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Journal of Physics B Atomic Molecular and Optical Physics

Laser frequency detunings for complete inversion and optimal inversion of a three-level atom by arbitrary Rabi frequencies

A. S. Choe, J Lee, Han Seb Moon, H A Kim, J. B. Kim

Published Oct 28, 1999• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0953-4075/32/21/308

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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.
For the purpose of an examination of coherence control, we study the dynamics of population inversion in the four-level λ system where initial populations are arbitrary coherently distributed in two lower levels. It is shown that the coherence control, which causes population transfer between the lower levels to be forbidden, is possible by using the ratio of Rabi frequencies. Under this condition, it is remarkable that the adiabatic following and the optimal detuning methods are useful to invert the four-level system completely, and it is shown that the two-photon coherences of the coupled three-level ladders are dispersive and absorptive in the former and the latter methods, respectively. From the geometrical interpretation, the Bloch vectors, describing the four-level inversions, could be defined as ones in a two-level system.
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.
In this research study, we derive the exact solutions of the Bloch equations describing the dynamics of a two-level atom with dephasing. In the two-level atom, a strong laser pump couples a ground state to an upper excited state with a time-dependent Rabi-frequency. The exact solutions are given for the atomic population inversion and the real and imaginary parts of the coherence while the input pulse is an asymmetric hyperbolic cosine form. Additionally, the system is under a chirped detuning. The method of solving the Bloch equations analytically is a very tedious part of the research, and as far as we know, there are few exact solutions available in this field. Hence, our solutions might be of great interest to various research areas, including nuclear magnetic resonance, where analytical solutions to the Bloch equations play a major role in the study of the information on the state of the medium as determined by the NMR signals.
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.
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.
We have performed a numerical calculation for the excitation spectra arising from the interaction of a three-level atom in the lambda configuration with a strong electromagnetic field whose frequency mode is initially populated. The excitation spectra are considered for equal detunings, which refer to the cooperative two-photon resonance process, as well as for different detunings. The computed cooperative two-photon resonance spectra are compared with those derived by analytical methods. In the presence of different detunings, conditions are established under which the laser field induces sidebands at the frequency equal to that for the forbidden transition. Numerical calculations for a wide range of Rabi frequencies and detunings are presented graphically. Detailed discussion of the computed spectral intensities is given and a comparison is made between the spectra of three-level atoms in the lambda and cascade configurations.