunings and equal Rabi frequencies. This three-level problem can be fully related to a two-level problem. We find that complete population depletion can be achieved even in the case of constant nonzero detunings when the three-level system is prepared initially in the common level of the two transitions. Complete population depletion with constant detunings can also occur in other odd-number multilevel systems. An explanation in terms of an equivalent resonant excitation is presented.
The population dynamics of a strongly excited four-level quantum system with allowed loss out of the system from the highest state are analysed. This work has been stimulated by the paper of Cardimona et al. and represents a more general treatment of the problem studied by them. In particular, we show that the reduction in the ground-state population decay rate for large losses is not a consequence of the two-level behaviour but is a more general phenomenon. On the basis of numerical and analytical solutions we demonstrate that for an arbitrary excitation regime, at sufficiently large decay rate, the population loss dynamics of the four-level system is reduced to that of a slowly damped three-level system. We demonstrate also that the detailed knowledge of the coherent population dynamics enables us to predict the effect of decay rate on the population's time evolution for arbitrary choice of dynamic parameters.
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.
It is shown that any pulse with a time-asymmetric envelope and a constant non-zero detuning excites a two-level quantum system with a probability of nearly one-half provided the pulse is very asymmetric, adiabatic in the slowly rising part of its envelope, sudden in the steep part and the peak Rabi frequency is much greater than the detuning. Three particular cases are considered analytically: the asymmetric hyperbolic-secant, the Bambini-Berman and the exponential pulse, which illustrate the general conclusions. The results are applied to a special three-level 'vee' system whose two transitions are driven by two asymmetric laser pulses of the same Rabi frequencies and the same detunings. Analysis shows that if such a system is prepared initially in its ground state, effective population depletion of this state can be achieved, the results being quite insensitive to variations in the Rabi frequency and the detuning.
We study numerically the solution to Schr\"odinger's equation for the radiative interaction of fictitious NNN-level model atomic and molecular systems with monochromatic radiation fields. The numerical method of solution allows us to study multiphoton transitions in NNN-level systems unhampered by the assumptions usually adopted, such as weak fields or large detunings of intermediate states, in perturbative and quasiperturbative analytic studies. We point out regularities and near regularities in the population dynamics that appear to be qualitatively different from those encountered in two- and three-level systems.