Using the numerical result, the influence of the Doppler broadening on the vacuum induced coherence (VIC) related probe field absorption is discussed. It is shown that if there exists no Doppler broadening, only when VIC is absent can the electromagnetically induced transparency (EIT) phenomenon occur; VIC leads the probe field absorption to vary obviously and the gain to appear; in both cases with and without VIC, the absorption curve has a double-peak structure which is symmetrical about the probe detuning. If there exists the Doppler broadening, in both cases with and without VIC, EIT phenomenon can always occur; VIC still leads the probe field absorption to vary obviously and the gain to appear; no matter whether the VIC is present. The probe field absorption has the following characteristics: the absorption curve no longer has symmetry about the probe field detuning and changes gradually from the double-peak structure to the single-peak structure with Doppler broadening width (D) increasing; the probe field absorption does not monotonically increase or decrease with D increasing; the probe field absorption, when the probe and driving fields propagate along the opposite directions, is smaller than that when the probe and driving fields propagate along the same directions.
Using the numerical result, the influence of the Doppler broadening on the vacuum induced coherence (VIC) related probe field absorption is discussed. It is shown that if there exists no Doppler broadening, only when VIC is absent can the electromagnetically induced transparency (EIT) phenomenon occur; VIC leads the probe field absorption to vary obviously and the gain to appear; in both cases with and without VIC, the absorption curve has a double-peak structure which is symmetrical about the probe detuning. If there exists the Doppler broadening, in both cases with and without VIC, EIT phenomenon can always occur; VIC still leads the probe field absorption to vary obviously and the gain to appear; no matter whether the VIC is present. The probe field absorption has the following characteristics: the absorption curve no longer has symmetry about the probe field detuning and changes gradually from the double-peak structure to the single-peak structure with Doppler broadening width (D) increasing; the probe field absorption does not monotonically increase or decrease with D increasing; the probe field absorption, when the probe and driving fields propagate along the opposite directions, is smaller than that when the probe and driving fields propagate along the same directions.
Using the numerical result, the influence of the Doppler broadening on the two-photon absorption related to vacuum induced coherence is discussed. In the absence of Doppler broadening, when VIC is absent, the absorption curve has a double-peak structure and the electromagnetically induced transparency phenomenon can occur; when VIC is present, the absorption curve has a single-peak structure and EIT phenomenon does not appear. In the presence of Doppler broadening, regardless of VIC being present or not, EIT phenomenon always can occur; when VIC is absent, no matter whether the propagation directions of the probe and driving fields are the same or opposite, with the Doppler broadening width (D) increasing, the absorption first increases and then decreases and the absorption curve changes gradually from a double-peak structure to a single-peak structure; when VIC is present, if propagation directions of the probe and driving fields are the same, with the value of D increasing, the absorption first increases and then decreases and the absorption curve changes gradually from a single-peak structure to a double-peak structure; if propagation directions of the probe and driving fields are opposite, with the value of D increasing, the absorption decreases monotonieally and the absorption curve remains a single-peak structure.
In this paper, we investigate theoretically the effect of the relative phase ($\ensuremath{\phi}$) between the probe and driving fields on gain (absorption) and dispersion of the probe field in a Doppler-broadened N-type four-level system with spontaneously generated coherence from different respects. It is shown that gain (absorption) and dispersion are very sensitive to variations in the relative phase, and changing the Doppler width also has an obvious effect on the phase-dependent gain (absorption) and dispersion. When the probe and driving fields have the same propagation directions (copropagating), for the same Doppler width, the dispersion curve with $\ensuremath{\phi}=\ensuremath{\alpha}$ is the same as the gain (absorption) curve with $\ensuremath{\phi}=\ensuremath{\alpha}+\ensuremath{\pi}/2$; however, when the probe and driving fields have opposite propagation directions (counterpropagating), the dispersion curve and gain (absorption) curve are different and the difference becomes more considerable with an increase in Doppler width. In the co- and counterpropagating cases, gain (absorption) and dispersion always vary periodically with varying $\ensuremath{\phi}$, and the period is 2\ensuremath{\pi}. By adjusting the value of $\ensuremath{\phi}$, the largest gain (absorption) and dispersion can be obtained, and a large index of refraction without absorption can be realized. Generally speaking, gain decreases with an increase in Doppler width, but by adjusting value of $\ensuremath{\phi}$, at some special values of Doppler width, a larger gain than that without Doppler broadening can be obtained. Our study also shows that gain in the copropagating case is much larger than that in the counterpropagating case.
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.
When the interactions of the two coupling transitions from an excited level to two nearly degenerate ground levels with the same vacuum occur in a four-level tripod-scheme atomic system, vacuum-induced coherence (VIC) results from the quantum interference between the two spontaneous transitions. We investigate the effects of VIC and the relative phase between the two coupling fields on the probe absorption and dispersion properties as well as the group velocity of the probe field. We find that by adjusting the incoherent pumping field and VIC as well as the relative phase, the central absorption peak in the double transparency spectrum reduces, even develops into a gain dip, and the probe field propagates at a velocity from superluminal to subluminal. It is particularly pointed out that the subluminal light propagation with gain without inversion can be realized in such a system. The physical interpretation of the phenomena has been given.
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 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.