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基于里德堡原子的无线电光学测量基本原理如图1左图所示,对应的传统标准传感器相应部分示意图如图1右图所示[62]。该技术的核心器件为一个几微米至几厘米大小的常温碱金属原子泡,其在激光的精确调控下转变为里德堡原子,并使其探测光透射光谱产生EIT效应,进而在输入的无线电信号的作用下,使其透明光谱发生AT劈裂,完成无线电信号到光学信号的转化,进而实现无线电信号频率、幅度、相位等信息的提取。里德堡原子是一种处于高激发态的原子,通常使用铷原子或铯原子,因其原子序数大,相比原子序数较小的碱金属原子,其最外层电子基态能级更高,更易被激发到高激发态。这种原子具有特殊的量子特性见表1,包括相邻能级间隔差在无线电频段(DC~THz)、原子半径大、寿命长等[16, 20-23]。相邻能级间隔差在无线电频段使其可以对无线电信号进行响应,且原子传感器尺寸与无线电信号波长无关;而其原子半径大,导致其电偶极矩很大,因此对无线电信号电场非常敏感;长寿命则导致其与外场可以有很长的相干时间,增强光学信号的同时,也为实验操控提供了便利。
表 1 碱金属原子量子特性对主量子数(n)的依赖关系[23]
Table 1. Alkali atom principal quantum number (n) scaling of the most important properties of Rydberg states[23]
Property Quantity Scaling Energy levels En n−2 Level spacing ∆En n−3 Radius 〈r〉 n2 Transition dipole moment ground to $|\langle n \ell|-e r| g\rangle| $ n−3/2 Rydberg states Radiative lifetime $\tau $ n3 Transition dipole moment for adjacent $\left|\left\langle n \ell|-e r| n \ell^{\prime}\right\rangle\right|$ n2 Rydberg states Rcsonant dipole-dipole interaction coefficient C3 n4 polarisability $\alpha $ n7 van der Waals interaction coefficient C6 n11 基于里德堡原子的无线电光学测量在技术实现上通常采用双光子激发方案,主要实验装置包括:铷原子或铯原子蒸气室、480 nm (或510 nm)的控制光激光器、780 nm (或850 nm)的探测光激光器以及探测光的光电转换器件等部分,见图2[62]。其中图2(a)为实验设置,红光和蓝光分别代表探测光(probe laser)和控制光(control laser或耦合光coupling laser),两束激光对向重合入射通过原子泡以尽可能抵消多普勒展宽效应,图2(b)为原子能级结构设置,探测光与原子的基态$ 2\; \mathrm{kHz} $和第一激发态$ |2\rangle $发生电偶极耦合,频率失谐量为$ \Delta_{p} $;耦合光与原子的第一激发态$ |2\rangle $和里德堡态$ |3\rangle $发生电偶极耦合,频率失谐量为$ \Delta_ c $,无线电信号(射频场RF或微波场MW)与原子的里德堡态$ |3\rangle $和里德堡态$ |4\rangle $发生电偶极耦合,频率失谐量为$ \Delta_{R P} $。两个激光场激发原子到里德堡态,此时价电子距离原子实较远,可以看成是对某些频率($ \omega_{RF} $)非常敏感的偶极子。如要激发铷(铯)原子到Rydberg态,可以应用波长为$ \lambda p \approx 780\; \mathrm{nm}(\lambda p\approx 852\; \mathrm{nm}) $的近红外激光,和波长为$ \lambda c \approx 480 \; \mathrm{nm}(\lambda c \approx 510 \; \mathrm{nm}) $的可见激光。利用EIT-AT效应检测无线电信号时,通常扫描或锁定$ \Delta_{c} $(或$ \Delta_{p} $),此时$ \Delta_{c} $≈0(或$ \Delta_{p} $≈0)和$ \Delta_{R F} $≈0[62]。其中两个光场在原子泡中反向传播,以尽可能抵消多普勒效应。探测光与控制光和原子发生量子相干过程,产生EIT现象。无线电信号作为缀饰场与原子进行耦合,改变原子的量子状态,进而对通过原子的探测光光场进行调制,产生EIT光谱的AT劈裂现象。与传统天线不同,原子天线不会吸收无线电信号的能量,可以实现隐蔽传感[16]。除了这种典型的双光子激发方案之外,还有三光子激发方案等[37, 46, 71-73]。
当原子在激光激励下被制备到Rydberg态$ |3\rangle $时,原子将对与邻近Rydberg态$ |4\rangle $的跃迁共振或近共振的无线电信号非常敏感。如果入射的无线电信号与原子的量子状态远离共振区域,此时仍会引起能级$ |3\rangle $的Stark频移[26]。通过对出射探测光的光学检测,进行光谱分析,可以提取入射无线电信号的特性。
图3显示了在理想情况下不同外场对探测光输出光谱的影响。在只有探测光通过原子的情况下,当调整光的频率与原子接近共振时,会发生强烈吸收现象,见图3(a)。当控制光被打开时,一部分原子被激发到Rydberg态,此时会出现EIT的现象,即在探测光的吸收光谱中出现一个窄带宽的高透明窗口,见图3(b)和图3(c)。最后,当与邻近的里德堡态发生共振或近共振的无线电信号入射时,诱发EIT光谱的AT劈裂[27],见图3(d)。这种原子与外场量子干涉产生的EIT-AT效应,即是基于里德堡原子的无线电光学测量的基本原理。
事实上,发生AT劈裂现象时,里德堡原子对外界无线电最敏感,此时RF或微波场与特定原子能级跃迁处于谐振或接近谐振状态。由于原子的里德堡能级十分丰富,因此可以谐振响应的无线电频段可以包含DC~THz频段范围内的数万个离散载波频率[16, 23, 68]。然而当无线电信号频率低于100 MHz时,原子接收机谐振响应频点非常密集,相互干扰会较大。因此,为了减少干扰,还可利用非谐振时的AC Stark频移效应用于测量载波频率低于UHF的场。非谐振区域的灵敏度比谐振区域差,但已经有原理验证实验表明,对于足够强的电场,该传感器可以感知连续可调频率直至接近DC[21, 24, 49]。
在探测光透射光谱发生AT劈裂现象时, AT劈裂宽度$ \Delta f_{P} $与无线电信号的强度$\vec{E}_{{RF}}$及原子跃迁电偶极矩$\; \overline{\mu}_{{RF}}$成线性关系:
$$ \quad \quad \Delta f_p=\left\{\begin{array}{cl} \dfrac{\lambda_c}{\lambda_p} \dfrac{\varOmega_{{RF}}}{2 \pi} & \text { if } \Delta_p \text { is scanned } \;\; \quad \quad \quad \quad (\text{1a})\\ \quad \quad \dfrac{\varOmega_{{RF}}}{2 \pi} & \text { if } \Delta_c \text { is scanned } \quad \;\; \quad \quad \quad (\text{1b}) \end{array}\right. $$ 式中:控制光波长和探测光波长之比($ \lambda_{c} / \lambda_{p} $)源自于扫描探测光时的两个激光场之间的多普勒失配[74-75];${\varOmega}_{{RF}}$为无线电信号对应的原子跃迁Rabi频率。${\varOmega}_{{RF}}$与电场强度成正比为:
$$ \varOmega_{{RF}}=\frac{\vec{\mu}_{{R} E} \cdot \vec{E}_{{R} E}}{\hbar} $$ (2) 式中:$ \hbar $为约化普朗克常数。根据公式(2)可以发现,基于里德堡原子的无线电光学测量技术无需像偶极天线一样进行校准,可以直接溯源到基本物理学常数,即普朗克常数。此外,最小可感知的电场强度${E}_{\text {min }}$由最小可分辨的AT劈裂宽度$ \Delta f_{P} $决定。在AT劈裂区域,最小可感知的电场强度与测量时间和相互作用强度成反比[51]:
$$ {E_{{\text{min}}}} = \frac{h}{{|{{\vec \mu }_{{{RF}}}}|{T_{{\text{meas}}}}\sqrt N }} $$ (3) 式中:$ h $为普朗克常数;$ {T}_{{\rm{meas}}} $为测量时间;$ N $为独立重复测量次数[51]。可以看到,电偶极矩越大,测量时间越长,有效参与测量的原子数目越多,基于里德堡原子的无线电光学测量的最小可测场强越小[69]。由于原子波函数的投影测量具有概率性,因此这种关系通常被称为原子散粒噪声极限。
