基于简并二能级原子系统的电磁诱导增益

韩宇宏; 车少娜; 王丹; 周海涛

doi:doi:10.3788/AOS201838.0302001

光学学报, 2018, 38 (3): 0302001, 网络出版: 2018-03-20

基于简并二能级原子系统的电磁诱导增益下载： 853次

Electromagnetically Induced Gain Based on Degenerate Two-Level Atomic System

论文大纲

韩宇宏 ^*车少娜王丹周海涛

作者单位

山西大学物理电子工程学院, 山西太原 030006

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摘要

理论和实验研究了基于简并二能级原子系统的电磁诱导增益(EIG)效应, 构建了一个N型简并二能级系统, 分析了在不同多普勒频移下信号光增益随抽运光拉比频率的变化规律。结果表明：在增大区间, 增益谱一直保持线宽极窄的单峰结构；而在减小区间, 增益谱产生类拉比分裂, 并且呈现出对称的双峰结构。选择Cs原子基态和激发态角动量相同条件下的简并能级结构, 实验研究了EIG的产生特点, 并进一步分析了抽运光强度及信号光偏振对增益峰值效率的影响。

Abstract

The electromagnetic induced gain (EIG) effects based on the degenerate two-level atomic system are theoretically and experimentally studied. By constructing a N-type degenerate two-level system, the variations of signal light gain with Rabi frequency of pumping light are theoretically analyzed under different Doppler shifts. The results show that, in the rising range, the gain spectrum keeps a single peak structure with a narrow linewidth; while in the decreasing range, it generates a Rabi-like splitting and exhibits a symmetrical two-peak profile. Based on the degenerate energy levels of Cs atoms in which the angular momenta of ground and excited states are same, the generation feature of EIG is experimentally investigated. Furthermore, the influences of pumping intensity and signal light polarization on the peak gain efficiency are also analyzed.

1 引言

光诱导原子介质产生的相干干涉包括电磁诱导透明(EIT)^[1-3]、电磁诱导吸收(EIA)^[4-8]、相干布居俘获(CPT)^[9-11]和无粒子数反转(LWI)^[12-13]等物理现象,是当前的研究热点之一。特别是EIT介质对弱光的无吸收正常色散效应,可以大大减小光在介质中的传播速度,从而实现信息在光与介质之间的交换和存储,在量子信息存储领域有着潜在的应用价值。通过调制相干耦合光场的数量和方向,比如用对向入射的两束耦合场代替一束单向入射的耦合场,可以使介质的色散特性由正常转为反常,EIT变为EIA效应,这不但可以实现减光速向超光速的转变^[14],同时还会产生Bragg反射^[15]或四波混频效应^[16-18]。研究发现,上述原子的相干干涉效应不但存在于Λ型或V型三能级原子结构中^[19-20],还可以在基于Λ型或V型结构的简并二能级系统中得以实现。Akulshin等^[21-22]在类简并二能级系统中,基于原子基态的塞曼子能级分裂,研究了光诱导相干现象并且观察到了EIT及EIA。Ye等^[23]发现,在类简并的铷原子系统中,无论是封闭还是开放的跃迁,原子基态与激发态之间都可发生EIA现象。

近年来,基于LWI的电磁诱导增益(EIG)现象引起了学者们的研究兴趣。EIG是指在强的相干抽运场驱动下,弱探测场出现增益放大(即负吸收)的现象。在多普勒展宽的Λ型或V型三能级系统中,通过引入一束非相干抽运场,可实现EIT向EIG的转换^[24-26]。而在基于原子腔耦合的系统中,仅凭单束相干抽运场,同样可以实现LWI^[27-28];在引入两束相干抽运场的条件下,可实现内腔EIT的光放大^[29]。基于双Λ型三能级系统,在单束相干抽运场驱动下,通过增大介质的粒子数密度和抽运强度,不但可以实现弱信号光的增益放大,还可产生相位共轭的Stokes或Anti-Stokes场,从而在远失谐条件下制备出大频差的关联光子对^[30-31]。以上研究都是在三能级原子系统下进行的,Mukherjee等^[32]则在分子系统中,基于N型简并结构,理论分析并实验研究了基于LWI的EIG效应,但该效应在原子系统中鲜有报道。

本文基于开放的N型简并二能级原子系统模型,理论分析了在单束相干抽运场作用下产生EIG的特点,并基于热的Cs原子介质,在基态和激发态角动量相同的条件下进行了实验验证。

