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Journal of Modern Optics

Positive and negative dispersion in a three-level Λ system driven by a single pump

A. D. Wilson‐Gordon, Harry Friedmann

Published Jan 1, 2002• 35 citations
Publisher

Abstract

We extend our previous study of a nearly degenerate Λ three-level system that exhibits population trapping when driven by a single pump and produces an absorption or gain doublet in the probe absorption spectrum. In particular, we show that the probe dispersion is positive or negative between the doublet lines, and can survive Doppler broadening. For certain values of the pump Rabi frequency, the sign of the dispersion can be changed by altering the ratio of the splitting between the lower levels to the Doppler width.

DOI
10.1080/09500340110074727

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We calculate the absorption spectrum of a weak probe interacting with a \ensuremath{\Lambda}-shaped three-level system driven by a single pump. We find that there are four types of terms that contribute to the probe absorption: population-difference and two-photon coherence terms which derive solely from interaction with the pump (dc terms) and population-difference and two-photon coherence terms that pulsate at the pump-probe frequency offset. We find that the main features of the probe spectrum derive from the pulsating terms whereas the dc terms either interfere destructively with each other or with the pulsating terms. This is a clear extension to the three-level system of the concept of light amplification by coherence. We calculate the spectrum for three cases: (i) a degenerate population-trapped system, (ii) a degenerate system in which both transitions are population inverted, and (iii) a nondegenerate population-trapped system. The results of case (i) are similar to those for the two-level system but the population-trapped system has the advantage of avoiding pump absorption. We show that the Rabi frequency of the nonabsorbed pump can be found by determining the probe frequencies at which probe nonabsorption occurs. In (ii), the results are compared with the case where two pumps interact resonantly with a nondegenerate system. In (iii), we find that the populations in the lower states behave dispersively as a function of the pump detuning. For Rabi frequencies that are small compared to the separation between the lower levels, the lower level nearer to resonance is less populated than the other level. However, at higher Rabi frequencies, the situation is reversed. The probe spectrum contains two absorption peaks when the pump Rabi frequency is small and two emission peaks when it is large.