当测量时间大于退相干时间$ {T}_{2} $时,公式(3)的定义必须进行调整,此时可将$ {T}_{{\rm{meas}}} $取为$ {T}_{2} $,并且将独立测量次数$ N $取为$N=N_{{a}} T_{\text {int }} / T_{2}$,其中${T}_{\rm{int}}$是总积分时间,$ {N}_{a} $是激发的Rydberg原子的平均数量,每个原子单次参与测量的时间为$ {T}_{2} $,则原子散粒噪声下的最小可测场强为[51]:
$$ E_{\min }=\frac{h}{\left|\vec{\mu}_{{RF}}\right| \sqrt{N_{a} T_{{\rm{int}} } T_{2}}} $$ (4) 需要注意的是,在给定体积内的Rydberg原子密度受到阻塞半径(blockade radius)的限制,而Rydberg原子的总数受到两束激光场与原子泡重叠体积大小的限制。当原子气体温度从常温到超冷变化时,人们对Rydberg原子数量$ {N}_{a} $的估计值在100[24]和1000[76]之间,远低于阻塞半径的限制,可以改进的方法包括使用更高功率的激光、专门的磁光陷阱等[62]。对于热原子,退相干速率会受到渡越时间展宽的限制,即原子离开光场横截面区域所需的时间。渡越时间引起的退相干速率由光束宽度和原子温度决定;对于$1 / \rm{e}^{2}$束腰半径为$ 100\; \text{μm}\left(1 \;{\rm{mm}}\right) $的光束,该速率在室温下约为$ 2 \pi \times 370 \;{\rm{kHz}}\left(2\pi \times 37 \; {\rm{kHz}}\right) $[77]。对于冷原子,由于原子可在光场横截面内停留更长时间,因此其退相干速率较低,约为1 kHz~1 MHz[77]。
基于里德堡原子的无线电光学测量还可通过交流斯塔克效应[29],分析与原子能级相关联的探测光输出光谱特征的变化,测量与量子态$ |4\rangle $态非共振的射频或微波场,但相比于利用共振干涉的EIT-AT效应的无线电光学测量灵敏度要低,非共振场测量技术包括混频检测方案[14, 21, 49]、自校准方案[24, 44]等,可用于精密计量[44]和超宽带频谱分析[21]。
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基于里德堡原子的无线电光学测量的实验设置包括3个方面:(1)是原子系统内部量子状态(能级系统)的选择;(2)是影响或改变原子系统量子状态的外场设置;(3)是将原子感知到的状态变化通过特定的物理现象转化为便于读取的信号。
从基于里德堡原子的无线电光学测量的基本原理可以发现,无线电信号信息快速准确读取的关键在于对原子系统输出光谱特征的分析。针对静态无线电信号、动态无线电信号、单频无线电信号、多频无线电信号等不同类型的无线电信号,对应的信息提取和光谱处理方式也不同,将在下文进行详细介绍。
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基于里德堡原子的无线电光学测量技术,最先被用于单频静态无线电信号的传感,包括射频信号、微波信号、甚至太赫兹波段,以实现无需校准的电场强度的绝对测量及成像应用。
2012年11月,美国俄克拉荷马大学和德国斯图加特大学的James P. Shaffer等人首次报道了基于里德堡原子EIT-AT现象的($ 14.233\;0\pm 0.000\;1 )\;{\rm{GHz}} $静态微波场的光学测量实验,能级系统和实验装置如图4所示,其中图4(a)右侧插图为微波场关闭和打开时分别对应的探测光透射光谱中的EIT和EIT-AT现象,微波电场测量灵敏度达到30 μV·cm−1·Hz−1/2,可探测的最小场强达到8 μV·cm−1 [15];2013年,这个研究小组首次实验演示了单频静态微波电场的矢量测量,实现微波电场偏振分辨率为0.5°[40],并在2014年首次将该传感技术用于微波电场成像,在6.9 GHz上的成像空间分辨率为66 μm (~λ/650)[68];2015~2017年又分别采用了基于Mach-Zehnder干涉仪的零差探测技术和频率调制技术改进了测量,并将微波电场探测的灵敏度优化至3 μV·cm−1·Hz−1/2[45, 51, 78] 。美国国家标准技术研究院的Christopher L. Holloway等人分别在2014、2016、2017年进行了跟进研究,开展了里德堡原子电场计的创新应用,把可探测场推进至毫米波,甚至是太赫兹波段[54, 79-80]。美国密歇根大学G. Raithel教授等人则在2016、2017年重点研究了微波强电场测量,通过比对Floquet模型和实验结果,在Ka波段实现了±1 GHz带宽、强度达到2.3~10 V·cm−1的强微波电场的测量,精度达到6%[31, 81],并于2019年基于改进的Floquet模型,实现了50~500 MHz频段高达50 V·cm−1强微波电场的测量,频率精度和场强精度分别达到1%和1.5%[82]。
图 4 针对单频静态微波电场的里德堡原子光学测量的能级设置和实验装置示意图[15]。(a)四能级系统的能级图,插图顶部为关闭微波场时的EIT光谱,插图底部为打开微波场时的EIT-AT光谱;(b)实验设置
Figure 4. Level scheme and experimental setup for Rydberg atomic optical measurement of a single-frequency static microwave electric field[15]. (a) Level diagram of the four-level system, with the top inset showing the EIT spectrum when the microwave field is off and the bottom inset showing the EIT-AT spectrum when the microwave field is on; (b) Experimental setup
国内相关团队在微波电场测量研究方面也有显著进展。2020年,山西大学由贾锁堂和肖连团等人带头的激光光谱研究团队,在基于里德堡原子的微波精密测量研究中取得了突破性进展,在国际上首次实现里德堡原子微波超外差接收机样机,极大地提升了微波电场场强的探测灵敏度,微波测量灵敏度达到55 nV·cm−1·Hz−1/2,最小可探测到的微波场强约为780 pV·cm−1,大大超过了原有相关记录[20]。2020年,南京航空航天大学的潘时龙等人提出了一种光子辅助的原子系统,用于在大光谱范围内测量微波信号的频率和相位噪声,待测量的频率和相位噪声均从被测信号与其参考信号之间的相位差中提取,该相位差被可变光延迟线(VODL)所延迟。系统校准、频率测量和相位噪声测量是通过在不同的工作模式下调整VODL来执行的,实验证明了在5~50 GHz较大频率范围内对微波信号的频率和相位噪声的精确测量[83]。2021年,中国科学院大学的贾凤东等人设计了一种配置有辅助微波的里德堡原子微波电场计,最小可测场强达到μV·cm−1,该方法比测量探测光透光率变化的方法更准确、直观和方便[36];并于2023年提出在不加本地辅助微波场情况下,基于EIT-AT效应的色散光谱直接测量微波场电场强度的新方法,测得的最小电场强度可达0.056 mV·cm−1,比通常采用的通过EIT-AT透射光强劈裂宽度直接测得的最小值低30倍[84]。2020年,华南师范大学的廖开宇等人将冷原子样品中的电磁感应吸收(Electromagnetically Induced Absorption, EIA)线宽缩小到500 kHz,进一步利用EIA-AT分裂,实现了在线性区域内可测量的最小微波场强度的分辨率为100 μV·cm−1[35];并于2022年提出应用两个失谐微波场作为可调谐本地振荡场的新型外差技术方案,从而可以在超过1 GHz的连续频率范围检测信号微波的幅度、相位和频率信息,远超传统谐振外差的频带范围,灵敏度可达1.5 μV·cm−1·Hz−1/2,实现80 dB的线性动态范围[34]。2022年,中国科学技术大学丁冬生等人基于AC Stark效应和非共振外差技术,通过引入一个本地振荡电场来放大系统对微弱信号电场的响应,通过测量探测光的电磁诱导透明光谱得到信号电场的强度,实现了对30 MHz微波电场的高灵敏度测量,最小电场强度为37.3 µV·cm−1,灵敏度为−65 dBm/Hz,动态范围超过65 dB[57];并紧接着提出利用相变临界点处强相互作用的多体原子系统代替单原子系统测量微波电场的新方法,显著提高了测量微波的精度和灵敏度,灵敏度达到49 nV·cm–1·Hz–1/2[85]。
总体来看,基于里德堡原子的单频静态无线电信号传感的光谱处理主要分为四种情形,分别对应输入的无线电信号强度为微弱、中等强度(较弱、较强)和很强。其中中等强度无线电信号的测量相对容易实现。
