We consider the most accurate tests of bound state QED theory of the hyperfine splitting in two-body atoms related to the HFS interval of the 1s state in muonium and positronium and the 2s state in hydrogen, deuterium and the helium-3 ion. We summarize their QED theory and pay special attention to involved effects of strong interactions and to recent optical measurements of the 2s HFS interval in hydrogen and deuterium. We present results for specific ratios of the 1s-2s frequencies in hydrogen and deuterium which happen to be among the most accurately measured and calculated quantities.
The unusually large hyperfine structure splittings in the 23P state of the 3He isotope is measured using electro-optic techniques with high precision laser spectroscopy. Originally designed to probe the fine structure of the 4He atom, this experimental setup along with special modifications I implemented to resolve certain 3He related issues has made possible new high precision hyperfine structure measurements. Discussed are the details of the experimental setup and the modifications, including in depth information necessary to consider while performing these measurements. The results of these…
We have measured hyperfine structure in the first-excited $P$ state ($D$ lines) of all the naturally-occurring alkali atoms. We use high-resolution laser spectroscopy to resolve hyperfine transitions, and measure intervals by locking the frequency shift produced by an acousto-optic modulator to the difference between two transitions. In most cases, the hyperfine coupling constants derived from our measurements improve previous values significantly.
The precision measurements of the ratio of hyperfine structure constants for $s_{1/2}$ and $p_{1/2}$ states allow us to estimate the difference between hyperfine magnetic anomalies for these levels. We calculate the atomic factor in order to recover the absolute values of the hyperfine magnetic anomalies from their difference. Taking into account the hyperfine anomaly correction allows one to increase the accuracy of determining the g-factors of short-lived isotopes by more than an order of magnitude.
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 structures of the triplet $n^3S-$states in the four-electron Be-atom(s) and Be-like ions are considered. It is shown that to determine the hyperfine structure splitting in such atomic systems one needs to know the triplet electron density at the central atomic nucleus $ρ_T(0)$. We have developed the procedure which allows allows one to determine such an electron density $ρ_T(0)$ for arbitrary four-electron atoms and ions.
Spherically-symmetric ground states of alkali-metal atoms do not posses electric quadrupole moments. However, the hyperfine interaction between nuclear moments and atomic electrons distorts the spherical symmetry of electronic clouds and leads to non-vanishing atomic quadrupole moments. We evaluate these hyperfine-induced quadrupole moments using techniques of relativistic many-body theory and compile results for Li, Na, K, Rb, and Cs atoms. For heavy atoms we find that the hyperfine-induced quadrupole moments are strongly (two orders of magnitude) enhanced by correlation effects. We further a…
Collisions with chemically inert atoms or molecules change the hyperfine coupling of an alkali-metal atom through the hyperfine-shift interaction. This interaction is responsible for the pressure shifts of the microwave resonances of alkali-metal atoms in buffer gases, is an important spin interaction in alkali-metal--noble-gas van der Waals molecules, and is anticipated to enable the magnetoassociation of ultracold molecules such as RbSr. An improved estimate is presented for the long-range asymptote of this interaction for Na, K, Rb, and Cs. To test the results, the change in hyperfine coupl…
We report on our calculations of differential hyperfine anomalies in the nuclear single-particle model for a number of atoms and ions of interest for studies of fundamental symmetries violations. Comparison with available experimental data allows one to discriminate between different nuclear magnetization models, and this data supports the use of the nuclear single-particle model over the commonly-used uniform ball model. Accurate modelling of the nuclear magnetization distribution is important for testing atomic theory through hyperfine comparisons. The magnetization distribution must be adeq…
