Effects of relative phase in an open ladder system without incoherent pumping

We studied effects of the relative phase between the probe and driving fields on the absorption and dispersion properties in an open three-level ladder system with spontaneously generated coherence but without incoherent pumping. It is shown that by the phase controlling, switching from absorption to lasing without inversion (LWI) and enhancing remarkablely LWI gain can be realized; large index of refraction with zero absorption and the electromagnetically induced transparency can be obtained. We also find that varying the atomic injection and exit rates has a considerable influence on the phase dependent-absorption property of the probe field, existent of the atomic injection and exit rates gives the necessary condition of the realization of LWI, getting LWI is impossible in the corresponding closed system without incoherent pumping.     

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.     

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.     

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.     

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 modulation of propagation effect with Doppler broadening

This paper studies the propagation effect in a closed lambda-type three-level atomic system with Doppler broadening. It is shown that, Doppler broadening due to atomic motion and propagation effect associated with driving field depletion along the active medium decreases obviously the gain and output of the lasing without inversion （LWI）; the relative phase between the probe and driving fields has a remarkable modulation role to the propagation effect on LWI when Doppler broadening presents; by choosing suitable value of the relative phase, we can get the largest gain and output of LWI.     

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.     

失谐对开放的四能级系统无粒子数反转激光的影响

提出开放的四能级双驱动场无反转激光系统的理论模型,由电偶极和旋转波近似得到其密度矩阵方程,讨论无反转激光产生的物理机制,利用数值计算结果分析探测场和驱动场失谐对系统无反转激光增益和粒子数差的影响.     

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.     

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.     

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.     

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.     

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.     

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.     

开放的V型三能级系统中原子注入和退出速率对位相相关的无反转激光增益和强度空间演化的调制作用

利用数值计算结果, 研究了具有自发辐射诱导相干的开放V 型三能级原子系统中的传播效应. 研究表明: 改变探测场和驱动场之间的相对位相对无反转激光(LWI)增益和 强度随传播距离的变化即空间演化具有重要的影响; 而原子的注入速率比(S)和退出速率(r₀)的改变将对位相相关的LWI增益和强度的空间演化产生明显的调制作用. 在S(r₀)的一定取值范围内, S(r₀)的值越大, LWI增益和强度越大且强度达到极大值需要的传播距离越长; 相应封闭系统中LWI增益和强度的最大值及能产生增益的传播距离都小于开放系统. Doppler效应对LWI增益和强度的空间演化也具有明显的影响, 存在Doppler效应时得到的LWI增益和强度明显小于无Doppler效应时的值.     

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.     

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.     

开放的非共振梯型无粒子数反转激光系统非线性增益与色散的研究

本文给出了开放的非共振ladder型三能级无粒子数反转激光系统的非线性精确解,利用数值计算结果讨论了系统各参量的变化对激光场的增益和色散的影响.作者得到以下结论:当探测激光场和驱动场都共振时,无论其他参量如何变化,色散为零.当仅有探测场失谐(驱动场失谐)时,增益和色散随探测场失谐(驱动场失谐)的变化曲线分别具有偶对称性和中心对称性,当探测场和驱动场皆失谐时,这种对称性消失;适当调节探测激光场或(和)驱动场的失谐可获得最大或较大的无粒子数反转激光增益和无吸收高色散.增益和色散(粒子数差绝对值)随原子注入速率之比的增加单调增加(单调减小),且原子退出速率越大增加(减小)得越快.在探测场和驱动场适当失谐的情况下,保持系统其他参量不变,非相干泵浦速率只有在一定范围内取值时,才能获得无粒子数反转激光增益,并存在一个增益极大值.改变探测场或驱动场Rabi频率对无粒子数反转激光增益的影响与非相干泵浦速率改变时的情况类似.