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对于中等强度的无线电信号,探测光输出光谱主要特征表现为EIT透明峰的下降(较弱强度)和AT劈裂(较强强度)如图5所示[15]。当选择使用的原子里德堡态不同时,该方案适用的信号电场强度也不同,总体处在0.1 mV·cm−1~0.1 V·cm−1之间[40, 51, 61]。此时,探测光输出光谱的特征提取是通过读取AT劈裂宽度来实现的。根据公式(1)中所给出的无线电电场强度与AT劈裂宽度成正比的关系即可得到电场强度的大小。其中图5(a)为较弱微波电场强度下EIT透射峰的衰减(黑色)及其理论光谱曲线(红色)。理论和实验之间的差异归因于这些图中使用的是忽略了精细能级的四能级理论而不是包含精细劈裂能级的完整52能级理论,以及渡越时间展宽具有随机性。图5(b)为较强微波电场强度下发生的53D5/2→54P3/2里德堡跃迁的AT劈裂光谱,劈裂宽度为$\lambda_{v} / \lambda_{p} \varOmega_{{\rm{M W}}} / 2 \pi$(公式(1a))[15]。
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对于微弱强度的无线电信号,此时里德堡原子与无线电信号的相互作用强度不足以使EIT峰发生AT劈裂,探测光输出光谱主要特征表现为EIT透明峰增强,见图6[15]。图6(a)为EIT峰值增强程度随电场强度的变化,红线代表理论,黑线代表实验数据。随着电场强度逐渐增加到Autler-Townes区域,峰值处的透射率开始降低。图6(b)为在微弱强度下,当增加微波电场强度时,EIT透射率增强的物理机理,即EIT透射率增加是由原子速度空间扩展引起的。当选择使用的原子里德堡态不同时,该方案适用信号电场强度也不同,总体处于μV·cm−1~mV·cm−1之间[15, 20, 34]。
此时,探测光输出光谱的特征提取是通过读取EIT透明峰的高度变化来实现的,如图7所示。图7(a)为微波场微弱区域电场强度和频率失谐量对探测光透射光谱的影响。黑色曲线是实验数据,进行了9 000次平均;红色曲线是对数据进行高斯拟合得到的结果。图7(b)为EIT透明峰高度对微波电场强度的依赖情况。2012年,美国俄克拉荷马大学和德国斯图加特大学的James P. Shaffer等人据此测得的灵敏度为~30 μV·cm−1·Hz−1/2,最小场强为8.33 μV·cm−1[15]。需注意在弱场时,无线电信号电场强度与EIT透明峰高度之间的关系是复杂的非线性关系(见图7(b))[15],难以表述成为一个简单的比例公式,在理论上,可通过光学布洛赫方程(Optical Bloch Equation, OBE)来进行严格求解[18, 86]。
图 7 微弱微波电场测量的光谱图[15]。(a)微波场对探测光透射光谱的影响;(b) EIT透明峰高度对微波电场强度的依赖
Figure 7. Transmission spectrum induced by a weak microwave electric field[15]. (a) Effect of the microwave field on the transmission spectrum of the probe laser; (b) Dependence of the EIT transparency peak height on the microwave electric field strength
实际中,除了对微弱信号直接探测以外,人们还可以采用增加本地微波场,如超外差方法[20, 34, 48, 57, 85],使输出光谱状态处于EIT区域,然后再对微弱信号进行传感接收,优点在于能够根据光谱特性,选择灵敏度较高的测量点进行测量,对于特定微波场强产生尽可能大的光学信号变化,可以提高灵敏度,代价则是需要本地微波天线,这可能限制原子天线本身优势的发挥,比如超宽频谱特性等。
2020年,山西大学贾锁堂和肖连团等人针对拉比频率$ {\mathrm{\varOmega }}_{s} $远小于EIT线宽的6.947 GHz超弱微波场,提出了基于里德堡原子的无线电超外差接收机,实验设置如图8所示[20]。图8(a)为能级结构设置,态$|1\rangle $、$|2\rangle $和里德堡态$3\rangle $分别通过探测光场($ {\varOmega }_{p} $)和控制光场($ {\varOmega }_{c} $)场进行共振耦合。本地微波电场(蓝色)通过拉比频率$ {\varOmega }_{L} $共振驱动电偶极跃迁$|3\rangle \text{-}|4\rangle $。微弱信号微波(红色)与本地微波具有相位差$ {\phi }_{s} $和频率差$ {\delta }_{s} $的耦合$\varOmega_{s} {\rm{e}}^{-i\left(2 \pi \delta_{s} t+\phi_{s}\right)}$。图8(b)为在本地场调制下的微波电场测量示意图。在较强本地微波的作用下,探测光透射率发生EIT峰的Autler-Townes劈裂现象[18]。共振透射点$ {\overline{p}}_{0} $位于EIT谱线半腰上(斜率为$ \mid \kappa \mid $),在里德堡缀饰态$ \left|\pm \right.⟩ $中会出现能量位移:$\pm E_{1}= \pm \hbar \varOmega_{s} \cos \left(2 \pi \delta_{s} t+\phi_{{s}}\right) / 2$,此时透射率处于线性变化区间。当能量扰动$ \pm {E}_{1} $将两条EIT线向外移动时,这种移动以速率$ \mid \kappa \mid $线性地转化为共振处光透射率的变化。
因此,通过调节$ {\varOmega }_{L} $,可以调整EIT线的轮廓,从而使得$ {\overline{p}}_{0} $处的斜率$ \mid {\kappa }_{0}\mid $最大,即检测$ {E}_{1} $的最佳点。图8(c)为由本地微波 $ {E}_{L\left(t\right)} $缀饰的里德堡原子组成的超外差接收机实验设置示意图,可以检测信号微波的频差、相位和线性放大的探测光输出${P}_{\rm{out}}\left(t\right)$:
$$ P_{\text {out }}(t)=P(t)-\bar{P}_{0} = \left|P\left(\delta_{s}\right)\right| \cos \left(2 \pi \delta_{s} t+\phi_{s}\right) $$ (5) 由共振点处输出光信号的变化量$ \left|F\left(\delta_{s}\right)\right| $可以获得信号微波场的拉比频率$ {{\varOmega }}_{s} $:
$$ \varOmega_{s}=\frac{\left|P\left(\delta_{{s}}\right)\right|}{\left|\kappa_{0}\right|} $$ (6) 然后再由公式(2)即可获知$ {E}_{s} $。基于里德堡原子的超外差无线电光学测量输出光谱处理如图9所示。其中图9(a)为不同本地场强$ {E}_{L} $下的$\left|F\left(\delta_{s}\right)\right| $,可以看到最佳测量点的存在,该点对应的EIT-AT光谱见图9(b),对应的本地场电场强度${E}_{L} = 3.0 \;{\rm{mV}} \cdot{{\rm{cm}}}^{-1}$,对应的拉比频率${{\varOmega }}_{L} = 2\pi \times 7.9 \;{\rm{MHz}}\sim {{\varGamma }}_{EIT}$。图9(c)为分别利用原子超外差检测共振频率处探测光透射率变化、使用标准原子电场计[15, 51]检测共振频率处探测光透射率变化和根据公式(1)测量AT劈裂宽度等三种不同方法来测量信号微波电场强度时的光谱处理结果。最终发现,使用原子超外差方法具有更大的线性动态范围,可达90 dB,并极大地提升了微波电场场强的探测灵敏度,可达55 nV·cm−1·Hz−1/2,最小可探测微波场强可达780 pV·cm−1,超过了原有相关记录[20]。
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传统无线电信号电场测量主要是基于电偶极天线和整流二极管实现的[3-4],由于金属结构感应电场的干扰、工艺差异、短期和长期漂移等因素,使用中需要定期校准,对高强度无线电信号电场测量精度有限,不确定度通常大于1 dB或5%[87-89]。
对于强场无线电信号,原子对外界微波场的响应已经超出了探测光输出光谱的AT劈裂线性动态范围,此时探测光输出光谱主要特征表现为强烈的AC Stark频移效应,如图10所示[81],实验光谱图用线性灰度表示,理论仿真结果用圆点表示。当选择使用的原子里德堡态不同时,该方案适用的信号电场的强度也不同,总体处在0.1~10 V·cm−1之间[31, 81-82]。其中图10(a)为相对较弱场强下,与铷原子26D5/2-27P3/2耦合的132.6495 GHz微波场引起的原子能级频率偏移量与电场强度的关系,此时光谱表现为线性度较好的AT劈裂;图10(b)为相对强场情形下,与铷原子65D–66D耦合的12.4611548 GHz微波场引起的原子能级频率偏移量与电场强度的关系,此时光谱表现为非线性的AC Stark频移[81]。
