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随着X射线光源的进步和量子光学的发展, 形成了X射线量子光学这一前沿分支学科. 原子内壳层跃迁是重要的X射线量子光学体系, 它具有跃迁种类丰富和表征手段多样、覆盖波段范围宽等优势. 但内壳层空穴的自然线宽较宽且受局域电子结构影响, 使得实验上缺乏纯粹的二能级跃迁, 成了制约X射线量子光学发展的瓶颈之一. 本文利用共振非弹性X射线散射技术, 在实验上分离了WSi2 中W-L3边的白线, 从而为基于原子内壳层跃迁的X射线量子光学体系提供了二能级方案, 也为这一领域的发展提供了强有力的实验技术支持.
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关键词:
- X射线量子光学 /
- 内壳层跃迁 /
- 共振非弹性X射线散射 /
- 二能级
With the advancement of synchrotron and free-electron laser, X-ray quantum optics has emerged as a novel frontier for exploring light-matter interactions at high photon energies. A significant challenge in this field is achieving well-defined two-level systems through atomic inner-shell transitions, which are often hindered by broad natural linewidths and local electronic structure effects. This study aims to explore the potential of tungsten disilicide (WSi2) as a two-level system for X-ray quantum optics applications. Utilizing high-resolution resonant inelastic X-ray scattering (RIXS) near the W-L3 edge, in this work, the white line of bulk WSi2 is experimentally distinguished, overcoming the spectral broadening caused by short core-hole lifetime. The measurements are conducted by using a von Hamos spectrometer at the GALAXIES beamline of the SOLEIL synchrotron. The results reveal a single resonant emission feature with a fixed energy transfer, confirming the presence of a discrete 2p-5d transition characteristic of a two-level system. Additional high-resolution XAS spectra, obtained via high energy resolution fluorescence detection method and reconstructed from off-resonant emission (free from self-absorption effect for bulk WSi2 sample) method, further support the identification of a sharp white line. These findings demonstrate the feasibility of using WSi2 as a model system in X-ray cavity quantum optics and establish RIXS as a powerful technique to resolve fine inner-shell structures.-
Keywords:
- X-ray quantum optics /
- inner-shell transition /
- resonant inelastic X-ray scattering /
- two-level system
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图 1 W原子2p-3d共振非弹性X射线散射(RIXS)过程示意图(两图中由左至右分别展示散射过程中的初始态、中间态和末态) (a) 经由$ {\rm{2 p}}^{-1}{\rm{5 d}} $中间态, 吸收和散射是不可分离的两步过程; (b) 经由$ {\rm{2 p}}^{-1}\epsilon {\mathrm{d}} $中间态, 表现为吸收和发射两步过程
Fig. 1. Schematic illustration of the W atom 2p-3d resonant inelastic X-ray scattering (RIXS) process with its initial, intermediate and final states shown from left to right: (a) Via the $ {\rm{2 p}}^{-1}{\rm{5 d}} $ intermediate state, during which absorption and scattering are inseparable; (b) via the $ {\rm{2 p}}^{-1}\epsilon {\mathrm{d}} $ intermediate state, manifested as a two-step process of absorption and emission.
图 2 von Hamos谱仪原理示意图, 所测光子能量约为8397 eV. 谱仪的能量色散方向由图中X射线颜色标识, 红色示意低能方向
Fig. 2. Schematic illustration of the von Hamos spectrometer, set to measure photon energies around 8397 eV. The energy dispersion direction is indicated by the color gradient of the X-ray beam, with red representing lower photon energies.
图 3 (a) 弹性散射标定发射谱能量以及(b) 对标定峰位的拟合结果. 图(a)每个峰为不同入射光能量下的弹性散射信号, 代表了出现在色散方向的不同位置, 通过提取峰位代入(b)中拟合得到色散关系
Fig. 3. (a) Elastic scattering spectra measured at different incident photon energies; (b) each peak corresponds to a distinct position on detector along the energy-dispersive axis of the spectrometer. The dispersion relation derived by fitting the peak positions from panel (a) to panel (b), establishing the energy calibration function.
