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Chinese Physics

Effect of relaxation rate on population distribution, EIT and refraction in and V systems

Sun Qing-Qing, Ying Gu, Gong Qi-Huang

Published Sep 28, 2004• 3 citations
Publisher

Abstract

In the three-level Λ-type and V -type systems, we find that the same pump-effect parameter R = 2| V c | 2 γ/((ω ac −ω c ) 2 +γ 2 ) determines the population distributions, while the probe field leads to population fluctuations near the absorption peaks. With the increasing of the relaxation rate γ, the population distributions are shifted and their fluctuation amplitudes decrease. At the same time the electromagnetically induced transparency window becomes a broadened absorption peak and the dispersion at the zero probe detuning changes from positive to negative. Large population fluctuation and non-fluctuation observed in different systems are attributed to the different relaxation rates.

DOI
10.1088/1009-1963/13/10/024

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Chinese Journal of Lasers•Jan 1, 2004•0 citations
In the three-level Λ-type and V -type systems, we find that the same pump-effect parameter R = 2| V c | 2 γ/((ω ac −ω c ) 2 +γ 2 ) determines the population distributions, while the probe field leads to population fluctuations near the absorption peaks. With the increasing of the relaxation rate γ, the population distributions are shifted and their fluctuation amplitudes decrease. At the same time the electromagnetically induced transparency window becomes a broadened absorption peak and the dispersion at the zero probe detuning changes from positive to negative. Large population fluctuation and non-fluctuation observed in different systems are attributed to the different relaxation rates.
We have theoretically studied the atomic populations, electromagnetically induced transparency (EIT), and dispersion in a three-level Λ-type system. The density matrix equations are set up with regard for the relaxation of populations of the ground states, and the optical Bloch equations are solved analytically in the weak probe field approximation. Decoherence effects in the ground and excited states on the EIT line shape and dispersive signals are studied, and it is found that the EIT line width increases and the peak height decreases, as the decoherence rates increase in the ground and excited states. On the other hand, we have observed that the dispersive signals are steeper and of high contrast for the lower decoherence rates in the ground and excited states. We have also analyzed the variations of atomic populations of the energy levels at the pump Rabi frequency, as well as the decoherence rate in the ground state.
In this paper, we present the theoretical study of double electromagnetically induced transparency (EIT) in a four-level V-type system which is formed by two co-propagating laser fields and the Zeeman sublevels of hyperfine transitions of 87Rb D2 line. The density matrix equations for the four-level V-type system are derived from the Liouville’s equation of motion and numerically solved under steady state condition to get the EIT signals. We consider both the probe and pump transmission spectra for the observation of double EIT signals under both Doppler free and Doppler broadened conditions. In case of Doppler free medium, two EIT peaks are formed in the two Lorentzian shape dips present in the both Doppler free probe and pump transmission spectra. When the medium becomes Doppler broadened, the two EIT peaks are formed in the probe transmission spectrum having Doppler broadened background, but the pump transmission spectrum gives two EIT peaks in the Doppler free background. The effect of probe intensity variation on the two EIT peaks is studied in case of Doppler broadened probe transmission spectrum. It is found that the heights of the EIT peaks decrease as the probe intensity increases, and interestingly one EIT peak converts into EIA (electromagnetically induced absorption) dip at some strong probe intensity value. The depth of the EIA dip is significantly increased as the intensity of the probe field increases. We also present the effect of probe intensity variation on the EIT peaks in the pump transmission spectrum and found that the EIT peak heights are increased as the probe intensity increases.
The absorption and dispersion properties of an N-type four-level system with Doppler(broadening) effect were investigated.In this system we considered two coherent fields and a probe field.When the second coherent field is absent,this system is a single three-level configuration,and the absorption line is just one clear electromagnetically induced transparency(EIT) window.While the second coherent field exists,there are two EIT windows which become wide and deep with the(coherent) intensity increasing.The position width and absorbance of the transparency windows can be manipulated by adjusting the detuning of the driving field.In addition,we also found that the medium shows a large refractive index at each transparency window,and the group velocity of the probe laser can be reduced.
Abstract We have theoretically studied the multi-window electromagnetically induced transparency (EIT) and the related dispersive signals in multi-level V-type systems which are formed by the co-propagating circularly polarized pump ( σ − ) and probe ( σ + ) laser fields in the Zeeman sublevels of hyperfine states of 87 Rb-D 2 line. The optical Bloch equations (OBEs) are derived and numerically solved under the steady-state condition to obtain the probe absorption and dispersion spectra. We present the study of a single-window EIT for the three-level, double-window EIT for the four-level and triple-window EIT for the five-level V-type systems under both Doppler-free and Doppler-broadened conditions. The dispersive signals corresponding to the multi EIT windows for each system are also observed separately. From the knowledge of the slopes of the probe dispersion signals, we have calculated group index ( n g ) of the medium considering three different V-type schemes. The effect of temperature on the EIT, dispersion and group index profiles is also studied in detail. It is found that the amplitudes of EIT and dispersion signals and also the positive and negative values of n g are decreased as the temperature of the medium increases. To understand the Doppler-broadening effect on the group index profiles, we have considered three different velocity groups of atoms in the calculation of group index profiles. Moreover, the effects of probe intensity variation on the Doppler-broadened EIT and dispersive signals are studied extensively, and the conversions of EIT to EIA and dispersive positive slope to negative slope are observed under strong probe regime. Also, we have investigated the variation of dispersive slope and group index with the variation of probe intensity and probe frequency, respectively, at the multi-frequency position of the multi-window EIT. Finally, the switching between subluminal (slow light) to superluminal (fast light) propagation of light with the variation of both probe intensity and probe frequency is discussed in detail.
Variations of the coherent resonance, i.e. an electromagnetically induced transparency (EIT) peak with the cell temperature in Λ- and V-type systems are observed for the 85 Rb-D 2 transition. In a Λ-type system, the amplitude of the EIT peak gradually decreases and it is finally masked by the broadened optical pumping dips with the increase of the cell temperature. But for the V-type system, the EIT and the saturation peaks are greatly enhanced with the increase of the cell temperature. The effect of the external magnetic field on the EIT resonance is also investigated considering both types of systems. For the Λ-type system in place of a single EIT resonance, five transparency windows with broadened width and reduced contrast are obtained depending on the Zeeman levels formed by the applied magnetic field. In the V-type system, the coherent resonance peak could not be resolved in the presence of the external magnetic field, but a greater number of saturation peaks with broadened width appear in the probe transmission spectrum. A theoretical model is adopted to represent the experimental results. Good agreement is found between the experimental and numerically simulated results.
The transient properties of electromagnetically induced transparency (EIT) with different pump laser energies in a Λ-type three-level system are studied by solving the time-dependent matrix equation. The time evolution of the probe laser absorption, the population of the three levels and the coherent term ρ 23 are analyzed. It is shown that transient amplification without inversion can be realized with high pump laser energy and that transient EIT would reduce and transient amplification without inversion would disappear with the decrease of the pump laser energy. Since the probe absorption depends on the product of Rabi frequency of the pump laser and the coherent term ρ 23, the nonzero damping coherent term ρ 23 results in the transient absorption and amplification without inversion at high pump laser energy, and the decrease of the coherence with the decrease of the pump laser energy leads to the disappearance of the amplification and enhancement of absorption.