探测光透射EIT光谱反映了里德堡原子对高强度无线电信号电场的量子响应,进一步将实验光谱图与Floquet模型计算的参考光谱进行比较,即可读取无线电信号电场幅度、频率和相位等参数的测量值[81]。
在强直流电场中,不同角动量对应的精细结构能级发生退简并,能级重新耦合成Stark态,在弱场中表现出近似二次移位,在强场中表现出线性移位[16]。典型实验方案如图11所示。图11(a)为设备设置和能级结构设置。其中85Rb原子玻璃泡是圆柱形结构,横截面为10 mm×10 mm;电场由泡内的两个平面金属电极产生,两个电极长度为9 mm、宽度为0.5 mm、厚度为3 mm、间距为d=(380±15) μm,电场强度可达10 kV/m;原子能级结构为三能级阶梯型结构[90],两束窄线宽激光(线宽小于1 MHz,光斑FWHM小于70 μm)与原子量子干涉,在780 nm探测光透射光谱上形成电磁诱导透明(EIT)现象。图11(b)为探测光透射光强随着480 nm控制光频率失谐量变化的光谱图,当控制光的频率恰好与某个原子里德堡态能级共振时,可以看到探测光透射率急剧增加,即出现EIT峰。在控制光2 GHz频率扫描范围内,可以看到在35D5/2和35D3/2两个能级处出现了两个ETI透明峰。在直流电场下,探测光透射光谱随着电场强度的变化情况,其中品红色实线是Floquet模型[81]计算的结果,见图11(c)。
在强交流电场下,交流电场频率的偶次谐波会出现在探测光的EIT光谱中[28],并会产生复杂的射频调制边带,具有交流斯塔克位移和交叉或反交叉现象[91],如图12所示。图12(a)为里德堡原子在50 MHz视频交流电场耦合下的EIT光谱随场强的变化,在控制光的2 GHz扫描范围内存在30D5/2和30D3/2两个里德堡能级,随着电场强度的增加,偶次谐波分量出现,对应的AC斯塔克频移为$ 2 n \nu_{rf} $,蓝色和红色圆圈分别对应$ m_{J}=1 / 2 $和$ m_{J}=3 / 2 $情形下的Floquet模型计算结果;图12(b)为电场强度为41.5 dBI时,里德堡原子在50 MHz交流电场耦合下的EIT光谱,在光谱上出现了6个谐波峰,平均频率间距为$( 99 \pm 4) \;{\rm{M H z}}= 2 v_{r f} $,考虑了$ m_{J}=1 / 2 $和$ m_{J}=3 / 2 $的总贡献之后,Floquet模型计算的结果用圆圈表示;图12(c)为电场强度为46 dBI时,里德堡原子在不同频率交流电场耦合下的EIT光谱,其中难以分辨的小峰的包络存在$ -5 \nu_{rf} $大小的周期。实际在强场下,n阶谐波诱导的n阶边带的频率位置有经验公式$ \Delta_{c}=-(\alpha / 4) E_{r f}^{2}-n h V_{r f} $[28]。
图 12 射频强交流电场下的探测光EIT光谱图[82]。(a)里德堡原子在50 MHz交流电场耦合下的EIT光谱随场强的变化;(b)电场强度为41.5 dBI时,里德堡原子在50 MHz交流电场耦合下的EIT光谱;(c)电场强度为46 dBI时,里德堡原子在不同频率交流电场耦合下的EIT光谱
Figure 12. EIT spectrum of the probe laser under strong ac fields[82]. (a) EIT spectrum of Rydberg atoms coupled to a 50 MHz ac field as a function of field strength; (b) EIT spectrum of Rydberg atoms coupled to a 50 MHz ac field with an electric field intensity of 41.5 dBI; (c) EIT spectrum of Rydberg atoms coupled to ac fields at different frequencies with an electric field intensity of 46 dBI
通过比较实验测得的EIT光谱和Floquet模型计算得到的EIT光谱,美国密歇根大学G. Raithel等人在Ka波段实现了±1 GHz带宽、强度达到2.3~10 V·cm−1的强无线电信号电场的测量,精度达到6%[31, 81],在50~500 MHz频段实现了高达50 V·cm−1强无线电信号电场的测量,频率精度和场强精度分别达到1%和1.5%[82],高于传统测量方式。
从相关文献可以看出,对于不同强度范围的无线电信号,必须利用不同的物理效应来进行信息的光学读取,光谱处理方法也有差别。进一步说明了里德堡原子与激光和无线电信号之间有着非常丰富的物理现象,可以用来应对各种不同的应用场景,在取代部分传统天线上具有前景。
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随着静态无线电信号测量技术的发展,人们开始考虑推广该技术的应用场景,首先即是基于单频动态无线电信号测量的无线通信接收,其中里德堡原子无线通信接收机与传统无线通信接收机的信号解调过程基本原理对比如图13所示。
2018年3月,美国陆军研究实验室首次提出将基于里德堡原子的无线电光学测量技术拓展应用到无线通信领域,并开展了具体的原理验证。在美国国防部长办公厅“量子科学与工程”项目支持下,美陆军研究实验室在国际上率先发表了基于里德堡原子EIT-AT效应的微波通信原理验证实验,D. H. Meyer等人利用铷87原子的里德堡能级50D5/2和51P3/2实现了17 GHz微波载频下基于8PSK调制方式的8.2 Mbit/s通信速率的实验演示[61];该团队在DARPA项目支持下,2020年1月从理论角度分析了从1 kHz~1 THz宽频谱和宽振幅范围的微波电场灵敏度,并且利用铷87原子的里德堡能级50D5/2、60D5/2和70D5/2开展了对1~20 GHz微波频率的探测实验,通过与电光晶体接收机和偶极子耦合无源接收机进行对比,发现里德堡原子无线通信接收机的灵敏度与这两种典型无线接收机相当[14];同样在DARPA项目支持下,2021年1月通过微波波导耦合增强和大失谐下交流Stark效应这两个技术手段的改进,该团队开发了基于里德堡原子的微波传感器和频谱分析仪并对0~20 GHz的无线电信号进行采样,实验信号包括调幅(AM)、调频(FM)、Wi-Fi、蓝牙以及其他通信信号,结果表明新系统能够超越传统射频传感器、接收机和频谱分析仪的灵敏度、带宽和精度极限[21];并于2023年提出了多波带通信和空分复用通信技术的新方案[92-93]。
此外,其他国外研究团队也对基于里德堡原子的无线通信接收机开展了相关研究。2019年,美国国家标准技术研究院和美国科罗拉多大学Christopher L. Holloway等人开展了相位调制方面的实验研究,通过引入一个与探测光频率极其接近的本地光信号,利用零差探测或外差探测将20 GHz高频电磁波的相位探测转换为kHz量级的零差或外差信号的相位探测,实验证实了该方法可以较为精确地探测出电磁波的相位信息,与理论值的误差可以缩小到0.1%以内[41];并于2022年通过调整原子响应速率,实现了480 i NTSC格式彩色电视和游戏视频信号的实时接收[65]。2021年,美国里德堡技术公司的Anderson等人进行了AM和FM通信实验,实现基带3 dB带宽为100 kHz,初步论证了全光电路、多波带、高灵敏度和对电磁干扰可恢复性强等特点[60]。2018年,新西兰奥塔哥大学Amita B. Deb等人尝试了无损光纤直连光电检测器的方案,并通过实验测试到信号带宽为1 MHz,论证了通信带宽主要受限于控制光光强和原子的光学密度[94]。2023年,英国电信和伯明翰大学的Marco Menchetti等人报道了基于里德堡原子的5 G频率载波(3.5 GHz)信号通信接收技术的实验验证,通信速率达到238 kbps[95]。
国内相关团队在原子无线电信号接收研究方面也展开了初步的探索。2019年,中国计量院宋振飞等人在10.22 GHz处开展了原子通信实验,通过探测对称或不对称的EIT-AT劈裂峰中心频率处的探测光场强来实现,实现了200 MHz以内的500 kbps速率的可调带宽数字通信[64]。同年,山西大学焦月春等人利用16.98 GHz载波与铯原子60S1/2-60P1/2跃迁共振诱导产生EIT-AT分裂,验证了幅度调制AM通信接收的可行性,信号保真度>95%,基带带宽约为60 kHz,动态范围约为30 dB[59]。2023年,中国科学院精密测量科学与技术创新研究院刘红平等人报道了基于里德堡原子的1.2 GHz和31.9 GHz双微波场同时通信接收实验,发现两个微波场的通信质量会相互影响,并验证了多波带通信的可行性[73]。2023年,华南师范大学和中国科学院精密测量科学与技术创新研究院的朱诗亮和颜辉等人报道了基于里德堡原子的8 PSK调制方式下的338.7 GHz太赫兹通信实验,通信距离有望达到18 km[96]。