2 理论模型及数值模拟

考虑图1所示的N型简并二能级原子系统,其中能级|1>和|3>为简并的基态能级,能级|2>和|4>为简并的激发态能级。一束频率为ω_p的强抽运光以π偏振同时作用于能级|1>↔|2>与|3>↔|4>的跃迁;一束频率为ω_s的弱探测光与抽运光偏振垂直,因此可看作是左旋圆偏光L和右旋圆偏光R的叠加,并分别作用于能级|4>↔|1>和|2>↔|3>的跃迁。在相互作用绘景和旋波近似下,系统的哈密顿量表示为

\begin{matrix} \begin{matrix} H = ћ Δ_{p} σ_{22} + ћ (Δ_{p} - Δ_{s}) σ_{33} + ћ (2 Δ_{p} - Δ_{s}) σ_{44} - \\ ћ (Ω_{p} σ_{21} + Ω_{p}^{*} σ_{12} + Ω_{s} σ_{41} + Ω_{s}^{*} σ_{14} + \\ Ω_{p} σ_{43} + Ω_{p}^{*} σ_{34} + Ω_{s} σ_{23} + Ω_{s}^{*} σ_{32}), (1) \end{matrix} \end{matrix}

式中Δ_p=ω_p-ω₂₁=ω_p-ω₄₃,Δ_s=ω_s-ω₂₃=ω_s-ω₄₁分别为抽运光与探测光的频率失谐;ω_p、ω_s分别为抽运光与探测光的圆频率;Ω_p、Ω_s分别为抽运光和探测光的拉比频率; $\begin{matrix} Ω_{p}^{*} \end{matrix}$ 、 $\begin{matrix} Ω_{s}^{*} \end{matrix}$ 分别为抽运光和探测光的共轭拉比频率;ћ为约化普朗克常量。系统的约化密度矩阵主方程表示为

\begin{matrix} \overset{\cdot}{ρ} = - \frac{i}{ћ} [H, ρ] + γ_{21} l_{12}^{21} ρ + γ_{23} l_{32}^{23} ρ + γ_{41} l_{14}^{41} ρ + γ_{43} l_{34}^{43} ρ, (2) \end{matrix}

式中γ₂₁,γ₂₃分别为激发态|2>到基态|1>和|3>的自发衰减率,γ₄₁,γ₄₃分别为激发态|4>到基态|1>和|3>的自发衰减率,ρ为系统总的态密度算符, $\begin{matrix} \overset{\cdot}{ρ} \end{matrix}$ 为态密度算符随时间的一阶导数, $\begin{matrix} l_{ij}^{ji} \end{matrix}$ (i=1,3;j=2,4)为原子态|i>与态|j>之间的相干转移率。

图 1. N型简并二能级系统的示意图

Fig. 1. Schematic of N-type degenerate two-level system

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原子布居数的转移表示为

\begin{matrix} l_{ij}^{ji} ρ = \frac{1}{2} (2 σ_{ij} ρ σ_{ji} - σ_{ji} σ_{ij} ρ - ρ σ_{ji} σ_{ij}), (3) \end{matrix}

