Influence of Doppler broadening and spontaneously generated coherence on propagation effect in a quasi lambda-type four-level system

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.     

Inversionless gain enhancing due to Doppler broadening in a closed lambda-type system

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 {\it et al}, {\it Laser Phys.} {\bf 6} 436 (1996)).     

Effect of spontaneously generated coherence on inversionless lasing gain in an atomic system with Doppler broadening

We have studied the effect of the spontaneously generated coherence (SGC) on gain of lasing without inversion (LWI) in a closed three-level $\Lambda $-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.     

Doppler展宽的封闭原子系统中无反转增益的相位控制

研究了在具有自发辐射诱导相干性的Doppler展宽的封闭Λ型三能级系统中探测场和驱动场之间的相对位相对探测场无反转增益的控制作用. 研究结果表明: 1) 不管探测场和驱动场是同向传播还是反向传播, 驱动场是失谐还是共振,无反转增益总是随相对位相的改变而作周期性变化,周期为2π. 2) 驱动场共振时,无反转增益极大值随Doppler展宽值的增大而单调减小,且反向传播时比同向传播时减小的速度更快;驱动场失谐时,无反转增益的极大值随Doppler展宽值的增大不再单调地减小或增大. 在以上两种情况下,均可以通过调 关键词： 自发辐射诱导相干 相位控制 Doppler展宽 无反转增益     

Doppler展宽的封闭原子系统中无反转增益的相位控制

研究了在具有自发辐射诱导相干性的Doppler展宽的封闭Λ型三能级系统中探测场和驱动场之间的相对位相对探测场无反转增益的控制作用. 研究结果表明: 1) 不管探测场和驱动场是同向传播还是反向传播, 驱动场是失谐还是共振，无反转增益总是随相对位相的改变而作周期性变化，周期为2π. 2) 驱动场共振时，无反转增益极大值随Doppler展宽值的增大而单调减小，且反向传播时比同向传播时减小的速度更快；驱动场失谐时，无反转增益的极大值随Doppler展宽值的增大不再单调地减小或增大. 在以上两种情况下，均可以通过调     

Doppler展宽准Λ型四能级系统中传播效应的位相相关性

利用数值计算详细研究具有真空诱导相干的准Λ型四能级原子系统中探测场和驱动场之间的相对位相(Φ)对传播效应的影响。结果表明:通过选择Φ的取值可以获得更大的GWI和更长的存在无反转增益的传播距离,从而获得更高的LWI强度;Doppler展宽存在时,Doppler展宽宽度及探测场和驱动场传播方向对位相相关的GWI和LWI强度的空间演化有明显的调制作用。     

Comparison between effects of Doppler broadening on pure and non-pure inversionless gains with frequency up-conversion

A study is made of the effects of Doppler broadening on pure gain without inversion, which means that neither one-photon nor two-photon inversions are allowed, and non-pure gain without inversion, which means that one-photon inversion does not occur but two-photon inversion is present, in a closed Λ-type three-level system with incoherent pumping. It is shown that when the driving field is resonant but the probe field is not, in a certain range of Doppler width, for the case of the lower degree of frequency up-conversion, generally, pure gain without inversion increases monotonically and non-pure gain without inversion does not monotonically increase or decrease with increasing Doppler width; for the case of the higher degree of frequency up-conversion, pure gain without inversion decreases monotonically but non-pure gain without inversion cannot be produced. In the case of two-photon resonance, in some range of Doppler width, pure gain without inversion does not monotonically increase or decrease while non-pure gain without inversion decreases monotonically with Doppler width increasing. Finally, an experimental scheme for examining our theoretical result is given.     

