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Chinese Physics

Variation of the absorption and dispersion profiles in a ladder-four-level system

Li Yongfang, Jianfeng Sun, Niu Yue-Ping

Published Jul 29, 2004• 0 citations
Publisher

Abstract

A theoretical research on the variation of the absorption and dispersion profiles and population distribution of each level in a ladder-four-level system driven by two coherent fields has been made. Whether the variation occurs or not depends on the effect of quantum interference, the detuning of the upper coherent field and the separation of the two intermediate levels. A dressed-state analysis is introduced to explain the numerical results.

DOI
10.1088/1009-1963/13/8/012

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A theoretical research on the variation of the absorption and dispersion profiles and population distribution of each level in a ladder-four-level system driven by two coherent fields has been made. Whether the variation occurs or not depends on the effect of quantum interference, the detuning of the upper coherent field and the separation of the two intermediate levels. A dressed-state analysis is introduced to explain the numerical results.
The absorption profile of a four-level ladder atomic system interacting with three driving fields is studied perturbatively and analytical results are presented. Numerical results where the driving field strengths are treated up to all orders are presented. The absorption features are studied in two regimes—(i) the weak middle transition coupling, i.e. Ω 2 ≪ Ω 1,3 and (ii) the strong middle transition coupling Ω 2 ≫ Ω 1,3 . In case (i), it is shown that the ground-state absorption and the saturation characteristics of the population of level |2⟩ reveal deviation due to the presence of upper level couplings. In particular, the saturation curve for the population of level |2⟩ shows a dip for Ω 1 = Ω 3 . While the populations of levels |3⟩ and |4⟩ show a maxima when this resonance condition is satisfied. Thus the resonance condition provides a criterion for maximally populating the upper levels. A second-order perturbation calculation reveals the nature of these minima (maxima). In the second case, I report two important features: (a) filtering of the Aulter–Townes doublet in the three-peak absorption profile of the ground state, which is achieved by detuning only the uppermost coupling field and (b) control of line-width by controlling the strength of the upper coupling fields. This filtering technique coupled with the control of linewidth could prove to be very useful for high resolution studies.
When a two-level system interacts resonantly with a saturating pump laser, the absorption profile of a probe wave in the Rabi sidebands resembles two separate dispersion profiles. At sufficiently high probe intensity this effect is accompanied by a dispersive profile in the pump-wave absorption, considered as a function of the probe-wave frequency, and also by a dip in the population of the upper state of the two-level system. The relative stabilization of the ground state is interpreted in terms of two-laser-photon processes where absorption of a pump (probe) photon is followed by stimulated emission of a probe (pump) photon. The dispersive absorption profile is attributed to the competition between three- and four-photon scattering processes.
An unconventional perturbation treatment of the theory of two-photon absorption in a four-level atomic system close to two-photon resonance is developed on the basis of the optical Bloch equations. The results for the longtime populations of the intermediate and upper states are valid in low- and medium-intensity regimes. In both regimes the upper state population shows a lorentzian resonance centred on zero two-photon detuning with a width equal to the natural linewidth of the upper state. The intermediate state population shows a similar behaviour in the intermediate regime only, with no significant dependence on two-photon detuning in the low-intensity regime. However, in both regimes the population of the virtual intermediate state is at least comparable to that of the resonant upper state. The perturbation theory results have been checked by direct numerical calculations based on the Bloch equations. Numerical calculations confirm the presence of a high-intensity regime characterized by power shifts, broadening and saturation effects.
We have studied the absorption spectrum of a Doppler-broadened ladder system,where the highest level is coupled into two middle hyperfine sublevels by a strong coherent field.We find that,when the system is considered as homogeneous,either two or three spectral components are observed,depending on the detuning of the coherent field.but when the velocity distribution of atoms is considered,we can always observe one electromagnetically induced transparency (EIT) window with high dispersion.So the atomic hyperfine structure cannot be an impediment for obtaining EIT.