We demonstrate the first application of a liquid-metal ion source for collinear laser spectroscopy in proof-of-principle measurements on naturally abundant In$^+$. The superior beam quality, i.e., the actively stabilized current and energy of a beam with very low transverse emittance, allowed us to perform precision spectroscopy on the $5s^2\;^1\mathrm{S}_0 \rightarrow 5s5p\;^3\mathrm{P}_1$ intercombination transition in $^{115}$In$^+$, which is to our knowledge the slowest transition measured with collinear fluorescence laser spectroscopy so far. By applying collinear and anticollinear spectroscopy, we improved the center-of-gravity frequency $ν_\mathrm{cg}=1\,299\,617\,759.\,3\,(1.2)$ and the hyperfine constants $A=6957.19\,(28)$\,MHz and $B=-443.7\,(2.4)$\,MHz by more than two orders of magnitude. A similar accuracy was reached for $^{113}$In$^+$ in combination with literature data and the isotope shift between both naturally abundant isotopes was deduced to $ν(^{113}\mathrm{In})-ν(^{115}\mathrm{In})=696.3\,(3.1)$\,MHz. Nuclear alignment induced by optical pumping in a preparation section of the ion beamline was demonstrated as a pump-and-probe approach to provide sharp features on top of the Doppler broadened resonance profile.
The hyperfine constants of the $^3$P$^{\circ}_2$ state in neutral Yb have been measured using three different dipole transitions. This state was recently shown to have a comparatively large hyperfine magnetic octupole splitting, and thus a puzzlingly large magnetic octupole moment. The measurement is performed using collinear laser spectroscopy on a fast atomic beam, which provides a straightforward route to probing long-lived metastable atomic states with high resolution. From the combined analysis of all three lines we find no significant evidence for a non-zero octupole moment in $^{173}$Yb…
Collinear Laser Spectroscopy of the $1s2s\,^3\!S_1\rightarrow 1s2p\,^3\!P_{0,2}$ Transitions in Helium-like $^{11}$B$^{3+}$
Institut für Kernphysik, Universität Münster（明斯特大学核物理研究所）；Institut für Kernphysik, Technische Universität Darmstadt（达姆施塔特工业大学核物理研究所）；Helmholtz Research Academy Hesse for FAIR, GSI Helmholtzzentrum für Schwerionenforschung GmbH（黑森州FAIR亥姆霍兹研究院，GSI重离子研究中心有限公司）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心有限公司）；Argonne National Laboratory（阿贡国家实验室）
We experimentally study the breakdown of hyperfine coupling for an atom in a deep optical-dipole trap. One-color laser spectroscopy is performed at the resonance lines of a single $^{87}$Rb atom for a trap wavelength of 1064 nm. Evidence of hyperfine breakdown comes from three observations, namely a nonlinear dependence of the transition frequencies on the trap intensity, a splitting of lines which are degenerate for small intensities, and the ability to drive transitions which would be forbidden by selection rules in the absence of hyperfine breakdown. From the data, we infer the hyperfine in…
Large-scale $\textit{ab initio}$ calculations of the electric field gradient, which constitutes the electronic contribution to the electric quadrupole hyperfine constant $B$, were performed for the $5s^25p6s$ $^{1,3}\!P^{\rm o}_1$ excited states of tin, using three independent computational strategies of the variational multiconfiguration Dirac-Hartree-Fock method and a fourth approach based on the configuration interaction Dirac-Fock-Sturm theory. For the $5s^25p6s$ $^{1}\!P^{\rm o}_1$ state, the final value of $B/Q =703(50)$ MHz/b differs by $0.4\%$ from the one recently used by Yordanov ${\…
Precision measurement of the ground-state hyperfine constant for $^9Be^+$ in a linear Paul trap via magnetically insensitive hyperfine transitions
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（精密测量科学与技术创新院，中国科学院）；University of the Chinese Academy of Sciences（中国科学院大学）；School of Electronics and IoT, Chongqing Polytechnic University of Electronic Technology（重庆电子工程职业学院电子信息学院）
Hyperfine structure $A$ and $B$ factors of the atomic $5s\,5p\,\; ^3\rm{P}_2 \rightarrow 5s\,6s\,\; ^3\rm{S}_1$ transition are determined from collinear laser spectroscopy data of $^{107-123}$Cd and $^{111m-123m}$Cd. Nuclear magnetic moments and electric quadrupole moments are extracted using reference dipole moments and calculated electric field gradients, respectively. The hyperfine structure anomaly for isotopes with $s_{1/2}$ and $d_{5/2}$ nuclear ground states and isomeric $h_{11/2}$ states is evaluated and a linear relationship is observed for all nuclear states except $s_{1/2}$. This co…
Long-lived isotopes of plutonium were studied using two complementary techniques, high-resolution resonance ionisation spectroscopy (HR-RIS) and collinear laser spectroscopy (CLS). Isotope shifts have been measured on the $5f^67s^2\ ^7F_0 \rightarrow 5f^56d^27s\ (J=1)$ and $5f^67s^2\ ^7F_1 \rightarrow 5f^67s7p\ (J=2)$ atomic transitions using the HR-RIS method and the hyperfine factors have been extracted for the odd mass nuclei $^{239,241}$Pu. Collinear laser spectroscopy was performed on the $5f^67s\ ^8F_{1/2} \rightarrow J=1/2\; (27523.61\text{cm}^{-1})$ ionic transition with the hyperfine …