The static and dynamic electric-dipole polarizabilities and tune-out wavelengths for the ground state of Cs atoms are calculated by using a semiempirical relativistic configuration interaction plus core polarization approach. By considering the hyperfine splittings, the static and dynamic polarizabilities, hyperfine Stark shifts, and tune-out wavelengths of the hyperfine components of the ground level of $^{133}$Cs atoms are determined. It is found that the hyperfine shifts of the first primary tune-out wavelengths are about $-$0.0135 nm and 0.0106 nm, which are very close to the hyperfine int…
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…
We apply relativistic many-body methods to compute static differential polarizabilities for transitions inside the ground-state hyperfine manifolds of monovalent atoms and ions. Knowing this transition polarizability is required in a number of high-precision experiments, such as microwave atomic clocks and searches for CP-violating permanent electric dipole moments. While the traditional polarizability arises in the second-order of interaction with the externally-applied electric field, the differential polarizability involves additional contribution from the hyperfine interaction of atomic el…
The hyperfine structures of the $2\,^3\!S_1$ and $2\,^3\!P_J$ states of the $^7$Be$^{2+}$ and $^9$Be$^{2+}$ ions are investigated within the framework of the nonrelativistic quantum electrodynamics (NRQED). The uncertainties of present hyperfine splitting results of $^9$Be$^{2+}$ are in the order of several tens of ppm, where two orders of magnitude improvement over the previous theory and experiment values has been achieved. The contribution of nuclear electric quadrupole moment to hyperfine splitting of $^7$Be$^{2+}$ has been studied. A scheme for determining the properties of Be nuclei in t…
We report a hyperfine-states related weak equivalence principle (WEP) test which searches for possible WEP violation signal in single atom interferometer. With the ground hyperfine states $\left|F=1\right\rangle$ and $\left|F=2\right\rangle$ of $^{87}$Rb atoms simultaneously scanned over different paths in a Raman Mach-Zehnder interferometer (MZI), the difference of the free fall accelerations for the atom in the two hyperfine states is encoded into the phase shift of the MZI, contributing a WEP test signal. The test signal can be extracted out by reversing the direction of the effective wave …
Ultracold molecules with both electron spin and an electric dipole moment offer new possibilities in quantum science. We use density-functional theory to calculate hyperfine coupling constants for a selection of molecules important in this area, including RbSr, LiYb, RbYb, CaF and SrF. We find substantial hyperfine coupling constants for the fermionic isotopes of the alkaline-earth and Yb atoms. We discuss the hyperfine level patterns and Zeeman splittings expected for these molecules. The results will be important both to experiments aimed at forming ultracold open-shell molecules and to thei…
We measured the ground-state hyperfine splitting of trapped ${}^{113}$Cd${}^{+}$ ions to be 15199862855.02799(27) Hz with a fractional uncertainty of $1.8\times10^{-14}$. The ions were trapped and laser-cooled in a linear quadrupole Paul trap. The fractional frequency stability was measured to be ${4.2} \times 10^{-13}/\sqrtτ $, obtained from Ramsey fringes of high signal-to-noise ratio and taken over a measurement time of nearly 5 hours, which is close to the short-term stability limit estimated from the Dick effect. Our result is consistent with previous reported values, but the measurement …
A number of bound states properties and the hyperfine structure of the 23S(L=0)-state in the Be atom are determined from the results of highly accurate computations. The energies of the hyperfine structure levels for this state are ε(F=12) = -13725.635(7) MHz, ε(F=32) = -5490.254(7) MHz and ε(F=52) = 8235.381(7) MHz, respectively. The hyperfine structure splittings are Δ12 = 8235.381(7) MHz and Δ23 = 13725.635(7) MHz, respectively. The spectrum of low-lying (bound) triplet states in the Be atom is briefly investigated.
We present measurements of the hyperfine splitting in the Yb-173 $6s6p~^1P_1^{\rm o} (F^{\prime}=3/2,7/2)$ states that disagree significantly with those measured previously by Das and Natarajan [Phys. Rev. A 76, 062505 (2007)]. We point out inconsistencies in their measurements and suggest that their error is due to optical pumping and improper determination of the atomic line center. Our measurements are made using an optical frequency comb. We use an optical pumping scheme to improve the signal-to-background ratio for the $F^{\prime}=3/2$ component.