图 4 W的L3吸收边(10208 eV)附近的RIXS二维图 (a)及能量转移图 (b). 白色虚线对应发射光能量为8397.6 eV, 对应2p电子电离产生$ {\rm{2 p}}^{-1}\epsilon {\mathrm{d}} $中间态过程. 此时随入射光能量的增加发射光子能量不变, 能量转移变大. 黑色虚线对应能量转移约为1809 eV, 对应2p-5d共振产生$ {\rm{2 p}}^{-1}{\rm{5 d}} $中间态过程. 此时随入射光能量的增加, 发射光子能量增加但能量转移保持不变
Fig. 4. (a) Two-dimensional RIXS map near the W-L3 absorption edge (10208 eV); (b) corresponding energy transfer. The white dashed line indicates an emission photon energy of 8397.6 eV, corresponding to the ionization of a 2p electron and the formation of a $ {\rm{2 p}}^{-1}\epsilon {\mathrm{d }}$ intermediate state. In this process, the emission energy remains constant as the incident photon energy increases, leading to a progressive increase in energy transfer. The black dashed line indicates a constant energy transfer of 1809 eV, corresponding to the 2p-5d resonant scattering process via a $ {\rm{2 p}}^{-1}{\rm{5 d}} $ intermediate state, where the emission energy increases with increasing the incident energy while the energy transfer remains fixed.
图 5 WSi2在10206—10222 eV入射光能量激发下的荧光谱, 对应图4(a)垂直剖线. 其中蓝色虚线对应2p-5d共振荧光峰(A峰); 红色虚线对应8397.6 eV的W-Lα1非共振荧光峰(B峰)
Fig. 5. Fluorescence spectra of WSi2 excited by incident photon energies from 10206 to 10222 eV, corresponding to the vertical cut shown in Fig. 4(a). The blue dashed line corresponds to the 2p-5d resonance fluorescence peak (Peak A); the red dashed line corresponds to the non-resonance fluorescence peak of W-Lα1 at 8397.6 eV (Peak B).
图 6 WSi2在10206—10222 eV入射光能量激发下以能量转移为横坐标的荧光谱, 对应图4(b)垂直剖线. 红蓝虚线与图5中含义相同
Fig. 6. Fluorescence spectra of WSi2 excited with incident photon energies from 10206 to 10222 eV, displayed as a function of energy transfer, corresponding to the vertical cut shown in Fig. 4(b). The red and blue dashed lines represent the same as those in Fig. 5.
图 7 荧光模式下的总荧光产额谱与HERFD谱. 高能量分辨率的HERFD光谱是积分W的Lα1(L3M5) 荧光线(8397.6 eV) 中心(图4(a)白色虚线)处0.6 eV能量窗口(8397—8398.4 eV)的XES数据得到的. 值得注意的是, 积分能量区间比初态能级的自然线宽7.2 eV要小很多. 而TFY-XAS光谱则是积分XES整个W-$ {\mathrm{L}}\alpha_{1}\left({\mathrm{L}}_{3} {\mathrm{M}}_{5}\right) $范围得到的
Fig. 7. Total fluorescence yield (TFY) spectrum and high-energy resolution fluorescence detected (HERFD) spectrum in fluorescence mode. The high-resolution HERFD spectrum is obtained by integrating the X-ray emission spectroscopy (XES) data within a 0.6 eV energy window (8397–8398.4 eV) centered at the W ${\mathrm{L}}{\alpha_1}\;({\mathrm{L}}_3 {\mathrm{M}}_5) $ fluorescence line at 8397.6 eV (indicated by the white dashed line in Fig. 4(a)). Notably, the integrated energy window is much narrower than the natural linewidth 7.2 eV of the initial state. The TFY-XAS spectrum, on the other hand, is obtained by integrating the XES intensity over the entire W ${\mathrm{L}}{\alpha_1}\;({\mathrm{L}}_3 {\mathrm{M}}_5) $ emission range.