与单频静态无线电信号的测量不同,无线通信接收要求里德堡原子系统能够对快速时变的无线电信号实时跟踪响应,并在末端实现EIT光谱变化特征的快速读取。基于单频动态无线电信号测量的无线通信接收实验设置如图14所示[61]。图14 (a)为两束激光对向入射与铷原子相互作用的双光子激发方案,波长分别为780 nm和480 nm,对应耦合的原子能级跃迁分别为5S1/2-5P3/2和5P3/2-50D5/2,原子能级结构如图14 (b)所示。微波场载波频率是$ \omega_{\mu}=17\; \mathrm{GHz} $,与原子能级跃迁50D5/2-51P3/2耦合,拉比频率为$ \varOmega_{\mu} $,同时微波场还叠加有基带信号,调制频率为$ f_{m} $,调制方式为8 PSK。图14 (c)和(d)为两种可选的探测光输出光谱读取方式,分别是直接探测和外差探测。
基于单频动态无线电信号测量的无线通信接收光谱处理如图15所示。图15 (a)为微波场打开和关闭时的EIT和EIT-AT光谱图。通信中采用8PSK的微波场幅度调制,对应图15 (b)右上角相图中的8个取值。通过与微波关闭时的EIT谱相减,图15 (b)给出了其中5个取值时的探测光输出光谱图。$ V_{I} $和$ V_{Q} $分别为锁相放大器的两个输出电压,信号微波的调制相位为$ \phi_{\mu}=\arctan \left(V_{Q} / V_{I}\right) $。图15 (c)即为输出的相位图。
图 15 基于单频动态无线电信号测量的无线通信接收光谱处理过程[61]。(a) EIT-AT光谱;(b)加上8 PSK调制后的光谱图;(c)输入输出的相位对比;(d)输出相位的轨迹图
Figure 15. Wireless communication receiver spectral processing based on single-frequency dynamic radio signal measurement[61]. (a) EIT-AT spectrum; (b) Spectrum with 8 PSK modulation; (c) Phase comparison between input and output; (d) Trajectory of the output phase
根据图15得到的探测光输出光谱,可以分析出基于单频动态无线电信号测量的无线通信的性能,其中最重要的是信道容量。估计信道容量的关键是带宽,即光电探测器输出电压或探测光输出光强变化的最小切换时间,即所谓的上升、下降时间。图16 (a)为探测光输出光强随信号微波调制的时域轨迹图;图16 (b)和图16 (c)分别为下降、上升时间与对应的主要影响因素的依赖关系,可以看到上升、下降时间主要受到控制光光功率的制约,且下降时间存在极限;图16 (d)为符号速率与信道容量的关系。通过优化,马里兰大学和美国陆军研究实验室的David H. Meyer等人将信道容量提高到了8.2 Mbit/s[61]。
图 16 基于单频动态无线电信号测量的无线通信接收信道容量估计。(a)通信接收时的探测光信号时域图;(b)和(c)为不同泵浦速率下的上升沿和下降沿;(d) 信道容量与采样速率的关系[61]
Figure 16. Wireless communication receiver channel capacity estimation based on single-frequency dynamic radio signal measurement. (a) Time-domain plot of the detected optical signal during communication reception; (b) and (c) Rising and falling edges at different pump rates; (d) Relationship between channel capacity and sampling rate[61]
通过相关研究可以发现,基于里德堡原子的无线通信接收可以通过监测探测光EIT-AT光谱的实时变化将载波上的中频或基带信号直接转换为光信号,实现直接解调[61, 63-64, 70, 95],已经验证的通信方式包括幅度调制AM[59, 61, 97]、频率调制FM[21, 53, 63]、相位调制PM[41, 98-99]等。
值得注意的是,与单频静态无线电信号测量时通常对探测光或控制光扫谱不同,对于单频动态无线电信号,由于信号参数在快速实时变化,扫谱会限制调制速率。因此在文献中,人们通常是通过固定探测光频率到某一个数值,然后通过测量该频率点上的探测光透射率的快速变化,来实现调制解调的。但是这种方法也存在缺点,特别是当同时存在多个频率的无线电信号时,探测光输出光谱会变得非常复杂,此时仅从某一个频率上的探测光透射率的变化来同时解调出多个频率无线电信号的信息就会变得非常困难,甚至不可能,这时需要采用新的方法。
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里德堡原子具有丰富的能级结构,基于EIT效应,可以对DC~THz范围内几乎连续频谱的无线电信号进行共振或非共振的响应。因此,利用里德堡原子天然可以实现多频无线电信号的同时测量感知。对于多频无线电信号的测量,探测光输出光谱会变得非常复杂,如何快速有效地从中读取和分辨不同频率无线电信号的信息是一个很大的挑战,相关研究还相对较少。当前的相关研究集中在对于动态多频无线电信号,开展基于里德堡原子的通信接收验证上。
2019年,美国国家标准技术研究院Christopher L. Holloway等人将铷原子和铯原子放置在同一个原子泡内,并分别在各自的能级上加载20.644 GHz(FM)和19.626 GHz(AM)的无线电载波,首次实现了双频带通信接收能力,可以从AM和FM信号中实现高保真度的立体声接收,实验方案如图17所示[75],其中铷原子加载20.644 GHz无线电信号,调制方式为FM,激光器波长分别为780 nm和480 nm;铯原子加载19.623 GHz无线电信号,调制方式为AM,激光器波长为850 nm和510 nm。
2022年,美国陆军研究实验室David H. Meyer等人基于里德堡原子的无线电光学测量技术,报道了对几乎跨越6个八度(1.7~116 GHz)的1.72、12.11、27.42、65.11、115.75 GHz等5个无线电信号同时测量和解调的实验进展,实验中展示了每个频率的相位和幅度的连续恢复,并报告了该系统在多频段检测方面的灵敏度和带宽能力[92]。实验设置如图18所示,图18(a)为能级结构设置,在前3个能级构成探测光EIT光谱的基础上,叠加5个不同波长的无线电信号(5个信号微波场由同一个喇叭天线叠加发射,并搭配4个不同的本地强场,由4个喇叭天线发射),分别与EIT效应中的里德堡态56D5/2和另外4个不同的里德堡态59P3/2、57P3/2、54F7/2、52F7/2发生电偶极耦合,其中第5个无线电信号1.72 GHz相对共振里德堡态57P3/2远失谐至−10.287 GHz;图18(b)为设备配置,5个喇叭共发射出5个信号无线电,光探测方式为平衡零差探测;图18(c)为该探测方式中相位分量的EIT光谱图。
根据图18所示,EIT光谱对无线电信号最灵敏的频点位于谐振频率处,在该探测光频率处,5个无线电信号同时解调得到的输出光强时域图如图19所示,图19(a)为总的光电探测器输出信号的时域图以及恢复出来的5个无线电信号的幅度(蓝色曲线)和相位(红色曲线)时域图,需要注意的是幅度都是恒定值,而在相位上,对1、2、5这3个无线电信号分别加载了205、110、100 Hz的调制;图19(b)为图19(a)的快速傅里叶变换(FFT),分辨率设为1 Hz,图(ii)为图(i)的局部放大。
基于里德堡原子的多波带无线电接收机总容量由基带瞬时带宽决定[61],对EIT输出光谱通过频谱分析仪得到的结果如图20所示,图20(a)和图20(b)为不同基带频率下的功率谱,图20(c)中,文中通过传输具有固定幅度和变化频率的傅里叶分量的射频来直接测量带宽,即通过改变第2个信号频率的相位调制频率来实现,再利用双极低通滤波器对数据进行拟合,可得其3 dB带宽为6.11(16) MHz。
原则上可同时测量的拍频数量取决于带宽和测量的分辨率带宽,比如在此处以10 kHz间隔输出拍频信号,6.1 MHz带宽名义上可以允许610个拍频信号。通过参数优化,David H. Meyer等人最终实现各通道通信速率在4~40 kbit/s情况下,误码率均保持在10−3~10−5的水平,证实了利用里德堡原子同时实现超宽带频谱范围内(跨越1.7~116 GHz)多频率同时通信的可行性。
此外,针对多频无线电信号同时注入时探测光输出光谱非常复杂,读取有效信息困难的问题,中国科学技术大学郭光灿等人于2022年将里德堡原子与深度学习模型结合来解决干扰环境下的多频无线电信号电场识别问题[100]。
