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Physical Review A

Phase control of probe response in a Doppler-broadened N -type four-level system

Xijun Fan, Zhongbo Liu, Ying Liang, Kening Jia, D. M. Tong

Published Apr 6, 2011• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.83.043805

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In this paper, we investigate theoretically the effect of the relative phase (\ensuremathϕ\ensuremath{\phi}\ensuremathϕ) between the probe and driving fields on gain (absorption) and dispersion of the probe field in a Doppler-broadened NNN-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 \ensuremathϕ=\ensuremathα\ensuremath{\phi}=\ensuremath{\alpha}\ensuremathϕ=\ensuremathα is the same as the gain (absorption) curve with \ensuremathϕ=\ensuremathα+\ensuremathπ/2\ensuremath{\phi}=\ensuremath{\alpha}+\ensuremath{\pi}/2\ensuremathϕ=\ensuremathα+\ensuremathπ/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 \ensuremathϕ\ensuremath{\phi}\ensuremathϕ, and the period is 2\ensuremath{\pi}. By adjusting the value of \ensuremathϕ\ensuremath{\phi}\ensuremathϕ, 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 \ensuremathϕ\ensuremath{\phi}\ensuremathϕ, 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.
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.
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.
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.
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 influences of Doppler broadening, spontaneously generated coherence, and other system parameters on propagation effect in a quasi lambda-type four-level atomic system. It is shown that when the Doppler broadening is present, generally speaking, the values of gain and intensity of lasing without inversion (i.e. the probe field) in the co-propagating probe and driving fields case are much larger than those in the counter-propagating case; considerably larger gain and intensity of lasing without inversion than those without the Doppler broadening can be obtained by choosing appropriate values of the Doppler broadening width and spontaneously generated coherence strength. The gain and intensity of lasing without inversion increase with the increase of spontaneously generated coherence strength; when spontaneously generated coherence is present, much larger gain and intensity of lasing without inversion than those in the case without spontaneously generated coherence can be obtained. Choosing suitable values of the probe detuning, Rabi frequencies of the driving and pump fields at the entrance of the medium also can remarkably enhance the gain and intensity of lasing without inversion.