式中σ_ij=|i><j|为原子极化算符(i≠j)和布居数算符(i=j)。

系统的约化密度矩阵元方程为

\begin{matrix} \{\begin{matrix} \overset{\cdot}{ρ_{11}} = γ_{21} ρ_{22} + γ_{41} ρ_{44} + i Ω_{p}^{*} ρ_{21} - i Ω_{p} ρ_{12} + i Ω_{s}^{*} ρ_{41} - i Ω_{s} ρ_{14} \\ \overset{\cdot}{ρ_{22}} = - (γ_{21} + γ_{23}) ρ_{22} + i Ω_{p} ρ_{12} - i Ω_{p}^{*} ρ_{21} + i Ω_{s} ρ_{32} - i {Ω^{*}}_{s} ρ_{23} \\ \overset{\cdot}{ρ_{33}} = γ_{23} ρ_{22} + γ_{43} ρ_{44} + i {Ω^{*}}_{s} ρ_{23} - i Ω_{s} ρ_{32} + i {Ω^{*}}_{p} ρ_{43} - i Ω_{p} ρ_{34} \\ \overset{\cdot}{ρ_{44}} = - (γ_{43} + γ_{41}) ρ_{44} + i Ω_{s} ρ_{14} - i {Ω^{*}}_{s} ρ_{41} + i Ω_{p} ρ_{34} - i {Ω^{*}}_{p} ρ_{43} \\ \overset{\cdot}{ρ_{12}} = - Γ_{12} ρ_{12} - i {Ω^{*}}_{p} ρ_{11} + i {Ω^{*}}_{p} ρ_{22} - i {Ω^{*}}_{s} ρ_{13} + i {Ω^{*}}_{s} ρ_{42} \\ \overset{\cdot}{ρ_{34}} = - Γ_{13} ρ_{34} - i {Ω^{*}}_{s} ρ_{31} + i {Ω^{*}}_{s} ρ_{24} - i {Ω^{*}}_{p} ρ_{33} + i {Ω^{*}}_{p} ρ_{44} \\ \overset{\cdot}{ρ_{13}} = Γ_{14} ρ_{13} + i {Ω^{*}}_{p} ρ_{23} - i Ω_{s} ρ_{12} - i Ω_{p} ρ_{14} + i Ω_{s}^{*} ρ_{43} \\ \overset{\cdot}{ρ_{14}} = - Γ_{23} ρ_{14} - i {Ω^{*}}_{s} ρ_{11} + i {Ω^{*}}_{p} ρ_{24} - i {Ω^{*}}_{p} ρ_{13} + i {Ω^{*}}_{s} ρ_{44} \\ \overset{\cdot}{ρ_{23}} = - Γ_{24} ρ_{23} + i Ω_{p} ρ_{13} - i Ω_{s} ρ_{22} + i Ω_{s} ρ_{33} - i Ω_{p} ρ_{24} \\ \overset{\cdot}{ρ_{24}} = - Γ_{34} ρ_{24} + i Ω_{p} ρ_{14} - i {Ω^{*}}_{s} ρ_{21} + i Ω_{s} ρ_{34} - i {Ω^{*}}_{p} ρ_{23} \end{matrix}, (4) \end{matrix}

式中ρ_ij(i,j=1,2,3,4)为任意两态之间的态密度元算符, $\begin{matrix} {\overset{\cdot}{ρ}}_{ij} \end{matrix}$ 为态密度元算符随时间的一阶导数,原子布居数满足ρ₁₁+ρ₂₂+ρ₃₃+ρ₄₄=1,其他参数分别为

\begin{matrix} \{\begin{matrix} Γ_{12} = \frac{1}{2} (γ_{21} + γ_{23}) - i Δ_{p} \\ Γ_{13} = \frac{1}{2} (γ_{43} + γ_{41}) - i Δ_{p} \\ Γ_{14} = i (Δ_{p} - Δ_{s}) \\ Γ_{23} = \frac{1}{2} (γ_{43} + γ_{41}) - i (2 Δ_{p} - Δ_{s}) \\ Γ_{24} = \frac{1}{2} (γ_{21} + γ_{23}) + i Δ_{s} \\ Γ_{34} = \frac{1}{2} (γ_{21} + γ_{23} + γ_{41} + γ_{43}) - i (Δ_{p} - Δ_{s}) \end{matrix} 。 (5) \end{matrix}

由于介质对探测光的L和R成分的作用效果相同,因此只计算ρ₂₃(或ρ₁₄)即可。假设初始状态下原子均匀布居在两个基态上,并且探测光强度很弱,忽略其高阶项,则通过对(4)式求导,可获得各项的定态解,从而求得ρ₂₃的解析表达式为

\begin{matrix} \begin{matrix} ρ_{23} = - \frac{i Ω_{p}^{2} Ω_{s}}{2 Γ_{13} Γ_{12} D_{4}} - \frac{i Ω_{p}^{2} Ω_{s}}{2 Γ_{13} Γ_{14} D_{4}} + \frac{D_{3}}{Γ_{13} Γ_{14} D_{4}} - \frac{i Ω_{p}^{2} Ω_{s}}{2 Γ_{13} Γ_{43} D_{4}} + i \frac{Ω_{s}}{2 D_{4}} - \frac{i Ω_{p}^{2} Ω_{s}}{2 Γ_{24} Γ_{14} D_{4}} + \\ \frac{D_{3}}{Γ_{24} Γ_{14} D_{4}} - \frac{i Ω_{p}^{2} Ω_{s}}{2 Γ_{24} Γ_{21} D_{4}} - \frac{i Ω_{p}^{2} Ω_{s}}{2 Γ_{24} Γ_{34} D_{4}}, (6) \end{matrix} \end{matrix}