实验设置如图21所示。图21(a)为铷原子能级结构设置,特别是与两个里德堡能级51D3/2和50F5/2耦合的四路频分复用(Frequency-division multiplexing. FDM)无线电信号:
$$ \begin{split} E=& A_{1} \cos \left[\left(\omega_{0}+\omega_{1}\right) t+\varphi_{1}\right]+A_{2} \cos \left[\left(\omega_{1}+\omega_{2}\right) t+\varphi_{2}\right]+ \\ & A_{3} \cos \left[\left(\omega_{0}+\omega_{3}\right) t+\varphi_{3}\right]+A_{4} \cos \left[\left(\omega_{0}+\omega_{4}\right) t+\varphi_{4}\right] \\ \end{split} $$ (7) 式中:$ 2 \pi \omega_{0}=17.62 \;{\rm{G H z}} $为共振频率。输入无线电信号的频率分别为:
$$ \begin{split} \\ 2 \pi\left(\omega_{0}+\omega_{1}\right)=17.62\; {\rm{G Hz}}- 3 \;{\rm{k H z}} \end{split}$$ $$ 2 \pi\left(\omega_{0}+\omega_{2}\right)=17.62 \;{\rm{G H z}}-1\; {\rm{k H z}} $$ $$ 2 \pi\left(\omega_{0}+\omega_{3}\right)=17.62 \;{\rm{G {H} z}}+1 \;{{\rm{kHz}}} $$ $$ 2 \pi\left(\omega_{0}+\omega_{4}\right)=17.62 \;\mathrm{GHz}+3\; \mathrm{kHz}$$ 式中:相邻频率间隔为$ 2 \;{\rm{kHz}} $,各路无线电信号的幅度、频率和相位均可独立调控。相位矢量$ \left(\varphi_{1}, \varphi_{2}, \varphi_{3}, \varphi_{4}\right) $表示某一时刻的信息比特串,其中$ \varphi_{4}==0 $,$ \varphi_{1,2,3}=0 / \pi $代表二进制比特0/1。通过随时间变化$ \varphi_{1, 2,3} $的相位,即可获得二进制相移键控(binary phase-shift keying,2 PSK)调制的FDM信号。
实验中,信号受到的干扰来自环境和原子碰撞。由于原子对外场非常敏感,导致信号被噪声淹没,因此笔者采用深度学习模型来提取相对相位信息$ \left(\varphi_{1}, \varphi_{2}, \varphi_{3}\right) $。实验方案如图21(b)所示,FDM无线电信号经由一个喇叭天线垂直于探测光光路辐射入原子泡内,探测光的参考光信号(与耦合光不重合)与EIT信号(与耦合光重合)通过差分方式由光电探测器探测,最终形成的探测光输出光谱如左上角插图所示,该光谱信息直接输入到经过良好训练的神经网络中,以恢复出随时间变化的相位信息$ \left(\varphi_{1}, \varphi_{2}, \varphi_{3}\right) $。该神经网络由一维卷积层(图(c))、双向长短期记忆层(图(d))和密集层(图(e))组成。通过强化训练,对于4路FDM信号,信息恢复准确度可达到99.38%,优于Linblad主方程,如图22所示。
笔者还通过测试证明,深度学习模型除了对噪声的鲁棒性之外,还具有良好的可扩展性。特别是当通过增加频分复用的信道数量或信道间频率间隔来提升数据传输速率时,深度学习模型仍然表现良好,而主方程难以准确地识别和恢复信息,如图23所示。其中图23(a)、(b)、(e)为频分复用信道数量增加到20时(频率间隔为2 kHz)的深度学习模型和Lindblad主方程两种方法的信息恢复保真度对比,可以看到在经过78轮之后,深度学习的保真度达到了100% (如图23(b)所示),优于主方程的20.63% (如图23(e)所示);图23(c)、(d)、(f)为4路频分复用下将频率间隔增加到200 kHz时两种方法的信息恢复保真度对比,可以看到在经过83轮之后,深度学习的保真度达到了98.83% (如图23(d)所示),优于主方程的60.00% (如图23(f)所示)。
图 23 在增加频分复用的信道数量或信道间频率间隔来提升数据传输速率时,深度学习模型和Lindblad主方程两种探测光输出光谱处理方法的信息恢复效果对比[100]
Figure 23. Comparison of the information recovery effects between the deep learning model and the Lindblad master equation-based probe laser output spectrum processing methods when increasing the number of frequency division multiplexing channels or the frequency interval between channels to improve data transmission rate [100]
最后,中国科学技术大学郭光灿等人证实了深度学习模型在用于里德堡原子多频无线电信号光学测量时,可以充分利用里德堡原子的高灵敏度特性并能显著降低噪声影响,不需要求解Linblad主方程来分析探测光EIT输出光谱,且比主方程方法保真度更高,接近100%,原理上验证了这种基于深度学习增强的里德堡原子接收机允许直接解码频分复用信号。
总之,对于多频无线电信号的光谱处理方式,需要根据实际情况进行调整。一种方式是利用多谐波里德堡原子能级结构,通过在前端精细调整和优化激光和电场的频率和强度等参数,实现对多频无线电信号的测量[73, 75, 92];另一种方式是在后端,利用深度学习等光谱分析技术,将多个光谱的信息进行分离和提取,从而得到多个频率的光谱信息[100]。
Rydberg atomic radio-optical measurement and spectrum processing techniques (invited)
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摘要: 里德堡原子是一种高激发态的原子,具有较大电偶极矩,相邻能级差可覆盖DC~THz的超宽频谱范围,因而可以实现电磁场高灵敏、超宽带的传感接收。基于里德堡原子的无线电光学测量是通过碱金属原子在探测光和控制光等两束激光的精确调控下转变为里德堡原子,并使探测光透射光谱产生电磁诱导透明效应,进而在输入的无线电信号的作用下,使其透明光谱发生Autler-Townes (AT)劈裂,完成无线电信号到光学信号的转化,从而实现无线电信号频率、幅度、相位等信息的提取,具有直接解调、无需校准、抗电磁毁伤等特点。近年来,该技术在电场计量、电磁频谱侦测、通信、雷达等电子信息技术领域引起人们的强烈关注。该技术的关键在于如何从原子系统输出光谱中快速准确地提取出无线电信号的信息。针对静态无线电信号、动态无线电信号、单频无线电信号、多频无线电信号等不同类型的无线电信号,对应的信息提取和光谱处理方式也不同。依据不同类型的无线电信号,对基于里德堡原子的无线电光学测量及其光谱处理技术进行分类,并综述其原理、技术特点及国内外研究进展,最后结合该技术特点及其应用前景,对未来发展趋势作了展望。Abstract:
Significance Rydberg atoms are highly excited atoms with large electric dipole moments. The energy difference between adjacent levels can cover an ultra-wide frequency spectrum range from DC to THz, making it possible to achieve high-sensitivity and ultra-wideband reception of electromagnetic fields. Radio-optical measurements based on Rydberg atoms are achieved by precisely controlling two laser beams, the probe laser and the control laser, to transform ground state alkali metal atoms into Rydberg atoms and induce Electromagnetic Induced Transparency (EIT) in the transmitted spectrum of the probe laser. Under the interaction of the input radio