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Chinese Physics•Apr 1, 2001•7 citations
We extend our previous study of a nearly degenerate Λ three-level system that exhibits population trapping when driven by a single pump and produces an absorption or gain doublet in the probe absorption spectrum. In particular, we show that the probe dispersion is positive or negative between the doublet lines, and can survive Doppler broadening. For certain values of the pump Rabi frequency, the sign of the dispersion can be changed by altering the ratio of the splitting between the lower levels to the Doppler width.
We calculate the absorption spectrum of a weak probe interacting with a \ensuremath{\Lambda}-shaped three-level system driven by a single pump. We find that there are four types of terms that contribute to the probe absorption: population-difference and two-photon coherence terms which derive solely from interaction with the pump (dc terms) and population-difference and two-photon coherence terms that pulsate at the pump-probe frequency offset. We find that the main features of the probe spectrum derive from the pulsating terms whereas the dc terms either interfere destructively with each other or with the pulsating terms. This is a clear extension to the three-level system of the concept of light amplification by coherence. We calculate the spectrum for three cases: (i) a degenerate population-trapped system, (ii) a degenerate system in which both transitions are population inverted, and (iii) a nondegenerate population-trapped system. The results of case (i) are similar to those for the two-level system but the population-trapped system has the advantage of avoiding pump absorption. We show that the Rabi frequency of the nonabsorbed pump can be found by determining the probe frequencies at which probe nonabsorption occurs. In (ii), the results are compared with the case where two pumps interact resonantly with a nondegenerate system. In (iii), we find that the populations in the lower states behave dispersively as a function of the pump detuning. For Rabi frequencies that are small compared to the separation between the lower levels, the lower level nearer to resonance is less populated than the other level. However, at higher Rabi frequencies, the situation is reversed. The probe spectrum contains two absorption peaks when the pump Rabi frequency is small and two emission peaks when it is large.
We study the absorption and dispersion in the near-degenerate closed three-level V system, in which a single coherent driving field is tuned resonant with the average frequency of two dipole-allowed transitions. Firstly, the switching from positive to negative dispersion can be achieved simply by increasing the driving field intensity. This is the same as in the driven Λ system. Secondly, the common feature originates from the fact that both V and Λ systems have the same transitions in terms of atomic dressed states under given conditions. These dressed transitions interfere destructively in the central spectrum while the sideband resonance transitions determine the possible appearance of two pairs of absorption doublet lines and two pairs of gain doublet lines in the sideband spectrum. Thirdly, there are two minor differences between these two systems. For large driving field intensity, a narrow steep structure is always present in the central negative dispersion spectrum in the V system but it disappears in the Λ system. The driving field intensity for the appearance of the outer sideband absorption or gain peaks is larger in the V system than in the Λ system.
We investigate the dispersion and absorption in the coherently prepared two-level degenerate systems. Driven by a parallel polarized light and probed by a transverse polarized light, in the degeneracy case, only the positive dispersion is obtained at the zero pump-probe detuning, as well as electromagnetic induced transparency. When magnetic field breaks the degeneracy, we find that the dispersion is shifted from positive, via negative, to positive when varying the drive Rabi frequency, which means a transition between the superluminal and subluminel group velocity. Simultaneously, in these systems, the electromagnetic induced transparency, electromagnetic induced absorption and Mollow absorption spectrum are shown in the absorption spectra.
We investigate realistic atomic systems whose dispersion at line center switches from positive to negative and vice versa, as a particular experimental parameter is changed. We concentrate on those systems which have low probe absorption or gain at line center leading to a high figure of merit, and simultaneously have low pump absorption. For this purpose, we study both open and artificially closed ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=1$ and ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=2$ transitions in 87Rb,{}^{87}\mathrm{Rb},87Rb, in the absence and presence of an applied magnetic field. We find that the preferred system for observing switchover in the sign of the dispersion from positive to negative, as the pump Rabi frequency increases, is the open near-degenerate ${F}_{g}=\stackrel{\ensuremath{\rightarrow}}{1}{F}_{e}=1$ system. In the presence of Doppler broadening, the dispersion is positive for all realistic experimental parameters. Thus the switchover in the sign of the dispersion is only observable in the absence of Doppler broadening.
The coherent coupling of atomic levels under the action of driving electromagnetic fields is known to create unusual and interesting effects, such as the well-known population trapping phenomenon and subnatural line narrowing. In this paper we discuss two alternative configurations of three-level atoms, the cascade model and the inverted-V (lambda) model, in an effort to provide alternative options for experimental tests. In both cases we focus on the fluorescent emission spectrum of atom driven by two resonant fields and on the absorption spectrum of a weak probe passing through a gas in such a driven system. Subnatural line narrowing can be obtained from the cascade system but not from the lambda system. The lambda system, however, is characterized by strong population trapping so that it is not suitable for fluorescence studies (except out of resonance) because of its strongly reduced emission rate. The absorption spectrum of a weak probe displays gain features under high field conditions which suggest that useful amplification of a probe or laser-like emission should be possible over appropriate frequency ranges. We give a physical interpretation of the origin of the gain and explain why that in the case of a lambda system, but not a cascade system, steady-state population inversion can be obtained between both excited states relative to the lowest state of the atom. We also discuss the effect of Doppler broadening on the predicted emission and absorption lineshapes.
This paper deals with the absorption spectra of a weak probe in a four-level Doppler-broadened system driven by three coherent fields. The main aim is to extend earlier studies of the spontaneous emission spectrum and to present a comprehensive survey of the spectral features of this system. In addition to a derivation of exact formulae for the spectra, we give an explanation with the help of an appropriate set of dressed atomic states. We also get a deeper insight into the physical origin of gain in view of the existence of a population inversion between the levels of the lasing transition. Finally, we explore the effect of Doppler broadening on the absorption profile of the weak probe.