The simplest molecules in nature, molecular hydrogen ions in the form of H2+ and HD+, provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD+ by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but also enables the long predicted determination of the proton-to-electron mass ratio from a molecular system, as well as improved constraints on hypothetical fifth forces and compactified higher dimensions at the molecular scale. With the perspective of comparisons between theory and experiment at the 0.01 part-per-billion level, our work demonstrates the potential of molecular hydrogen ions as a probe of fundamental physical constants and laws.
Relativistic and QED corrections to the $2pσ_{u}(\upsilon = 1)$ vibrational state of the $H^{+}_{2}$ molecular ion
对最近发现的第一振动$2pσ_u$态进行了相对论和QED修正。这个态具有极小的非相对论结合能$E_B=1.085045252(1)\times10^{-9}$ a. u。它的波函数在$R\approx100$ a. u处具有最大值。并延伸到数百个。结果表明，这种状态不会消失，如果高阶相对论和QED的修正，包括Casimir--Polder效应，考虑。
Probing high-frequency gravitational waves with entangled vibrational qubits in linear Paul traps
KEK Theory Center（高能加速器研究机构理论中心）；The Graduate University for Advanced Studies, SOKENDAI（高级研究大学院大学（SOKENDAI））；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
Non-adiabatic, Relativistic, and Leading-order QED Corrections for Rovibrational Intervals of $^4$He$_2^+$ ($X\ ^2Σ_\mathrm{u}^+$)
计算了$^4$ He $_2^+$分子离子在其$X\ ^2Σ_\text{u}^+$基态电子态的振转间隔，包括非绝热、相对论和首阶量子电动力学修正.对基态和基振动的转动激发序列进行了理论和实验的一致性分析。计算得到的最低能量转动间隔为$70.937\ 69(10)$ cm $^{-1}$，与最近报道的实验值$70.937\ 589(23)(60)_\text{sys}$ cm $^{-1}$ [L. Semeria，P. Jansen，G. M. Camenisch，F. Mellini，H. Schmutz和F. Merkt，Phys. Rev. Lett. 124，213001（2020）]。
Precision measurements and test of molecular theory in highly-excited vibrational states of H$_2$ $(v=11)$
精确的$EF{}^1Σ^+_g-X{}^1Σ^+_g$跃迁能量在分子氢中被确定为跃迁起源于具有高激发振动量子数$v=11$的水平，在基态电子状态。无多普勒双光子光谱应用于振动激发H $_2^*$，产生通过光解H $_2$ S，产生的过渡频率与$45$ MHz或$0.0015$ cm $^{-1}$的精度。一个重要的改进是通过自电离$7pπ$电子里德堡态的共振激发来增强检测效率，从而由于降低的ac-斯塔克效应而导致窄跃迁。使用已知的$EF$能级能量，以通常为0.002 cm $^{-1}$的精度导出$X(v=11, J=1,3-5)$态的能级能量。这些实验值是在极好的协议，并比从最先进的从头计算分子理论计算，包括相对论和QED的贡献得到的结果更准确。
Bound-state QED test above the Schwinger limit with kaonic fluorine
Laboratori Nazionali di Frascati INFN（弗朗卡蒂国家实验室 INFN）；Università degli studi di Roma Tor Vergata（罗马托尔维尔塔大学）；Department of Physics and Chemistry (DiFC), Emilio Segrè, University of Palermo（巴勒莫大学埃米利奥·塞格雷物理与化学系）；Università degli studi di Roma Tre（罗马第三大学）；Politecnico di Milano（米兰理工大学）；INFN Sezione di Milano（INFN 米兰分部）；Department of Physics, Faculty of Science, University of Zagreb（萨格勒布大学理学院物理系）；IFIN-HH, Institutul National pentru Fizica si Inginerie Nucleara Horia Hulubei（霍里亚·胡卢贝伊国家核物理与核工程研究所 IFIN-HH）
