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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Phase-dependent gain without inversion in an inhomogeneous broadened quasi Λ-type four-level system with VIC

Zhongbo Liu, Zhendong Wang, Kening Jia, D. M. Tong, Xijun Fan

Published Oct 6, 2010• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.868434

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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.
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.
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.
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.
An analysis is made of the effect of Doppler broadening on gain without inversion (GWI) from different aspects in a closed lambda-type three-level system with an incoherent pump. It is shown that, regardless of the driving field being on resonance or not, for the counter- or co-propagating of the probe and driving fields (PDF), GWI does not monotonically decrease or increase with increasing Doppler width. Except for the case of counter-propagating PDF with off-resonance driving field, at a suitable Doppler width one can obtain a gain maximum value much larger than that without Doppler broadening; especially in the situation of the resonant driving field, the co-propagating geometry leads to a larger GWI. In addition, for the counter-propagating geometry, when Doppler width is larger enough, GWI oscillation occurs, and the oscillation amplitude and region increase with increasing Doppler width. These conclusions are very different from that obtained in previous investigation (Lukin et al, Laser Phys. 6 436 (1996)).
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 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 $\ensuremath{\phi}=\ensuremath{\alpha}$ 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.
Influence of relative phase between probe and driving fields(ф) on propagation effect of a Doppler broadened quasi-Λ type four-level atomic system with spontaneously generated coherence(SGC) is numerically studied.It is shown that by choosing ф,we can obtain greater GWI and longer propagation distance where GWI exists and hence obtain higher LWI intensity.Doppler broadening width and propagation directions of probe and driving fields have considerable effect on phase-dependent spatial evolutions of GWI and LWI intensity.