Effect of spontaneously generated coherence on probe response in an open system

The effect of spontaneously generated coherence on the probe response in an open ladder atomic system with equispaced levels is studied. The result shows that by adjusting the strength of spontaneously generated coherence (SGC), electromagnetically induced transparency (EIT) and high dispersion (index of refraction) with zero absorption can be realized, a much larger gain without inversion (GWI) than that without SGC can be obtained. Moreover, in the open system and for some strength of SGC, GWI without the incoherent pumping is much larger than that with the incoherent pumping; however, in the corresponding closed system, when the incoherent pumping is absent, we cannot obtain any gain (with or without inversion) for any strength of SGC. In addition, the manipulation role of the atomic exit and injection rates on SGC-dependent absorption property is analyzed for the case when the incoherence pumping does not exist.     

Phase control of probe response in an open ladder type system with spontaneously generated coherence

The control role of the relative phase between the probe and driving fields on the gain and dispersion in an open three-level ladder atomic system with incoherent pumping and spontaneously generated coherence is investigated. It is shown that by adjusting the value of the relative phase, the switching from lasing with inversion to lasing without inversion (LWI) can be realized; high index of the refraction with zero absorption can be achieved. It is also found that when the driving field is on resonance, the dispersion curve versus the probe detuning is very similar to the gain curve if the relative phase corresponding to the dispersion advances π/2 than that corresponding to the gain. LWI gain from the open system is obviously larger than that from corresponding closed system. When the incoherent pumping is absent, the open system can get LWI gain, moreover the gain is larger than that when the incoherent pumping presents for suitable value of the relative phase, but the corresponding closed system exhibits only absorption. In addition, manipulation effects of atomic exit and ratio of the injection rates on phase dependent gain are also analyzed.     

Obtaining high refractive index with vanishing absorption via spontaneously generated coherence and incoherent pumping

A three-level ∧-model atomic system with incoherent pumping is proposed to achieve high refractive index without absorption. In this kind of model, two lower levels are near-degenerate levels. It is found that high refractive index accompanied by vanishing absorption can be always accomplished by adjusting some related parameters. Although probe field is very weak, the SGC effect is prominent in the presence of incoherent pumping.     

Effects of the upper level coupling field on lasing without inversion in a V-type system

Driven by one upper level coupling field, a three-level V-type atomic system with a pair of upper levels is studied. With one strong coupling field and one weak probe field, it is found that, due to the effects of the upper level coupling field, the quantum coherence between the two upper levels can be induced, and the absorption of the probing field is very sensitive to the relative phase of the probe, the pumping and the upper level coupling fields. With proper parameters, lasing without inversion (LWI) can be realized.     

Gain enhancing due to quantum interference effect in an open four-level atomic system with Doppler broadening

The effect of vacuum-induced coherence (VIC) on the gain of lasing without inversion (LWI) is studied in an open four-level atomic system with Doppler broadening for both cases: co- and counter-propagating probe and driving fields. The results show that: (1) in general, for a fixed VIC strength, LWI gain decreases monotonously with the value of the Doppler broadening width increasing. Regardless of the Doppler broadening being obvious or not, the LWI gain much larger than that without VIC always can be gotten by choosing suitable VIC strength, i.e. values of two factors p₁ and p₂ which represent the VIC effect. (2) Varying p₁ or p₂ will produce remarkable different influence on the LWI gain, and the influence is closely related to the value of the Doppler broadening width. (3) In the case of counter-propagating probe and driving fields, when the Doppler broadening is large enough, gain oscillation occurs. For the same value of the Doppler broadening width, the oscillation amplitude increases with increasing values of strength of VIC. (4) The atomic exit and injection rates also can dramatically affect LWI gain. (5) The LWI gain for the co-propagating probe and driving fields is always larger than that for the counter-propagating probe and driving fields. (6) A much larger LWI gain in open system than that in the corresponding closed system can be obtained.     