式中

\begin{matrix} \{\begin{matrix} D_{1} = Γ_{24} + \frac{Ω_{p}^{2} + Ω_{p}^{2} \frac{Γ_{24}}{Γ_{13}}}{Γ_{14}} \\ D_{2} = Ω_{p}^{2} (i Ω_{p}^{*} + i Ω_{p}^{*} \frac{Γ_{24}}{Γ_{13}}) \frac{i Ω_{p}}{D_{1}} \\ D_{3} = Ω_{p}^{2} (i Ω_{p}^{*} + i Ω_{p}^{*} \frac{Γ_{24}}{Γ_{13}}) (\frac{Ω_{p} Ω_{s}^{*}}{2 Γ_{14} D_{1}} + \frac{Ω_{p} {Ω^{*}}_{s}}{2 Γ_{21} D_{1}} + \frac{Ω_{s} Ω_{p}}{2 Γ_{34} D_{1}}) \\ D_{4} = Γ_{23} + \frac{Ω_{p}^{2}}{Γ_{13}} + \frac{D_{2}}{Γ_{13} Γ_{14}} + \frac{D_{2}}{Γ_{24} Γ_{14}} + \frac{Ω_{p}^{2}}{Γ_{24}} \end{matrix} 。 (7) \end{matrix}

因此,在不考虑原子无规则运动引起的多普勒展宽效应下,得到介质对左旋探测光的极化率^[33]χ₀表示为

\begin{matrix} χ_{0} = \frac{2 N_{0} μ^{2}}{ε_{0} ћ Ω_{s}} ρ_{23}, (8) \end{matrix}

式中N₀为原子速度为0时的原子数密度,μ为偶极矩阵元,ε₀为真空介电常数。而χ₀的实部和虚部分别表征介质对信号光的色散大小和吸收强度。

图2所示为不同的抽运光拉比频率条件下,信号光穿过介质的透射率曲线,即介质对信号光的吸收曲线。可以看出,在无抽运光作用时(Ω_p=0),系统简化为纯二能级原子结构,因此在原子共振频率中心,介质对信号光产生很强的共振跃迁吸收,如图2黑色曲线所示。当加入强度很小的抽运光时,在单、双光子的共振中心(Δ_s=Δ_p=0)产生了EIT,并且随着抽运光拉比频率Ω_p的增大,EIT快速转变为EIG。当Ω_p=0.68 MHz时,信号光依然表现为EIT,其透射率约为0.8,如图2红色曲线所示。当Ω_p=0.69 MHz时,EIG已经产生,其透射率约为1.35,并且其增益峰依然保持线宽极窄的单峰结构,如图2蓝色曲线所示。图2中信号光的拉比频率设定为Ω_s=0.5 MHz。

图 2. 不同抽运光拉比频率下信号光的透射谱

Fig. 2. Signal transmission spectra under different Rabi frequencies of pumping light

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在实际的热原子气室中,考虑到原子运动引起的多普勒频移效应,(5)式中的Δ_p改写为Δ'_p=Δ_p-δ_D,Δ_s改写为Δ'_s=Δ_s-δ_D,其中δ_D=ωv/c为多普勒频移项(ω为圆频率,v为原子速度,c为光速)。因此很容易计算得到任意速度v下的密度算符ρ₂₃(v),而此时的粒子数密度为N_v= $\begin{matrix} \frac{N_{0} \exp (- v^{2} / u^{2})}{u \sqrt[]{π}} \end{matrix}$ dv,其中u为原子的均方根速度,其大小取决于热原子气室的温度T。考虑多普勒频移的极化率可表示为

\begin{matrix} χ (δ_{D}) = χ_{v} = \frac{2 N_{v} μ^{2}}{ε_{0} ћ Ω_{s}} ρ_{23} (v) 。 (9) \end{matrix}

定义介质的多普勒展宽为Δ_D=2ωu $\begin{matrix} \sqrt[]{\ln 2} \end{matrix}$ /c,考虑原子速度及多普勒展宽的影响,可得介质对探测光的平均极化率χ为

\begin{matrix} < χ >_{D} = \frac{1}{Δ_{D} \sqrt[]{π}} \int_{-}^{\infty} χ (δ_{D}) \exp [- (δ_{D} / Δ_{D})^{2}] d δ_{D} 。 (10) \end{matrix}

