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Journal of Foshan University

Effects of spontaneously induced coherence on laser without population inversion in a four-level Λ-type system

Weicheng Chen

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The coherence of a four-level Λ-type system with spontaneously generated coherence(SGC) is studied.With a weak probe and a strong coupling fields,whether the atomic system is on two-photon resonance or not,there is light without population inversion(LWI) on the probe field.On two-photon resonance,LWI is strengthened by SGC.On non-two-photon resonance,LWI can be controlled simply by adjusting the parameter of SGC and the two-upper-level separation.Meanwhile,the analytical solutions to the SGC parameter where LWI occurs are given in both cases.

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Journal of Physics B Atomic Molecular and Optical Physics•Oct 20, 2006•15 citations
The coherence of a four-level Λ-type system with spontaneously generated coherence(SGC) is studied.With a weak probe and a strong coupling fields,whether the atomic system is on two-photon resonance or not,there is light without population inversion(LWI) on the probe field.On two-photon resonance,LWI is strengthened by SGC.On non-two-photon resonance,LWI can be controlled simply by adjusting the parameter of SGC and the two-upper-level separation.Meanwhile,the analytical solutions to the SGC parameter where LWI occurs are given in both cases.
We provide a four-level double-V type atomic system driven by two week probe fields and two strong coupling laser beams. In the condition of resonant four-wave mixing, the two probe fields can be amplified without population inversion. Due to the fact that the two excited states are close- lying upper levels of hyperfine structure, the spontaneously generated coherence (SGC) effect must be considered. Interestingly, the amplitude of gain is sufficiently enhanced with the same parameters as those in the case without considering SGC. In addition, we find that the probe gain is sensitive to the phase of two laser fields which interact with the same lower level. To be more specific, the amplitude of gain is modulated by the phase periodically but restricted by θ (the angle between two induced dipole moments). At the same time, we also analyze the influence of the coherence pumping (strong coupling fields) detuning.
We put forward a model of an open quasi Λ-type four-level atomic system,and then investigate the effect of spontaneously generated coherence(SGC) on the gain of lasing without inversion from different respects by using the numerical calculation results of the system in the steady state.The study results show that,the switching from absorption to lasing without inversion(LWI) and the enhancement of the LWI gain can be realized by adjusting the strength of SGC;the variety of the two factors p1 to p2 which represent the SGC effect will produce remarkable different influence on the LWI gain.We also find that,the LWI gain is much larger in open system than that in the corresponding closed system;moreover,when the incoherent pump field is absent,the LWI gain can be obtained in the open system but cant in the closed system.
We have studied the effect of the spontaneously generated coherence (SGC) on gain of lasing without inversion (LWI) in a closed three-level Λ-type atomic system with Doppler broadening. It is shown that, regardless of the driving and probe fields being co- or counter-propagating, at a suitable value of the Doppler width, we can obtain a much larger LWI gain with SGC than that without SGC; and the region of the LWI gain spectrum with SGC is obviously larger than that without SGC. When the Doppler width takes a constant value, the gain does not monotonically decrease or increase with increasing strength of SGC, the largest LWI gain can be obtained by adjusting strength of SGC. Generally speaking, the co-propagating probe and driving fields is favourable to obtain a larger LWI gain.
In this paper, we investigate the effects of spontaneously generated coherence (SGC) on the conditions for exhibiting lasing without inversion (LWI) in the presence of a weak probe and a strong-coupling field. We find that owing to the effect of SGC, LWI can be realized without the incoherent pumping or the decay between two upper levels. However, in the region where LWI can be exhibited, the effect of SGC term on the exhibition of LWI is not always positive, sometimes it can even cumber the realization of LWI for some values of SGC. These values are given in this paper. In addition, we also analyze the essence of the generation of the probe field.
The effect of spontaneously generated coherence on the gain of lasing without inversion(LWI) is studied in an open quasi-Λ type four-level atomic system with Doppler broadening from different respects.The results show that,for a fixed SGC strength,LWI gain decreases with increasing the value of the Doppler width;no matter the Doppler broadening is obvious or not,the LWI gain larger than that without SGC always can be gotten by choosing suitable value of the SGC strength,and this difference becomes more evident with the Doppler width decreasing;the atomic exit and injection rates also can dramatically affect LWI gain;a much larger LWI gain in open system than that in the corresponding closed system can be obained.
In a three-level closed Λ system with incoherent pumping, both the dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) play a significant role in inducing different nonlinear processes like amplification without population inversion (AWI), electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). These two coherences can interfere destructively and constructively giving rise to different nonlinear processes (EIT, EIA, AWI) when the strength of these two coherences is comparable. Therefore the system can switch over from one nonlinear process to the other and the desired response of the system can be achieved by controlling the system parameters. It has been shown that this switching can occur by changing the relative strength of Rabi frequencies for the coherent and probe fields and the mode of incoherent pumping (unidirectional and bidirectional) for a chosen SGC parameter. Further control over the response can be achieved by changing the phase between two radiation fields. But the dependence on phase is different when both the coherences contribute than that obtained only from SGC. Exact analytical expressions for the coherences and populations in the steady state limit have been derived (keeping all orders of system parameters) to generalize the analysis and any restrictions over the system parameters (e.g. spontaneous decay widths on probe and coherent transitions are equal) have been avoided to make it applicable to various atomic and molecular systems. However the approximate expressions can be derived from these exact values. Numerical values obtained by solving the density matrix equations agreed well with these exact analytical values.