Absolute transition frequencies of the $2s\,^2{\rm{S}}_{1/2}$ $\rightarrow$ $2p\,^2{\rm{P}}_{1/2,3/2}$ transitions in Be$^+$ were measured with a frequency comb in stable and short-lived isotopes at ISOLDE (CERN) using collinear laser spectroscopy. Quasi-simultaneous measurements in copropagating and counterpropagating geometry were performed to become independent from acceleration voltage determinations for Doppler-shift corrections of the fast ion beam. Isotope shifts and fine structure splittings were obtained from the absolute transition frequencies with accuracies better than 1\,MHz and l…
We performed a laser spectroscopic determination of the $2s$ hyperfine splitting (HFS) of Li-like $^{209}\text{Bi}^{80+}$ and repeated the measurement of the $1s$ HFS of H-like $^{209}\text{Bi}^{82+}$. Both ion species were subsequently stored in the Experimental Storage Ring at the GSI Helmholtzzentrum für Schwerionenforschung Darmstadt and cooled with an electron cooler at a velocity of $\approx 0.71\,c$. Pulsed laser excitation of the $M1$ hyperfine-transition was performed in anticollinear and collinear geometry for $\text{Bi}^{82+}$ and $\text{Bi}^{80+}$, respectively, and observed by flu…
We demonstrate a technique to lock simultaneously two laser frequencies to each step of a two-photon transition in the presence of a magnetic field sufficiently large to gain access to the hyperfine Paschen-Back regime. A ladder configuration with the 5S$_{1/2}$, 5P$_{3/2}$ and 5D$_{5/2}$ terms in a thermal vapour of $^{87}$Rb atoms is used. The two lasers remain locked for more than 24 hours. For the sum of the laser frequencies, which represents the stability of the two-photon lock, we measure a frequency instability of less than the Rb D$_2$ natural linewidth of 6 MHz for nearly all measure…
Experimental and theoretical studies of hyperfine structures in $^{21}$Na
Center for Exotic Nuclear Studies, Institute for Basic Science（基础科学研究所奇异核研究中心）；Institute for Rare Isotope Science, Institute for Basic Science（基础科学研究所稀有同位素科学研究所）；Department of Physics, Sungkyunkwan University（成均馆大学物理系）；Department of Science Education, College of Education, Ewha Womans University（梨花女子大学教育学院科学教育系）
An approach to determine the kinetic beam energy at the $10^{-5}$ level is presented, which corresponds to an improvement by more than one order of magnitude compared to conventional methods. Particularly, collinear fluorescence and resonance ionization spectroscopy measurements on rare isotope beams, where the beam energy is a major contribution to the uncertainty, can benefit from this method. The approach is based on collinear spectroscopy and requires no special equipment besides a wavelength meter, which is commonly available. Its advent is demonstrated in a proof-of-principle experiment …
We report results of a theoretical investigation of hyperfine interactions in two homonuclear isotopologues of the hydrogen molecule: H$_{2}$ and D$_{2}$. We present a set of hyperfine coupling constants: spin-rotation, spin-spin dipole and, in the case of the D$_{2}$ molecule, electric quadrupole coupling constants for all bound states of the two isotopologues in their ground electronic $X^{1}Σ^{+}_{g}$ state. We provide a list of positions and intensities of 220 997 hyperfine components of 16 079 rovibrational quadrupole transitions of the O, Q and S branches. The positions and intensities o…
We demonstrate coherent control of both the rotational and hyperfine state of ultracold, chemically stable $^{87}$Rb$^{133}$Cs molecules with external microwave fields. We create a sample of ~2000 molecules in the lowest hyperfine level of the rovibronic ground state N = 0. We measure the transition frequencies to 8 different hyperfine levels of the N = 1 state at two magnetic fields ~23 G apart. We determine accurate values of rotational and hyperfine coupling constants that agree well with previous calculations. We observe Rabi oscillations on each transition, allowing complete population tr…
We report absolute frequency measurements of 81 hyperfine components of the rovibrational transitions of molecular iodine at 578 nm using the second harmonic generation of an 1156-nm external-cavity diode laser and a fiber-based optical frequency comb. The relative uncertainties of the measured absolute frequencies are typically $1.4\times10^{-11}$. Accurate hyperfine constants of four rovibrational transitions are obtained by fitting the measured hyperfine splittings to a four-term effective Hamiltonian including the electric quadrupole, spin-rotation, tensor spin-spin, and scalar spin-spin i…
Efficient Separation of the Isomeric State $^{26\text{m}}\text{Al}$ from the Intense Ground State Background via Sequential Optical Pumping in Collinear Laser Spectroscopy