图3比较了在原子共振频率中心,在不同原子速度引起的多普勒频移条件下,信号光的增益峰幅度随抽运光拉比频率的变化趋势。在无多普勒频移时(δ_D=0),信号光的增益峰幅度随Ω_p的增大先呈线性急剧增大,当Ω_p=1.8 MHz时,增益幅度达到最大(约为80),此后先快速后缓慢呈类指数式下降,如图3黑色曲线所示。而在考虑多普勒宽度时,信号光的增益峰幅度随Ω_p的增大虽整体仍然呈先增大后减小的变化趋势,但随着δ_D的增大,增益峰幅度增大和减小的趋势明显变缓,最大的增益峰幅度也逐渐减小,并且其对应的Ω_p也逐渐增大。当δ_D=70 MHz时,在Ω_p=10.2 MHz时产生最大增益幅度,增益峰幅度约为53,如图3红色曲线所示。而当δ_D=140 MHz时,在Ω_p=20 MHz条件下才达到最大增益幅度,并且增益峰幅度减小至35左右,如图3蓝色曲线所示。当多普勒频移增大至δ_D=280 MHz时,增益峰幅度随Ω_p的增大更加缓慢,且当Ω_p=42 MHz时才达到最大增益幅度,增益峰幅度在20左右达到饱和,如图3灰色曲线所示。产生该结果的原因是,在总原子数一定的条件下,随着原子运动的加剧,多普勒频移也相应增大,导致最大增益峰幅度对应的Ω_p也产生一定的Stark移动,同时满足增益条件的有效原子数减少,导致最大增益幅度变小。

图 3. 在不同的多普勒宽度条件下,信号光的增益峰幅度随抽运光拉比频率的变化

Fig. 3. Gain peak amplitude of signal light versus Rabi frequency of pumping light under different Doppler widths

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从图3可以看出,当原子介质的速度很小即多普勒频移很小时,信号光的增益峰幅度随Ω_p的增大呈现明显先增大后减小的变化趋势,但在增大和减小两个阶段,增益谱的线形及线宽却呈现出不同的变化趋势。在不考虑多普勒频移条件(δ_D=0)下,列举了三组分别在增大和减小区间,信号光在相同增益幅度下谱线形随频率失谐的变化,如图4所示。在增大区间,信号光的增益随着Ω_p快速增大的同时,依然保持线宽很窄的单峰结构,且线宽均为0.5 MHz左右,如图4(a1)~(a3)所示。而当增益达到饱和并进入减小区间后,随着增益的减小,谱线宽逐渐变宽。当Ω_p=4.9 MHz时,增益由最大减小至25左右,其谱线宽增大至约4 MHz,如图4(b3)所示。当Ω_p=7.06 MHz时,增益减小至12左右,线宽却增大至约7.5 MHz,如图4(b2)所示。而当Ω_p增大至大于原子的自发衰减率2γ时,随着增益幅度的减小,增益谱逐渐产生类拉比分裂,两个增益峰对称地远离原子共振中心,且随着Ω_p的增大,劈裂越明显。当Ω_p=20 MHz时,在偏离原子的共振中心Δ_s=±40 MHz处,产生两个对称的增益峰,且其峰值增益减小至1.5左右,如图4(b1)所示。此时增益谱产生劈裂,主要是由于在不考虑多普勒频移及展宽影响时,较小的抽运拉比频率导致信号光增益达到饱和,并在Ω_p进一步增大时,原子缀饰态产生明显的Autler-Townes分裂,且分裂间隔逐渐增大,导致增益谱由单峰结构变成对称的双峰分布^[34]。

图 4. 不考虑多普勒频移(δD=0)时,不同抽运光拉比频率下的信号光增益谱。(a1) Ωp=0.70 MHz; (a2) Ωp=0.83 MHz; (a3) Ωp=0.94 MHz; (b1) Ωp=20 MHz; (b2) Ωp=7.06 MHz; (b3) Ωp=4.9 MHz

Fig. 4. Gain profiles of signal light under different Rabi frequencies of pumping light when Doppler shift (δD=0) is not considered. (a1) Ωp=0.70 MHz; (a2) Ωp=0.83 MHz; (a3) Ωp=0.94 MHz; (b1) Ωp=20 MHz; (b2) Ωp=7.06 MHz; (b3)Ωp=4.9 MHz