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[1] Kuznetsova E, Kocharovskaya O 2017 Nat. Photonics 11 685
Google Scholar
[2] Wong L J, Kaminer I 2021 Appl. Phys. Lett. 119 130502
Google Scholar
[3] 汪书兴, 李天钧, 黄新朝, 朱林繁 2024 物理学报 73 246101
Google Scholar
Wang S X, Li T J, Huang X C, Zhu L F 2024 Acta Phys. Sin. 73 246101
Google Scholar
[4] Bostedt C, Boutet S, Fritz D M, Huang Z, Lee H J, Lemke H T, Robert A, Schlotter W F, Turner J J, Williams G J 2016 Rev. Mod. Phys. 88 015007
Google Scholar
[5] Ablett J M, Prieur D, Céolin D, et al. 2019 J. Synchrotron Radiat. 26 263
Google Scholar
[6] Rueff J P, Ablett J M, Céolin D, Prieur D, Moreno T, Balédent V, Lassalle-Kaiser B, Rault J E, Simon M, Shukla A 2015 J. Synchrotron Radiat. 22 175
Google Scholar
[7] Linker T M, Halavanau A, Kroll T, et al. 2025 Nature 642 934
Google Scholar
[8] Kroll T, Weninger C, Alonso-Mori R, et al. 2018 Phys. Rev. Lett. 120 133203
Google Scholar
[9] Nandi S, Olofsson E, Bertolino M, et al. 2022 Nature 608 488
Google Scholar
[10] Heeg K P, Evers J 2013 Phys. Rev. A 88 043828
Google Scholar
[11] Röhlsberger R, Wille H C, Schlage K, Sahoo B 2012 Nature 482 199
Google Scholar
[12] Haber J, Schulze K S, Schlage K, Loetzsch R, Bocklage L, Gurieva T, Bernhardt H, Wille H C, Rüffer R, Uschmann I, Paulus G G, Röhlsberger R 2016 Nat. Photonics 10 445
Google Scholar
[13] Heeg K P, Evers J 2015 Phys. Rev. A 91 063803
Google Scholar
[14] Lentrodt D, Heeg K P, Keitel C H, Evers J 2020 Phys. Rev. Res. 2 023396
Google Scholar
[15] Lentrodt D, Evers J 2020 Phys. Rev. X 10 011008
Google Scholar
[16] Kong X, Chang D E, Pálffy A 2020 Phys. Rev. A 102 033710
Google Scholar
[17] Andrejić P, Lohse L M, Pálffy A 2024 Phys. Rev. A 109 063702
Google Scholar
[18] Röhlsberger R, Schlage K, Klein T, Leupold O 2005 Phys. Rev. Lett. 95 097601
Google Scholar
[19] Ma Z R, Huang X C, Li T J, Wang H C, Liu G C, Wang Z S, Li B, Li W B, Zhu L F 2022 Phys. Rev. Lett. 129 213602
Google Scholar
[20] Heeg K P, Ott C, Schumacher D, Wille H C, Röhlsberger R, Pfeifer T, Evers J 2015 Phys. Rev. Lett. 114 207401
Google Scholar
[21] Huang X C, Kong X J, Li T J, Ma Z R, Wang H C, Liu G C, Wang Z S, Li W B, Zhu L F 2021 Phys. Rev. Res. 3 033063
Google Scholar
[22] Vassholz M, Salditt T 2021 Sci. Adv. 7 eabd5677
Google Scholar
[23] Huang X C, Li T J, Lima F A, Zhu L F 2024 Phys. Rev. A 109 033703
Google Scholar
[24] Ketenoglu D 2022 X-Ray Spectrom. 51 422
Google Scholar
[25] Dorenbos P 2003 J. Phys.: Condens. Matter 15 6249
Google Scholar
[26] Wach A, Sá J, Szlachetko J 2020 J. Synchrotron Radiat. 27 689
Google Scholar
[27] Khyzhun O Y, Strunskus T, Grünert W, Wöll C 2005 J. Electron Spectrosc. Relat. Phenom. 149 45
Google Scholar
[28] Kotani A, Kvashnina K O, Butorin S M, Glatzel P 2012 Eur. Phys. J. B 85 257
Google Scholar
[29] Maganas D, DeBeer S, Neese F 2017 Inorg. Chem. 56 11819
Google Scholar
[30] Błachucki W, Szlachetko J, Hoszowska J, Dousse J C, Kayser Y, Nachtegaal M, Sá J 2014 Phys. Rev. Lett. 112 173003
Google Scholar
[31] Pan Y, Jing C, Wu Y 2019 Vacuum 167 374
Google Scholar
[32] Szlachetko J, Nachtegaal M, de Boni E, Willimann M, Safonova O, Sa J, Smolentsev G, Szlachetko M, van Bokhoven J A, Dousse J C, Hoszowska J, Kayser Y, Jagodzinski P, Bergamaschi A, Schmitt B, David C, Lücke A 2012 Rev. Sci. Instrum. 83 103105
Google Scholar
[33] Veldkamp J 1935 Physica 2 25
Google Scholar
[34] Briand J P 1981 Phys. Rev. Lett. 46 1625
Google Scholar
[35] Tulkki J, Aberg T 1982 J. Phys. B 15 L435
Google Scholar
[36] Bergmann U, Glatzel P 2009 Photosynth. Res. 102 255
Google Scholar
[37] Błachucki W, Hoszowska J, Dousse J C, Kayser Y, Stachura R, Tyrała K, Wojtaszek K, Sá J, Szlachetko J 2017 Spectrochim. Acta B 136 23
Google Scholar
[38] Hayashi H, Takeda R, Udagawa Y, Nakamura T, Miyagawa H, Shoji H, Nanao S, Kawamura N 2003 Phys. Rev. B 68 045122
Google Scholar
[39] Hayashi H, Udagawa Y, Caliebe W A, Kao C C 2003 Chem. Phys. Lett. 371 125
Google Scholar
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