NRQED approach to the fine and hyperfine structure corrections of order m$α$ 6 and m$α$ 6 (m/M)-Application to the hydrogen atom The NRQED approach is applied to the calculation of relativistic corrections to the fine and hyperfine structure of hydrogenlike atoms at orders m$α$ 6 and m$α$ 6 (m/M). Results are found to be in agreement with those of the relativistic theory. This confirms that the derived NRQED effective potentials are correct, and may be used for studying more complex atoms or molecules. Furthermore, we verify the equivalence between different forms of the NRQED Lagrangian used …
Calculations of the magnetic hyperfine structure rely on the input of nuclear properties -- nuclear magnetic moments and nuclear magnetization distributions -- as well as quantum electrodynamic (QED) radiative corrections for high-accuracy evaluation in heavy atoms. The uncertainties associated with assumed values of these properties limit the accuracy of hyperfine calculations. For example, for the heavy alkali-metal atoms Cs and Fr, these uncertainties may amount collectively to almost 1\% or 2\%, respectively. In this paper we propose a method for removing the dependence of hyperfine struct…
Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements and static polarizabilities for alkali-metal atoms
We observe a density-dependent collective suppression of optical pumping between the hyperfine ground states in an array of submicrometer-sized clouds of cold rubidium atoms. The suppressed Raman transition rate can be explained by strong resonant dipole-dipole interactions that are enhanced by increasing atom density. The observations are consistent with stochastic electrodynamics simulations that incorporate the effects of the nonlinear population transfer via internal atomic levels embedded in a coupled-dipole model.
One of the ASACUSA (Atomic Spectroscopy And Collisions Using Slow Antiprotons) collaboration's goals is the measurement of the ground state hyperfine transition frequency in antihydrogen, the antimatter counterpart of one of the best known systems in physics. This high precision experiment yields a sensitive test of the fundamental symmetry of CPT. Numerical simulations of hyperfine transitions of antihydrogen atoms have been performed providing information on the required antihydrogen events and the achievable precision.
An optical measurement of the 2S hyperfine interval in atomic hydrogen using two-photon spectroscopy of the 1S-2S transition gives a value of 177 556 834.3(6.7) Hz. The uncertainty is 2.4 times smaller than achieved by our group in 2003 and more than 4 times smaller than for any independent radio-frequency measurement. The specific combination of the 2S and 1S hyperfine intervals predicted by QED theory $D_{21}=8 f_{\rm HFS}({2S}) - f_{\rm HFS}({1S})=48 953(3)$ Hz is in good agreement with the value of 48 923(54) Hz obtained from this experiment.
The creation and detection of atomic polarization is examined theoretically, through the study of basic optical-pumping mechanisms and absorption and fluorescence measurements, and the dependence of these processes on the size of ground- and excited-state hyperfine splittings is determined. The consequences of this dependence are studied in more detail for the case of nonlinear magneto-optical rotation in the Faraday geometry (an effect requiring the creation and detection of rank-two polarization in the ground state) with alkali atoms. Analytic formulas for the optical rotation signal under v…
A method for precise calculation of the energy corrections due to second order electric quadrupole interactions, as well as mixed electric quadrupole-vacuum polarization in the framework of the dynamic hyperfine structure in heavy muonic atoms is presented. For this, a multipole expansion of the Uehling potential is performed. The approach is applicable for an arbitrary nuclear electric charge distribution. By performing these calculations for muonic Rhenium and Uranium using a deformed Fermi distribution, it is shown that both corrections contribute on a level presumably visible in upcoming e…
Precision calculations of the fine and hyperfine structure of muonic atoms are performed in a relativistic approach and results for muonic 205 Bi, 147 Sm, and 89 Zr are presented. The hyperfine structure due to magnetic dipole and electric quadrupole splitting is calculated in first order perturbation theory, using extended nuclear charge and current distributions. The leading correction from quantum electrodynamics, namely vacuum polarization in Uehling approximation, is included as a potential directly in the Dirac equation. Also, an effective screening potential due to the surrounding elect…
The Zeeman hyperfine state dependent force in a Stern-Gerlach (SG) experiment has been exploited to separate and detect atoms having different Zeeman hyperfine states in a cold atom cloud. Utilizing this SG technique, we have made the quantitative estimate of atoms in different Zeeman hyperfine states in an atom cloud, which has been helpful in optimizing the optical pumping of atoms for efficient preparation of atomic state. Employing an optimized optical pumping, nearly $92 \% $ of cold $^{87}Rb$ atoms from a grey magneto-optical trap (G-MOT) on atom-chip have been optically pumped to the tr…