signal, Autler-Townes (AT) splitting occurs in the transparent EIT spectrum, completing the conversion of radio signals to optical signals (Fig.2-3), thereby extracting information such as frequency, amplitude, and phase of the radio signal. This technology has attracted great attention in electronic information fields such as electric field metrology, electromagnetic spectrum detection, communication, and radar in recent years. The physical implementation of this technology is simple and does not require strict physical conditions as usual quantum technologies such as single-photon sources or ultra-cold and superconducting conditions. It can be achieved at room temperature without being limited by the level of production technology. It is considered one of the fastest applicable quantum technologies with its high stability, accuracy, and repeatability that could partially replace existing radio reception technologies in the near future. Progress In the past decade, researchers have made significant progress in the study of radio-optical measurement techniques based on Rydberg atoms, from precise measurements of single-frequency static radio signals in electric field metrology applications to real-time reception of single-frequency dynamic radio signals in communication applications, and to spectrum detection and communication reception of complex multi-frequency radio signals. The key to this technology is how to quickly and accurately extract information about the radio signal from the output EIT spectrum of the atomic system. Different types of radio signals, such as static, dynamic, single-frequency, and multi-frequency radio signals, require different information extraction and spectral processing methods, as well as different experimental designs and implementations. For single-frequency static radio signals, researchers have already used Rydberg atoms in experiments to measure field strengths in the 0-320 GHz frequency range with a maximum coverage range of 780 pV·cm−1 to 50 V·cm−1. By using heterodyne technology (Fig.8) and critical phenomena in many-body Rydberg atomic system, the current sensitivity can reach as low as 49 nV·cm−1·Hz−1/2. Unlike measuring single-frequency static radio signals, for single-frequency dynamic radio signals, Rydberg atom systems are required to track and respond to rapidly changing radio signals in real-time and quickly read EIT spectral changes at the end point. Its primary application scenario is the communication reception. Since 2018, a large number of verification experiments on wireless communication reception principle have been carried out based on Rydberg atoms. This technology can directly convert intermediate frequency or baseband signals on the carrier into optical signals for direct demodulation. Verified communication methods include amplitude modulation (AM), frequency modulation (FM), and phase modulation (PM). When the input wireless signal becomes complex, especially for multi-frequency wireless signal input, the output EIT spectrum of the probe laser will become complicated. It will be a big challenge to quickly and effectively read and distinguish information from different frequency wireless signals. Currently, a small amount of research is focused on verifying dynamic multi-frequency wireless signals for communication reception, including using multi-harmonic Rydberg atomic level structures to finely adjust and optimize system parameters at the front end or using post-processing techniques such as deep learning at the back end to achieve recognition and reading of multiple frequency information. People have experimentally achieved simultaneous reception of five completely different frequency signals within a spectrum range of over 100 GHz (Fig.18) or 20 similar frequency signals within a range of 100 kHz (Fig.23). Conclusions and Prospects Through continuous research over the past 10 years, it has been experimentally verified that