Revision on the calculation of optically pumped FIR laser spectrum with Doppler broadening and pressure broadening effects

By means of iteration method and also taking into account Doppler broadening and pressure braodening effect of IR pumping laser, the output power density of optically pumped NH₃ molecules FIR laser is calculated by solving density matrix equations of three-level system. The results of theoretical calculation shows that, in comparison with the FIR laser under the assumption of ideal monochromatic IR pumping, the output power density of FIR laser in the case of Doppler broadening and pressure broadening IR pumping decreases much more. Meanwhile, via the revision of Doppler broadening and pressure broadening effect, the theoretical value of optimum operating gas pressure reduces, which is in better agreement with the experimental value. Further study shows that the revision of Doppler broadening effect is more fit for the conventional FIR laser with a 2m sample tuble and the revision of pressure broadening effect is much more suitable for the miniature FIR laser with a short sample tube of 5 to 20cm in length.Supported by the National Natural Sciences Foundation of P.R.China and the NSF of Guangdong Province.     

Phase-dependence of inversionless gain in a Doppler broadened open four-level system

The effect of the relative phase (?) between the probe and driving fields on the gain without inversion (GWI) in a Doppler broadened open quasi Λ-type four level atomic system with vacuum induced coherence (VIC) for both co- and counter-propagating probe and driving fields cases is studied. It is shown that: (1) GWI and the probe detuning region in which GWI exists are very sensitive to variation of the relative phase; when values of the other parameters keep unvarying, by adjusting value of ?, the largest GWI can be obtained. (2) The Doppler width (D) also has dramatically modulation role on the phase-dependent GWI. When value of D is smaller, the value of ? which corresponds to the largest value of GWI is about π, when value of D is large enough, it is about π/2. (3) GWI varies periodically with ? varying, the period is 2π, but the concrete variation rule is closely related to value of D. (4) In the co-propagating case we can obtain much larger GWI than that in the counter-propagating case.     

the phase-dependent gain without inversion in a Doppler broadened open four-level system

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.     

驱动场相位扩散对三能级梯型系统无反转激光的影响

在旋波、慢变振幅近似下,求解考虑了驱动场相位扩散后的系统密度矩阵运动方程,并给出了这个三能级梯型系统稳态线性解析解.利用得到的稳态线性解析解分析驱动场相位扩散是如何影响该系统输出无反转激光的.对稳态线性解析解数值计算的结果显示:由于驱动场相位扩散会导致无反转激光增益减小;即使由于驱动场相位扩散引起的线宽足够大,在该系统中仍能够获得无反转激光;线宽往往是破坏无反转激光产生和折射率的提高;因驱动场相位扩散导致无反转激光增益的减小,并不是总能够通过增大驱动场的Rabi频率得到补偿.     

The effect of Doppler broadening on dispersive and absorptive properties in atomic systems with two-photon interference

The effect of Doppler broadening on dispersive and absorptive properties is theoretically investigated in the hot four-level electromagnetically induced transparency (EIT) atomic systems with two different types of two-photon interference. It is found that the dispersive behavior for the probe in the ladder-type atomic system with two-photon constructive interference will be changed from anomalous in cold atoms to normal in hot atoms, and the three-peak absorptive profile is shifted to a broadened spectrum with a shallow dip at the line center; as a comparison, there is always normal dispersion at the line center for the invert-Y-type atomic system with two-photon destructive interference, but the EIT window in the absorptive profile will be narrowed to subnatural linewidth (0.01Γ) at room temperature. The physics of those two different behaviors are discussed and compared in the dressed-state theory.     

Modulation of atomic exit and injection rates on the phase-dependent gain without inversion in a Doppler broadened open four-level system

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.     

开放V型系统相对位相对LWI增益瞬态演化的影响

数值计算具有自发辐射诱导相干性的开放V型三能级原子系统密度矩阵运动方程,分析无反转激光(LWI)增益的瞬态演化.结果表明:无论是否存在非相干抽运,探测场和驱动场间的相对位相(Ф)对增益的瞬态演化都有显著的影响;通过选择的取值可以获得更大的瞬态和稳定增益;不存在非相干抽运时,系统达到瞬态增益最大值及获得增益稳定值所需要的时间更长,演化过程中振荡幅度更大,获得的增益更大;原子退出速率r0(原子注入速率比S)的变化将使增益瞬态演化的具体过程发生改变,在r0(S)的一定取值范围内,瞬态和稳定增益随S(r0)的增大而增大.     