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而当考虑原子的多普勒频移效应时,如图3所示,随着δ_D的增大,信号光峰值增益的最大幅度相应减小,且其所对应的Ω_p也相应增大。但在增大区间,除了其吸收背景变宽外,在原子的共振频率中心,增益谱依然保持线宽较窄的单峰结构。而在减小区间,需更大的Ω_p增益才能产生类拉比分裂。在考虑多普勒频移及展宽效应的条件下(δ_D=280 MHz),相同峰值下增益增大和减小区间的增益谱如图5所示。如图5(a)所示,当Ω_p=10 MHz时,正好处于增益增大区间,增益大小约为6.8,而其线宽约为0.9 MHz。而当Ω_p=150 MHz时,刚好对应减小区间的相同增益处,但增益谱显著拓宽,同时产生类拉比分裂,且单个类拉比增益峰的线宽增至约8 MHz,如图5(b)所示。

图 5. 考虑多普勒频移及展宽效应时信号光增益谱的线形变化。(a) Ωp=10 MHz;(b) Ωp=150 MHz

Fig. 5. Gain profile variation of signal light when Doppler shift and broadening effects are included. (a) Ωp=10 MHz; (b) Ωp=150 MHz

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3 实验测量及结果

根据上述理论分析,选择¹³³Cs原子D1线的超精细能级为研究对象,并分别选取基态6²S₁_/₂,F_g=4和第一激发态6²P₁_/₂,F_e=4作为该系统的两个跃迁能级,其中S、P分别表示原子基态和激发态,F表示对应态的总角动量。实验研究了基于热原子介质的EIG效应。两台波长为894.5 nm、频率可连续调谐的光栅反馈半导体激光器出射的光,经单模光纤整形后分别作为信号光和抽运光。图6所示为实验装置的示意图,抽运光以水平偏振(蓝色直线表示)通过一偏振分光棱镜(PBS)后,穿过Cs原子气室中心,并从另一个PBS透射出,利用一光垃圾桶(block)收集,其频率锁定在F_g=4↔F_e=4的跃迁中心;信号光通过一平面反射镜(M)反射,相对抽运光以微小角度穿过Cs泡,并从另一平面镜反射进入探测器(PD),通过控制信号光激光器上的扫描电压,信号光的频率在原子共振中心处连续变化。在信号光的入射光路上插入四分之一波片,定义其快轴方向与入射线偏光偏振方向的夹角为α,因此通过改变α角,可实现信号光的偏振从竖直线偏→左旋圆偏光→竖直线偏→右旋圆偏光→竖直线偏的连续变化。Cs泡内壁长50 mm,双端镀895 nm增透模,有效地减少了Cs泡对光场的线性损耗,紧贴Cs泡侧壁处先固定一热敏电阻,用于探测其温度,然后用三层箔包裹,用以屏蔽外界磁场的影响,屏蔽筒外侧再均匀缠绕电加热带,用于控制Cs泡的温度。信号光和抽运光光斑的有效直径分别为0.60 mm和1.20 mm,两束光之间的夹角约为0.3°。

图 6. 实验装置示意图

Fig. 6. Schematic of experimental setup

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经PD探测得到归一化的信号光透射谱,如图7所示,其中P_s为信号光入射Cs原子气室的入射功率,且P_s=50 μW,Cs原子气室的温度为95 ℃。可以看出,当抽运光功率较小时(P_p=10 mW),在单、双光子共振中心(Δ_s=Δ_p=0)产生的是EIT峰,如图7(a)所示。随着抽运功率的增大,EIT峰的强度也逐渐增大, EIT变为EIG,正如图3、5所示,在增益增大区间,EIG峰依然保持线宽较窄的单峰结构,当P_p=70 mW时,信号光的增益达到饱和,约为19,如图7(b)所示,而其线宽由EIT时的1 MHz增大至约1.8 MHz,如图7中的插图所示。

图 7. 当Ps=50 μW,Δp=0,T=95 ℃时,不同抽运光功率下测得的信号光增益峰幅度。(a) Pp=10 mW; (b) Pp=70 mW

Fig. 7. Experimentally measured gain peak amplitudes of signal light under different pumping powers when Ps=50 μW, Δp=0, and T=95 ℃. (a) Pp=10 mW; (b) Pp=70 mW

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图 8. 信号光增益峰幅度随不同参量的变化趋势。(a)抽运功率;(b)温度

Fig. 8. Gain peak amplitude of signal light with different parameters. (a) Pumping power; (b) temperature