radio-optical measurements based on Rydberg atoms have unique quantum advantages in spectrum range, sensitivity, minimum field strength, signal demodulation mechanism, and other aspects. This technology has demonstrated promising prospects in applications such as electric field metrology, electromagnetic spectrum detection, communication, radar, and more. In order to further develop this technology to fully leverage the unique quantum advantages of Rydberg atoms and achieve practical applications as soon as possible, researchers need to deepen their research on the comprehensive performance improvement, anti-interference ability enhancement, miniaturization integration and simultaneously reduce the costs of radio-optical measurements based on Rydberg atoms. -
图 4 针对单频静态微波电场的里德堡原子光学测量的能级设置和实验装置示意图[15]。(a)四能级系统的能级图,插图顶部为关闭微波场时的EIT光谱,插图底部为打开微波场时的EIT-AT光谱;(b)实验设置
Figure 4. Level scheme and experimental setup for Rydberg atomic optical measurement of a single-frequency static microwave electric field[15]. (a) Level diagram of the four-level system, with the top inset showing the EIT spectrum when the microwave field is off and the bottom inset showing the EIT-AT spectrum when the microwave field is on; (b) Experimental setup
图 7 微弱微波电场测量的光谱图[15]。(a)微波场对探测光透射光谱的影响;(b) EIT透明峰高度对微波电场强度的依赖
Figure 7. Transmission spectrum induced by a weak microwave electric field[15]. (a) Effect of the microwave field on the transmission spectrum of the probe laser; (b) Dependence of the EIT transparency peak height on the microwave electric field strength
图 12 射频强交流电场下的探测光EIT光谱图[82]。(a)里德堡原子在50 MHz交流电场耦合下的EIT光谱随场强的变化;(b)电场强度为41.5 dBI时,里德堡原子在50 MHz交流电场耦合下的EIT光谱;(c)电场强度为46 dBI时,里德堡原子在不同频率交流电场耦合下的EIT光谱
Figure 12. EIT spectrum of the probe laser under strong ac fields[82]. (a) EIT spectrum of Rydberg atoms coupled to a 50 MHz ac field as a function of field strength; (b) EIT spectrum of Rydberg atoms coupled to a 50 MHz ac field with an electric field intensity of 41.5 dBI; (c) EIT spectrum of Rydberg atoms coupled to ac fields at different frequencies with an electric field intensity of 46 dBI
图 15 基于单频动态无线电信号测量的无线通信接收光谱处理过程[61]。(a) EIT-AT光谱;(b)加上8 PSK调制后的光谱图;(c)输入输出的相位对比;(d)输出相位的轨迹图
Figure 15. Wireless communication receiver spectral processing based on single-frequency dynamic radio signal measurement[61]. (a) EIT-AT spectrum; (b) Spectrum with 8 PSK modulation; (c) Phase comparison between input and output; (d) Trajectory of the output phase
图 16 基于单频动态无线电信号测量的无线通信接收信道容量估计。(a)通信接收时的探测光信号时域图;(b)和(c)为不同泵浦速率下的上升沿和下降沿;(d) 信道容量与采样速率的关系[61]
Figure 16. Wireless communication receiver channel capacity estimation based on single-frequency dynamic radio signal measurement. (a) Time-domain plot of the detected optical signal during communication reception; (b) and (c) Rising and falling edges at different pump rates; (d) Relationship between channel capacity and sampling rate[61]
图 23 在增加频分复用的信道数量或信道间频率间隔来提升数据传输速率时,深度学习模型和Lindblad主方程两种探测光输出光谱处理方法的信息恢复效果对比[100]
Figure 23. Comparison of the information recovery effects between the deep learning model and the Lindblad master equation-based probe laser output spectrum processing methods when increasing the number of frequency division multiplexing channels or the frequency interval between channels to improve data transmission rate [100]
表 1 碱金属原子量子特性对主量子数(n)的依赖关系[23]
Table 1. Alkali atom principal quantum number (n) scaling of the most important properties of Rydberg states[23]
Property Quantity Scaling Energy levels En n−2 Level spacing ∆En n−3 Radius 〈r〉 n2 Transition dipole moment ground to $|\langle n \ell|-e r| g\rangle| $ n−3/2 Rydberg states Radiative lifetime $\tau $ n3 Transition dipole moment for adjacent $\left|\left\langle n \ell|-e r| n \ell^{\prime}\right\rangle\right|$ n2 Rydberg states Rcsonant dipole-dipole interaction coefficient C3 n4 polarisability $\alpha $ n7 van der Waals interaction coefficient C6 n11 -
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