Y型四能级系统中Doppler展宽对VIC相关的双光子吸收的影响

利用数值计算结果讨论了Doppler展宽对Y型四能级原子系统中真空诱导相干 性(VIC)相关的双光子吸收的影响. 研究结果表明: 1)在无Doppler展宽的情况中, 不存在VIC时, 吸收曲线具有双峰结构并产生电磁感应透明(EIT)现象, 存在VIC时吸收曲线具有单峰结构而EIT现象不再发生; 2)在有Doppler展宽的情况中, 不管是否存在VIC, EIT现象都能发生; 不存在VIC时, 不管探测场和驱动场传播方向相同还是相反, 随Doppler展宽宽度D值的增大, 吸收先增大后减小, 吸收曲线逐渐从双峰结构变为单峰结构; 存在VIC时, 若探测场和驱动场传播方向相同, 随D值的增大, 吸收先增大后减小, 吸收曲线逐渐从单峰结构变为双峰结构; 若探测场和驱动场传播方向相反, 随D值的增大, 吸收单调减小, 但吸收曲线仍保持单峰结构.     

吸收谱线Doppler展宽对原子多步光电离的影响

原子法激光同位素分离的核心之一是如何高效地将原子激发电离.本文从原子法激光同位素分离的实际情况出发,研究了原子吸收谱线的Doppler展宽对原子电离率的影响.研究中使用的理论工具是原子激发电离的密度矩阵方程,并利用数值计算方法对方程进行求解.研究结果表明:当吸收谱线有Doppler展宽时,在激光参数不变的条件下原子电离率会降低;且当激光功率固定时,存在使原子电离率为最大的线宽值.这与已发表文献中无Doppler展宽时的计算结果有很大不同.为了追求最佳的原子电离效果,在原子法激光同位素分离系统中激光应该尽可能地工作在最佳线宽条件下.如果激光线宽有不可控的随机波动,在技术上让激光线宽略大于最佳线宽更为有利.无论如何控制激光线宽,尽可能地降低原子吸收谱线的Doppler展宽都有利于原子电离率的提高.     

共振简并双光子激光近阈行为的理论研究

采用量子理论讨论共振简并双光子激光的小偏谐近阈行为，在一定条件下，系统能够呈现无反转激光，在另一条件下，系统则以于现无激光反转。     

开放Ⅴ型系统相对位相对LWI增益瞬态演化的影响

数值计算具有自发辐射诱导相干性的开放V型三能级原子系统密度矩阵运动方程,分析无反转激光(LWI)增益的瞬态演化.结果表明:无论是否存在非相干抽运,探测场和驱动场间的相对位相(Ф)对增益的瞬态演化都有显著的影响;通过选择Ф的取值可以获得更大的瞬态和稳定增益;不存在非相干抽运时,系统达到瞬态增益最大值及获得增益稳定值所需要的时间更长,演化过程中振荡幅度更大,获得的增益更大;原子退出速率r₀(原子注入速率比S)的变化将使增益瞬态演化的具体过程发生改变,在r₀(S)的一定取值范围内,瞬态和稳定增益随S(r₀)的增大而增大.     

Phase control in an open Λ-type system with spontaneously generated coherence

This paper investigates the control role of the relative phase between the probe and driving fields on the gain, dispersion and populations in an open A system with spontaneously generated coherence （SGC）. It shows that by adjusting the value of the relative phase, a change from lasing with inversion to lasing without inversion can be realized; the values and frequency spectrum regions of the inversionless gain and dispersion can be obviously varied; high refractive index with zero absorption and electromagnetically induced transparency can be achieved. It is also found that when the driving field is resonant, the shapes of the dispersion and the gain curves versus the probe detuning are very similar if the relative phase of the dispersion lags π/2 than that of the gain, however for the off-resonant driving field the similarity will disappear; the gain, dispersion and populations are periodical functions of the relative phase, the modulation period is always 2π; the contribution of SGC to the inversionless gain and dispersion is much larger than that of the dynamically induced coherence.