自发辐射诱导相干对开放的Ladder型系统无反转激光增益瞬态演化的影响

利用开放的Ladder型三能级原子系统密度矩阵运动方程的数值解,研究了在探测场和驱动场双共振条件下,自发辐射诱导相干（SGC） 对系统无反转激光（LWI）增益瞬态演化的影响以及注入速率比和退出速率对与SGC相关的增益的调制作用.研究结果表明：SGC强度的变化将使瞬态增益和最终的稳定增益发生显著的改变;存在非相干抽运时,LWI增益随注入速率比和退出速率的减小而增大,而不存在非相干抽运时的情况与此正好相反;通过选取适当的SGC强度、注入速率比和退出速率可得到最大的LWI增益的瞬态值和最终的稳定值. 关键词： 开放系统 自发辐射诱导相干 瞬态演化 无反转增益     

Phase-dependent properties for absorption and dispersion in a closed equispaced three-level ladder system

It is shown that in a closed equispaced three-level ladder system, by controlling the relative phase of two applied coherent fields, the conversion from absorption with inversion to lasing without inversion (LWI) can be realized; a large index of the refraction with zero absorption can be gotten; considerable increasing of the spectrum region and value of the LWI gain can be achieved. Our study also reveals that the incoherent pumping will produce a remarkable effect on the phase-dependent properties of the system. Modifying value of the incoherent pumping can change the property of the system from absorption to amplification and enhance significantly LWI gain. If the incoherent pumping is absent, we cannot get any gain for any value of the relative phase.     

Optical properties of an open three-level atomic system via coherent and incoherent fields

In this paper, coherent and incoherent control of optical properties of open ladder- type three-level atomic system is investigated. It is shown that in the presence of spontaneously generated coherence (SGC) and incoherent pumping filed, group velocity, absorption and dispersion of the probe field can be controlled by adjusting the ratio between atomic injection and exit rates. Also, the bistabal behaviors of the system are discussed. It is shown that the ratio between atomic injections and exit rate can influence the bistabal threshold intensity and related hysteresis loop. More interestingly, it is found that SGC and incoherent pumping field effects have a central role for distinguishing between open and closed system.     

开放四能级系统中相对位相对探测响应的影响

利用具有自发辐射诱导相干开放四能级系统的定态数值解,从不同角度分析了探测场和驱动场之间的相对位相Φ对探测场增益(吸收)以及粒子数差的影响.研究结果表明：通过对相对位相的控制,可以实现探测场无反转增益和色散的周期性放大和减弱,并能得到无吸收高色散;Φ=α的色散曲线与Φ=α+π/2的增益曲线相似;在探测场共振条件下,适当调节相对位相,可以使无反转激光（LWI）增益达到最大.还研究了粒子注入和退出速率的变化对位相相关的LWI增益的调制作用.     

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.     

Comparison of transient process between open and closed ladder-type systems with spontaneously generated coherence and incoherent pumping

We theoretically investigated transient response of open and closed three-level ladder-type atomic system with or without the spontaneously generated coherence (SGC) which could be satisfied with the help of an incoherent pumping. The existence of the SGC effect makes the open and closed system to be distinguished. We compared transient response of weak probe between open and closed system and found that transient properties exhibit different features by adjusting some related parameters, such as the relative phase between probe and coupling fields, the angle between two dipole moments.     

