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Chinese Physics B

Effects of relative phase on transient evolution in an open resonant ladder-type atomic system

Yanling Yang, Liu Zhong-Bo, Lei Wang, Tong Dian-Min, Fan Xi-jun

Published Mar 1, 2009• 6 citations
Publisher

Abstract

In an open ladder-type resonant atomic system, variation in relative phase between probe and driving fields does not affect the transient evolution of populations, but it has remarkable effects on gain and dispersion of the probe field. No matter whether an incoherent pump is present or absent, transient and stationary gains without inversion (GWI) always can be obtained by choosing an appropriate value of the relative phase. When the incoherent pump is absent, the values of transient and stationary GWIs are much larger and the time interval required to reach the stationary value is longer than those when the incoherent pump is present. Varying the exit rate and the ratio between injection rates can obviously change the phase-dependent GWI. In addition, in the transient evolution process, the phenomenon of high dispersion (refractive index) without absorption occurs at some values of relative phase. In the corresponding closed system, the stationary GWI can be obtained by choosing an appropriate value of relative phase only when incoherent pump exists, moreover the gain is smaller than that in the open system.

DOI
10.1088/1674-1056/18/3/036

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Chinese Physics B•Jan 1, 2012•0 citations
In an open ladder-type resonant atomic system, variation in relative phase between probe and driving fields does not affect the transient evolution of populations, but it has remarkable effects on gain and dispersion of the probe field. No matter whether an incoherent pump is present or absent, transient and stationary gains without inversion (GWI) always can be obtained by choosing an appropriate value of the relative phase. When the incoherent pump is absent, the values of transient and stationary GWIs are much larger and the time interval required to reach the stationary value is longer than those when the incoherent pump is present. Varying the exit rate and the ratio between injection rates can obviously change the phase-dependent GWI. In addition, in the transient evolution process, the phenomenon of high dispersion (refractive index) without absorption occurs at some values of relative phase. In the corresponding closed system, the stationary GWI can be obtained by choosing an appropriate value of relative phase only when incoherent pump exists, moreover the gain is smaller than that in the open system.
The control role of the relative phase between the probe and driving fields on gain, dispersion and populations in an open V-type three-level system with spontaneously generated coherence is studied. The result shows that by adjusting the value of the relative phase, the transformation between lasing with inversion and lasing without inversion (LWI) can be realized and high dispersion (refractive index) without absorption can be obtained. The shape and value range of the dispersion curve are similar to those of the gain curve, and this similarity is closely related to the relative phase. The effects of the atomic exit and injection rates and the incoherent pump rate on the control role of the relative phase are also analysed. It is found easier to get LWI by adjusting the value of the relative phase using the open system rather than the closed system, and using an incoherent pump rather than without using the incoherent pump. Moreover the open system can give a larger LWI gain than the closed system.
We find that in the open and closed ladder systems with vacuum induced coherence, the relative phase between the probe and driving fields has an important manipulation role on the absorption property, while the incoherent pumping has a considerable effect on the phase-dependent absorption property.In the both systems, by adjusting the incoherent pumping the switching from absorption to gain and from lasing with inversion to lasing without inversion (LWI) can be realized and the largest LWI gain can be gotten.However, when the incoherent pumping is absent, for any value of the relative phase, LWI still can't be obtained in the closed system but can in the open system; moreover, in the open system, for suitable values of the relative phase, LWI gain gotten when the incoherent pumping is absent is obviously larger than that obtained when the incoherent pumping presents.
In the open and closed ladder systems with vacuum induced coherence,it is found that the relative phase between the probe and driving fields has an important manipulation role on the absorption property,while the incoherent pumping has a considerable effect on the phase-dependent absorption property.In both systems,by adjusting the incoherent pumping the switching from absorption to gain and from lasing with inversion to lasing without inversion can be realized and the largest inversionless gain can be gotten.However,when the incoherent pumping is absent,for any value of the relative phase,lasing without inversion still can not be obtained in the closed system but it is able in the open system;and in the open system,for suitable values of the relative phase,inversionless gain gotten when the incoherent pumping is absent is obviously larger than that obtained when the incoherent pumping presents.
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.
The effect of spontaneously generated coherence (SGC) on transient evolution of gain of lasing without inversion (LWI) and modulation roles of the injection rate ratio and exit rate on SGC-dependent gain in an open Ladder type three level system are studied by using the numerical solution of the density matrix motion equation of the system. It was shown that: variation of SGC strength will make the transient and final stationary gains having a considerable changing; when incoherent pumping presents, LWI gain increases with the ratio of injection rates and exit rate decreasing, however, when incoherent pumping is absent, the case is just the opposite; by choosing suitable values of SGC strength, the injection rate ratio and exit rate, we can obtain the largest transient and final stationary gain.
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.