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图8(a)所示为信号光增益峰幅度随抽运功率的变化趋势。当Cs泡的温度较大时,即Cs泡内原子数密度较大时,原子运动速度加剧,引起的多普勒频移及展宽效应更加显著,因此得到与图3中曲线相似的变化趋势。然而,受限于激光器功率,没有测到增益随抽运光功率增大而减小的区间,故实验上并没有观察到增益谱产生的类拉比分裂现象。在固定信号光和抽运场功率的条件下,测量了信号光的增益幅度随Cs温度增大的饱和效应,如图8(b)所示。当Cs泡的温度小于75 ℃时,在双光子共振中心,信号光透射表现为EIT现象;当温度等于75 ℃时,增益产生,并随着温度增大近似呈线性增大;当温度等于95 ℃时,增益接近饱和,并经过近10 ℃左右的饱和区间后,增益随温度又近似呈线性减小。增益减小主要是由于温度增大,原子之间碰撞剧烈,基于基态相干的非线性效率减小,同时高温高粒子数密度的原子介质对抽运光产生的自聚焦效应分散了主导受激辐射的抽运能量。

为了进一步验证图1实验能级系统中左、右旋信号光的等效性,比较了不同的信号光偏振状态对EIG效率的影响,如图9所示。抽运光的偏振始终为水平偏振,当信号光初始为竖直偏振时,将四分之一波片的快轴旋转180°,发现信号光的增益峰幅度呈周期性正弦变化。当信号光和抽运光的偏振严格垂直时(α=0°,90°,180°),产生EIG的效率最大;而当信号光的偏振分别为左旋(α=45°)或右旋(α=135°)圆偏光时,EIG效率最小,如图9中的黑色圆形所示。这是因为,只有当信号光与抽运光的偏振严格垂直时,若定义抽运光为π偏光,信号光可以等效为L和R圆偏光两部分,二者均能产生EIG效应,并在探测时叠加增强;而当信号光为L或R圆偏光时,其可看作两束π/2相位差的相互垂直的线偏光,其中与抽运光偏振相同的那部分光不能产生EIG效应,因此此时的增益幅度最小。当信号光初始为水平偏振(与抽运光偏振相同)时,则在α=0°,90°,180°时,无EIG效应产生;而在右旋(α=45°)和左旋(α=135°)条件下,EIG效率最大,如图9中灰色圆环所示。

图 9. 信号光的偏振状态对增益峰幅度的影响

Fig. 9. Influence of signal light polarization state on gain peak amplitude

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4 结论

理论上讨论了N型简并二能级原子系统中的EIG现象,分析比较了在不同多普勒频移的条件下,信号光增益随抽运强度的变化规律,同时比较了增益谱的线形分别在上升和下降区间的变化特点,得出以下结论。随着抽运光强度的增大,信号光的增益呈现先增大后减小的变化趋势,并且多普勒频移越大,信号光达到最大增益所需的抽运能量越大,同时绝对增益减小。在增益增大区间,增益谱线形一直保持窄线宽的单峰结构;而在减小区间,当抽运光的拉比频率增大至一定程度时,增益谱发生类拉比分裂,产生两个对称分布的增益峰。选择Cs原子的简并二能级跃迁系统,实验上观察到了EIG现象,并进一步比较了抽运强度、Cs泡温度及信号光偏振对增益峰值效率的影响。这些结论丰富了原子相干效应的研究内容,对进一步开展简并能级系统下孪生光束的制备及量子噪声特性的研究提供了理论和实验基础,并对开展基于N形原子-腔耦合系统的光放大特性、多波混频效应及多通道量子态操控等应用研究具有一定的参考价值。

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韩宇宏, 车少娜, 王丹, 周海涛. 基于简并二能级原子系统的电磁诱导增益[J]. 光学学报, 2018, 38(3): 0302001. Han Yuhong, Che Shaona, Wang Dan, Zhou Haitao. Electromagnetically Induced Gain Based on Degenerate Two-Level Atomic System[J]. Acta Optica Sinica, 2018, 38(3): 0302001.