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 modulation of transient evolution of atomic response in open lambda-type system with spontaneously generated coherence

We study the effects of the relative phase, Φ, between the probe and driving fields on the transient evolution of the atomic response from different respects in an open lambda-type system with spontaneously generated coherence. We find that: variation of value of Φ will obviously change the transient evolution process, transient and stationary values of gain, absorption and dispersion but has no any effect on the transient evolution of populations. For the same value of Φ, the stationary gain without inversion (GWI) when the incoherent pumping exists is much larger than that when the incoherent pumping is absent, the time needed to reach at the stationary state when the incoherent pumping exists is much shorter than that when the incoherent pumping is absent. The initial condition varying has remarkable effects on the phase-dependent transient evolution process, transient value of GWI but doesn’t vary size of stationary value of GWI. Varying the ratio C of the atomic injection rates and exit rate γ₀ has evident effects on the phase-dependent transient evolution process, transient and stationary values of GWI. Our study result shows that the transient evolution of the atomic response in the open system presents some considerable difference from that in the corresponding closed system, specially in the open system we can get much larger GWI than that in the corresponding closed system. In addition, we give a brief discussion about effects of the relative phase on the transient evolution of the atomic response in the open system without SGC, and obtain some results much different from those obtained in the open system with SGC.     

Group velocity of the light pulse in an open V-type system

We investigate the group velocity of the probe light pulse in an open V-type system with spontaneously generated coherence. We find that, not only varying the relative phase between the probe and driving pulses can but varying the atomic exit rate or incoherent pumping rate also can manipulate dramatically the group velocity, even make the pulse propagation switching from subluminal to superluminal; the subliminal propagation can be companied with gain or absorption, but the superluminal propagation is always companied with absorption.     

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

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.     

Lasing with and without inversion due to spontaneously generated coherence in an open V-type system

It is shown that in an open V-type atomic system without incoherent pumping, the spontaneously generated coherence (SGC) can not only lead to lasing with inversion but also lead to lasing without inversion (LWI)including at resonance of the driving and probe fields. This conclusion is much different from that obtained in the corresponding closed V-type system.     

非相干泵浦对原子系统位相相关吸收性质的影响

研究发现在具有真空诱导相干性的开放和封闭ladder 型原子系统中,探测场和驱动场之间相对位相对吸收性质有重要的调制作用,同时非相干泵浦对位相相关的吸收性质有显著的影响.在这两种系统中,通过调节非相干泵浦,可以实现从吸收到增益和从粒子数反转激光到无粒子数反转激光的转化,并可获得最大的无反转激光增益.但是,当非相干泵浦不存在时,对相对位相的任意值,在封闭系统中只出现吸收而不能得到无反转激光增益;然而在开放系统中,对于适当的相对位相值甚至可以产生比有非相干泵浦时更大的无反转激光增益.     

开放四能级原子系统粒子数反转或无反转激光研究

在封闭的简单四能级原子系统模型的基础上提出了开放的四能级原子系统模型.通过在电偶极和旋转波近似下,解此系统的半经典密度矩阵运动方程得其稳态线性解析解.对该稳态解的数值模拟显示:随着驱动场的Rabi频率的连续增加系统会发生由输出的无粒子数反转激光到输出粒子数反转激光的转变;随着系统退出速率或者注入速率比的连续增大,系统会发生由输出的粒子数反转激光到输出无粒子数反转激光的转变;该系统能获得无吸收高色散;在稳态,探测激光上下能级粒子数差随探测场失谐的变化曲线呈弱矩形波.     

Impact of Interacting Quantum Coherence via Decays and Incoherent Pumping on Transient and Steady-State Behaviors of Absorption

The effects from quantum coherence via decays and incoherent pumping on the lasing without inversion(LWI) are investigated in a four-level system.By analyzing the transient and steady-state behaviors of the absorption,we find that the gain occurs when both spontaneously generated coherence(SGC) and coherence induced by incoherent pumping(IPC) are considered.We attribute the occurrence of the gain to the interaction of quantum coherence via decays and incoherent pumping.     

Effect of vacuum-induced coherence on lasing without inversion in an equispaced three-level ladder system

The effects of vacuum-induced coherence (VIC) on the properties of the absorption and gain of the probe field in an equispaced three-level ladder atomic system are investigated. It is found that lasing without inversion (LWI) is remarkably enhanced due to the effect of VIC in the case of the small incoherent pump rate.