Determination of nuclear moments for many nuclei relies on the computation of hyperfine constants, with theoretical uncertainties directly affecting the resulting uncertainties of the nuclear moments. In this work we improve the precision of such method by including for the first time an iterative solution of equations for the core triple cluster amplitudes into the relativistic coupled-cluster method, with large-scale complete basis sets. We carried out calculations of the energies and magnetic dipole and electric quadrupole hyperfine structure constants for the low-lying states of 229Th^(3+)…
Analysis of hyperfine structure constants of singly ionised cobalt (Co II) were performed on cobalt spectra measured by Fourier transform spectrometers in the region $3000-63000$ cm$^{-1}$ ($3333-159$ nm). Fits to over $700$ spectral lines led to measurements of $292$ magnetic dipole hyperfine interaction $A$ constants, with values between $-32.5$ mK and $59.5$ mK ($1$ mK $=0.001$ cm$^{-1}$). Uncertainties of $255$ A constants were between $\pm0.4$ mK and $\pm3.0$ mK, the remaining $37$ ranged up to $\pm7$ mK. The electric quadrupole hyperfine interaction $B$ constant could be estimated for on…
We report electromagnetically induced transparency (EIT) in cold 85Rb atoms, trapped in the lower hyperfine level F = 2, of the ground state 5$^{2}S_{1/2}$ (Tiwari V B \textit{et al} 2008 {\it Phys. Rev.} A {\bf 78} 063421). Two steady state $Λ$-type systems of hyperfine energy levels are investigated using probe transitions into the levels F$^{\prime}$ = 2 and F$^{\prime}$ = 3 of the excited state 5$^{2}P_{3/2}$ in the presence of coupling transitions F = 3 $\to$ F$^{\prime}$ = 2 and F = 3 $\to$ F$^{\prime}$ = 3, respectively. The effects of uncoupled magnetic sublevel transitions and couplin…
In previous work devoted to {\it ab initio} calculations of hyperfine structure constants in nitrogen and fluorine atoms, we observed sizeable relativistic effects, a priori unexpected for such light systems, that can even largely dominate over electron correlation. We observed that the atomic wave functions calculated in the Breit-Pauli approximation describe adequately the relevant atomic levels and hyperfine structures, even in cases for which a small relativistic $LS$-term mixing becomes crucial. In the present work we identify new levels belonging to the spectroscopic terms $2p^4(^3\!P) 3…
The theory is developed for one and two atom interactions when the atom has a Rydberg electron attached to a hyperfine split core state. This situation is relevant for some of the rare earth and alkaline earth atoms that have been proposed for experiments on Rydberg-Rydberg interactions. For the rare earth atoms, the core electrons can have a very substantial total angular momentum, $J$, and a non-zero nuclear spin, $I$. In the alkaline earth atoms there is a single, $s$, core electron whose spin can couple to a non-zero nuclear spin for odd isotopes. The resulting hyperfine splitting of the c…
This study addresses the effect of the magnetic hyperfine interaction on the relativistic H1s wave functions. These are used to calculate the electric, magnetic, and confinement force densities acting on the 1s electron. The magnetic field couples Dirac equations for different angular momenta. These are solved numerically for the hyperfine singlet and triplet, as well as for a classical magnetic dipole. In the singlet ground state the hyperfine interaction shifts the electron density toward the proton. A similar shift is found for the classical dipole, and an opposite shift for the triplet. Th…
We perform accurate calculations of energy levels as well as fine and hyperfine splittings of the lowest $^{1,3}\!P_J$, $^{3}\!S_1$, $^{3}\!P^e_J$, and $^{1,3}\!D_J$ excited states of the $^9$Be atom using explicitly correlated Gaussian functions and report on the breakdown of the standard hyperfine structure theory. Because of the strong hyperfine mixing, which prevents the use of common hyperfine constants, we formulate a description of the fine and hyperfine structure that is valid for an arbitrary coupling strength and may have wide applications in many other atomic systems.
The microwave resonant frequencies of ground-state 87Rb and 133Cs atoms in Xe buffer gas are shown to have a relatively large nonlinear dependence on the Xe pressure, presumably because of RbXe or CsXe van der Waals molecules. The nonlinear shifts for Xe are opposite in sign to the previously measured shifts for Ar and Kr, even though all three gases have negative linear shifts. The Xe data show striking discrepancies with the previous theory for nonlinear shifts. Most of this discrepancy is eliminated by accounting for the spin-rotation interaction in addition to the hyperfine-shift interacti…
