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Acta Physica Sinica

The frequency modulation effects of the probe field in three level Λ-system

Han Ding-An, Hong Guo, Hui Sun, Bai Yanfeng, 华南师范大学传输光学实验室,广州 510631

Published Jan 1, 2004• 0 citations
Publisher

Abstract

In this paper, the frequency modulation effect of the probe field in a three-level Λ system is discussed. According to the classical equation of motion for the electron, the dielectric susceptibility of the medium is not affected by frequency modulation. Based on the quantum theory and the frequency modulation term expanded in terms of Bessel functions, the effects of the frequency modulation of the probe field on the system are studied, in which, when the modulation frequency of the probe field is large enough, the periodical population evolutions exist in three levels. Meanwhile, the stationary susceptibility of the probe field is given.

DOI
10.7498/aps.53.1793

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Physical Review A•Dec 1, 1993•41 citations
In this paper, the frequency modulation effect of the probe field in a three-level Λ system is discussed. According to the classical equation of motion for the electron, the dielectric susceptibility of the medium is not affected by frequency modulation. Based on the quantum theory and the frequency modulation term expanded in terms of Bessel functions, the effects of the frequency modulation of the probe field on the system are studied, in which, when the modulation frequency of the probe field is large enough, the periodical population evolutions exist in three levels. Meanwhile, the stationary susceptibility of the probe field is given.
We study the interaction of the medium composed of three-level atoms in A configuration interacting with two laser fields: weak probe field and strong control field. The probe field enters the medium under a certain angle, and it is initially in the form of the spatial soliton, while the control field is periodically modulated. The system of optical Bloch equations is analytically solved in the stationary regime by the perturbation method in order to obtain linear and third-order nonlinear susceptibility of the medium with respect to the probe field. After a straightforward algebraic procedure, using the approximation of the slow-varying field envelope, the nonlinear Schrödinger equation for the probe field is obtained. It is numerically solved by applying the spectral Fourier split-step method. It is found that, for properly chosen values of the probe and control field detunings and control Rabi frequency, the probe field behaves as a solitary wave whose direction does not depend on the incident angle. Moreover, the regime consisting of Bloch-like oscillations can be identified. The simulation is performed by choosing the corresponding levels of Mg atoms.
The theoretical results on the study of the evolution of electromagnetically induced transparency probe pulses with frequency modulation on the input surface of the active medium and possible frequency modulation of the control field are presented. It was shown that the presence of a sufficiently large frequency modulation of the input probe pulse (an instantaneous frequency offset of the order of an inhomogeneous line width resonant with the probe field) does not lead to the mode structure destruction of this field inside the active medium. At the same time, the transparency of the medium for the probe field is noticeably reduced, but it remains quite large. With frequency modulation of the control radiation, the mode regime of the probe field propagation is realized at least as long as the deviation of the frequency of the control field is less than half the width of the line of the probe quantum transition. However, the transparency of the medium for the probe field decreases in comparison with the case of the absence of frequency modulation. The analysis is carried out for the Ʌ-scheme of inhomogeneously broadened quantum transitions between the 3P0, 3P01 and 3P2 levels of the 208Pb isotope.
We investigate the quantum interference effects in a cyclic three-level system with a microwave field driving transition between two low levels. By solving the relative density matrix equations of motion, we obtain the absorption profile of the probe field and identify the conditions under which gain may develop. We demonstrate numerically that the absorption line shape depends on the ratio of the intensities of coupling and driving microwave field. When the intensity of coupling field is much weaker than that of driving field, there is a multi-EITs in the probe absorption spectrum. However, if the intensity of both fields is strong, amplification without inversion occurs in different regime of probe frequency. In addition, we predict that larger amplification is obtained when the coupling field is detuned from exact resonance.
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.