We measure hyperfine structure in the metastable ${^3P}_2$ state of $^{173}$Yb and extract the nuclear magnetic octupole moment. We populate the state using dipole-allowed transitions through the ${^3P}_1$ and ${^3S}_1$ states. We measure frequencies of hyperfine transitions of the ${^3P}_2 \rightarrow {^3S}_1$ line at 770 nm using a Rb-stabilized ring cavity resonator with a precision of 200 kHz. Second-order corrections due to perturbations from the nearby ${^3P}_1$ and ${^1P}_1$ states are below 30 kHz. We obtain the hyperfine coefficients as: $A=-742.11(2)$ MHz, $B=1339.2(2)$ MHz, which re…
Global isotopic analysis of hyperfine-resolved rotational spectroscopic data for barium monofluoride, BaF
Pomona College（波莫纳学院）；Gottfried-Wilhelm-Leibniz-Universität, Institut für Physikalische Chemie and Elektrochemie, Lehrgebiet A（哥特弗里德·威廉·莱布尼茨大学，物理化学与电化学研究所，A教学组）
We perform high resolution spectroscopy on $^{176}$Lu$^+$ including the $^1S_0\leftrightarrow{^3}D_1$ and $^1S_0\leftrightarrow{^3}D_2$ clock transitions. Hyperfine structures and optical frequencies relative to the $^1S_0$ ground state of four low lying excited states are given to a few tens of kHz resolution. This covers the most relevant transitions involved in clock operation with this isotope. Additionally, measurements of the $^3D_2$ hyperfine structure may provide access to higher order nuclear moments, specifically the magnetic octupole and electric hexadecapole moments.
Sun's gravitation potential at earth varies during a year due to varying Earth-Sun distance. Comparing the results of very accurate measurements of atomic clock transitions performed at different time in the year allows us to study the dependence of the atomic frequencies on the gravitational potential. We examine the measurement data for the ratio of the frequencies in Hg$^+$ and Al$^+$ clock transitions and absolute frequency measurements (with respect to caesium frequency standard) for Dy, Sr, H, hyperfine transitions in Rb and H, and obtain significantly improved limits on the values of th…
This work reports on the application of a novel electric field-ionization setup for high-resolution laser spectroscopy measurements on bunched fast atomic beams in a collinear geometry. In combination with multi-step resonant excitation to Rydberg states using pulsed lasers, the field ionization technique demonstrates increased sensitivity for isotope separation and measurement of atomic parameters over non-resonant laser ionization methods. The setup was tested at the Collinear Resonance Ionization Spectroscopy experiment at ISOLDE-CERN to perform high-resolution measurements of transitions i…
Absolute frequency measurement of molecular iodine hyperfine transitions at 554 nm and its application to stabilize a 369 nm laser for Yb+ ions cooling
As a new method to determine the resonance frequency, Rabi-oscillation spectroscopy has been developed. In contrast to the conventional spectroscopy which draws the resonance curve, Rabi-oscillation spectroscopy fits the time evolution of the Rabi oscillation. By selecting the optimized frequency, it is shown that the precision is twice as good as the conventional spectroscopy with a frequency sweep. Furthermore, the data under different conditions can be treated in a unified manner, allowing more efficient measurements for systems consisting of a limited number of short-lived particles produc…
By use of the \textsc{grasp2018} package we perform Multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations with configuration interaction (CI) for the $^{1}S_{0}$ and $^{3}P_{0,1}^o$ levels in neutral cadmium and mercury. By supplying the resultant atomic state functions to the \textsc{ris4} program, we evaluate the mass and field shift parameters for the $^{1}S_{0}-\,^{3}P_{0}^o$ (clock) and $^{1}S_{0}-\,^{3}P_{1}^o$ (intercombination) lines. We make revised estimates of the nuclear charge parameters $λ^{A,A'}$ and differences in mean-square charge radii $δ\langle r^2\rangle^{A,A'}$ for b…
The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several $\mathrm{2S\rightarrow2P}$ transition frequencies in the muonic helium-3 ion, $\mathrm{μ^3He^+}$. This ion is the bound state of a single negative muon $μ^-$ and a bare helium-3 nucleus (helion), $\mathrm{^3He^{++}}$. A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-d…
The recently demonstrated trapping and laser cooling of $^{133}$Ba$^+$ has opened the door to the use of this nearly ideal atom for quantum information processing. However, before high fidelity qubit operations can be performed, a number of unknown state energies are needed. Here, we report measurements of the $^2$P$_{3/2}$ and $^2$D$_{5/2}$ hyperfine splittings, as well as the $^2$P$_{3/2}$$\leftrightarrow$ $^2$S$_{1/2}$and $^2$P$_{3/2}$ $\leftrightarrow$ $^2$D$_{5/2}$ transition frequencies. Using these transitions, we demonstrate high fidelity $^{133}$Ba$^+$ hyperfine qubit manipulation wit…