基于简并二能级原子系统的电磁诱导增益下载： 853次

1 引言

2 理论模型及数值模拟

图 1. N型简并二能级系统的示意图

Fig. 1. Schematic of N-type degenerate two-level system

图 2. 不同抽运光拉比频率下信号光的透射谱

Fig. 2. Signal transmission spectra under different Rabi frequencies of pumping light

图 3. 在不同的多普勒宽度条件下,信号光的增益峰幅度随抽运光拉比频率的变化

Fig. 3. Gain peak amplitude of signal light versus Rabi frequency of pumping light under different Doppler widths

图 4. 不考虑多普勒频移(δD=0)时,不同抽运光拉比频率下的信号光增益谱。(a1) Ωp=0.70 MHz; (a2) Ωp=0.83 MHz; (a3) Ωp=0.94 MHz; (b1) Ωp=20 MHz; (b2) Ωp=7.06 MHz; (b3) Ωp=4.9 MHz

Fig. 4. Gain profiles of signal light under different Rabi frequencies of pumping light when Doppler shift (δD=0) is not considered. (a1) Ωp=0.70 MHz; (a2) Ωp=0.83 MHz; (a3) Ωp=0.94 MHz; (b1) Ωp=20 MHz; (b2) Ωp=7.06 MHz; (b3)Ωp=4.9 MHz

图 5. 考虑多普勒频移及展宽效应时信号光增益谱的线形变化。(a) Ωp=10 MHz;(b) Ωp=150 MHz

Fig. 5. Gain profile variation of signal light when Doppler shift and broadening effects are included. (a) Ωp=10 MHz; (b) Ωp=150 MHz

3 实验测量及结果

图 6. 实验装置示意图

Fig. 6. Schematic of experimental setup

图 7. 当Ps=50 μW,Δp=0,T=95 ℃时,不同抽运光功率下测得的信号光增益峰幅度。(a) Pp=10 mW; (b) Pp=70 mW

Fig. 7. Experimentally measured gain peak amplitudes of signal light under different pumping powers when Ps=50 μW, Δp=0, and T=95 ℃. (a) Pp=10 mW; (b) Pp=70 mW

图 8. 信号光增益峰幅度随不同参量的变化趋势。(a)抽运功率;(b)温度

Fig. 8. Gain peak amplitude of signal light with different parameters. (a) Pumping power; (b) temperature

图 9. 信号光的偏振状态对增益峰幅度的影响

Fig. 9. Influence of signal light polarization state on gain peak amplitude

4 结论

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基于简并二能级原子系统的电磁诱导增益 下载： 853次

1 引言

2 理论模型及数值模拟

图 1. N型简并二能级系统的示意图

Fig. 1. Schematic of N-type degenerate two-level system

图 2. 不同抽运光拉比频率下信号光的透射谱

Fig. 2. Signal transmission spectra under different Rabi frequencies of pumping light

图 3. 在不同的多普勒宽度条件下,信号光的增益峰幅度随抽运光拉比频率的变化

Fig. 3. Gain peak amplitude of signal light versus Rabi frequency of pumping light under different Doppler widths

图 4. 不考虑多普勒频移(δD=0)时,不同抽运光拉比频率下的信号光增益谱。(a1) Ωp=0.70 MHz; (a2) Ωp=0.83 MHz; (a3) Ωp=0.94 MHz; (b1) Ωp=20 MHz; (b2) Ωp=7.06 MHz; (b3) Ωp=4.9 MHz

Fig. 4. Gain profiles of signal light under different Rabi frequencies of pumping light when Doppler shift (δD=0) is not considered. (a1) Ωp=0.70 MHz; (a2) Ωp=0.83 MHz; (a3) Ωp=0.94 MHz; (b1) Ωp=20 MHz; (b2) Ωp=7.06 MHz; (b3)Ωp=4.9 MHz

图 5. 考虑多普勒频移及展宽效应时信号光增益谱的线形变化。(a) Ωp=10 MHz;(b) Ωp=150 MHz

Fig. 5. Gain profile variation of signal light when Doppler shift and broadening effects are included. (a) Ωp=10 MHz; (b) Ωp=150 MHz

3 实验测量及结果

图 6. 实验装置示意图

Fig. 6. Schematic of experimental setup

图 7. 当Ps=50 μW,Δp=0,T=95 ℃时,不同抽运光功率下测得的信号光增益峰幅度。(a) Pp=10 mW; (b) Pp=70 mW

Fig. 7. Experimentally measured gain peak amplitudes of signal light under different pumping powers when Ps=50 μW, Δp=0, and T=95 ℃. (a) Pp=10 mW; (b) Pp=70 mW

图 8. 信号光增益峰幅度随不同参量的变化趋势。(a)抽运功率;(b)温度

Fig. 8. Gain peak amplitude of signal light with different parameters. (a) Pumping power; (b) temperature

图 9. 信号光的偏振状态对增益峰幅度的影响

Fig. 9. Influence of signal light polarization state on gain peak amplitude

4 结论

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基于简并二能级原子系统的电磁诱导增益下载： 853次