It is shown that in a Doppler broadened open N-type four-level atomic system with spontaneously generated coherence (SGC), the gain without inversion (GWI) is very sensitive to the variation of the relative phase between the probe field and the driving field; the atomic exit rate ( R 0 ) and the ratio ( S ) of the atomic injection rates have a considerable modulation effect on the phase-dependent GWI. GWI first increases and then decreases with Ro increasing; in a certain value range of S , GWI increases monotonically with S increasing; by adjusting the values of R 0 and S , in an open system a much larger GWI can be obtained than in the corresponding closed system [ 2011 Phys. Rev. A 83 043805 ]. The modulation effects of R 0 and S on the phase-dependent GWI in the case with the counter-propagating probe and driving fields are stronger than those in the co-propagating case, GWI in the co-propagating case is much larger than that in the counter-propagating case.
It is shown that in a Doppler broadened open N-type four-level atomic system with spontaneously generated coherence (SGC), the gain without inversion (GWI) is very sensitive to the variation of the relative phase between the probe field and the driving field; the atomic exit rate ( R 0 ) and the ratio ( S ) of the atomic injection rates have a considerable modulation effect on the phase-dependent GWI. GWI first increases and then decreases with Ro increasing; in a certain value range of S , GWI increases monotonically with S increasing; by adjusting the values of R 0 and S , in an open system a much larger GWI can be obtained than in the corresponding closed system [ 2011 Phys. Rev. A 83 043805 ]. The modulation effects of R 0 and S on the phase-dependent GWI in the case with the counter-propagating probe and driving fields are stronger than those in the co-propagating case, GWI in the co-propagating case is much larger than that in the counter-propagating case.
It is shown that in a Doppler broadened open N-type four-level atomic system with spontaneously generated coherence (SGC), the gain without inversion (GWI) is very sensitive to the variation of the relative phase between the probe field and the driving field; the atomic exit rate (R0) and the ratio (S) of the atomic injection rates have a considerable modulation effect on the phase-dependent GWI. GWI first increases and then decreases with R0 increasing; in a certain value range of S, GWI increases monotonically with S increasing; by adjusting the values of R0 and S, in an open system a much larger GWI can be obtained than in the corresponding closed system [2011 Phys. Rev. A 83 043805]. The modulation effects of R0 and S on the phase-dependent GWI in the case with the counter-propagating probe and driving fields are stronger than those in the co-propagating case, GWI in the co-propagating case is much larger than that in the counter-propagating case.
In this paper we study the influence of spontaneously generated coherence (SGC) on propagation effect and the modulation role of the atomic exit rate(r0)and ratio(S) of the atomic injection rates on the SGC-dependent propagation effect in an open V-type three-level lasing without inversion(LWI) system with Doppler broadening,by using the calculation results of the density matrix motion equations and the propagation equations of the driving and probe fields,in order to get larger LWI gain and intensity of the probe field.It is shown that with propagation distance increasing,LWI gain and Rabi frequency(intensity) of the probe field first increase and then decrease,while the Rabi frequency(intensity) of the driving field decreases monotonously;LWI gain and Rabi frequency(intensity) of the probe field increase with SGC strength(measured by θ) increasing.When θ=π,we can obtain the largest LWI gain and Rabi frequency(intensity) of the probe field;in the case with SGC,we can get much larger LWI gain and Rabi frequency(intensity) of the probe field than those in the case without SGC.In certain value ranges of r0 and S,LWI gain and Rabi frequency(intensity) of the probe field increase with r0 and S increasing.By choosing proper values of γ0 and S,in the open system we can obtain much higher LWI gain and Rabi frequency(intensity) of the probe field than those in the corresponding closed system.
The effect of the relative phase (φ) between the probe and driving fields on the gain without inversion (GWI) is studied in a Doppler broadened quasi Λ-type four-level atomic system with vacuum induced coherence (VIC). It is shown that: The probe detuning region in which GWI exists and size of GWI are very sensitive to variation of the relative phase, the Doppler width ( D ) also has dramatically modulation role on the phase-dependent GWI. The GWI maximum value ( Gmax ) varies periodically with the relative phase varying, the period is 2π; but the concrete varying rule is closely related to the value of the Doppler width. In the case of D = 0 (i.e. without Doppler broadening) , when 0 < φ < π, Gmax increases monotonously with φ increasing; when π <φ < 2π, Gmax decreases monotonously with φ increasing; when φ =π, Gmaxhas the largest value. Under the condition of D ≠ 0 (i.e. Doppler broadening presents), in both regions 0 < φ < π and π < φ < 2π, Gmax does not monotonically increase or decrease with φ increasing; the value of φ, which corresponds to the largest value of Gmax, decreases gradually from π with D increasing, when value of D is large enough, the value of φ, which corresponds to the largest value of Gmax, is about π/2. In general speaking, Gmax decreases with D increasing; but Gmax larger than that in the corresponding static atomic system ( D = 0 ) can be gotten by choosing suitable values of φ and D.
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.
We studied the controlling role played by the relative phase between the probe and driving fields on inversionless gain of the probe field in a closed and Doppler broadened Λ-type three-level system with spontaneously generated coherence (SGC). It was found that：(1) Regardless of the driving field being in or off resonance, and regardless of the probe and driving fields being co- or counter- propagating, the gain maximum value always varies periodically with variation of the relative phase with the period 2π. (2) When the driving field is in resonance, the gain maximum value decreases monotonicly with Doppler width increasing, and moreover, the decreasing in the counter-propagation case is faster than that in the co-propagation case. When the driving field is off resonance, the gain maximum value does not monotonicly decrease or increase with Doppler width increasing. In both above cases, the largest inversionless gain can be gotten by adjusting the relative phase. (3) The contribution of SGC to the inversionless gain is much larger than that of the dynamically induced coherence.
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.