We analyze second-order $M1$-$M1$ and $M1$-$E2$ effects to the hyperfine structure (HFS) of the lowest energy $P$ states of alkali-metal atoms arising from the coupling of the two ($J=1/2,3/2$) fine-structure levels through the hyperfine interaction. We find these effects to be especially sizable in Li, leading to a $9σ$ correction to the most accurate reported experimental value of the $A(P_{1/2})$ HFS constant of $^7$Li [D. Das and V. Natarajan, J. Phys. B \textbf{41}, 035001 (2008)]. For the remaining alkali-metal systems, the results tabulated within may be referenced as higher precision is sought in experimental determination of the HFS constants.
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 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.
We present calculations of the hyperfine coupling constants for all the heteronuclear alkali-metal diatomic molecules at the equilibrium geometry of the electronic ground state. These constants are important in developing methods to control ultracold polar molecules. The results are based on electronic structure calculations using density functional theory, and are in good agreement with experiment for the limited set of molecules for which experiments are so far available.
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…
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…
Removal energies and hyperfine constants of the lowest four $ns, np_{1/2}$ and $np_{3/2}$ states in Na, K, Rb and Cs are calculated; removal energies of the n=7--10 states and hyperfine constants of the n=7 and 8 states in Fr are also calculated. The calculations are based on the relativistic single-double (SD) approximation in which single and double excitations of Dirac-Hartree-Fock (DHF) wave functions are included to all-orders in perturbation theory. Using SD wave functions, accurate values of removal energies, electric-dipole matrix elements and static polarizabilities are obtained, howe…
The Z-vector method in the relativistic coupled-cluster framework is used to calculate magnetic hyperfine structure constant ($A_J$) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The Z-vector results are in very good agreement with the experiment. The $A_J$ values of Li, Na, K, Rb, Cs, Be$^{+}$, Mg$^{+}$, Ca$^{+}$, and Sr$^{+}$ obtained in the Z-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison sh…
We demonstrate a technique for directly measuring the fine-structure interval in alkali atoms using two frequency-stabilized diode lasers. Each laser has a linewidth of order 1 MHz and precise tunability: one laser is tuned to a hyperfine transition in the D_1 line, and the other laser to a hyperfine transition in the D_2 line. The outputs of the lasers are fed into a scanning Michelson interferometer that measures the ratio of their wavelengths accurately. To illustrate the technique, we measure the fine-structure interval in Rb, and obtain a value of 237.6000(3)(5) cm^-1 for the hyperfine-fr…
We investigate the hyperfine energy levels and Zeeman splittings for homonuclear alkali-metal dimers in low-lying rotational and vibrational states, which are important for experiments designed to produce quantum gases of deeply bound molecules. We carry out density-functional theory (DFT) calculations of the nuclear hyperfine coupling constants. For nonrotating states, the zero-field splittings are determined almost entirely by the scalar nuclear spin-spin coupling constant. By contrast with the heteronuclear case, the total nuclear spin remains a good quantum number in a magnetic field. We a…
We investigate the energy levels of heteronuclear alkali metal dimers in levels correlating with the lowest rotational level of the ground electronic state, which are important in efforts to produce ground-state ultracold molecules. We use density-functional theory to calculate nuclear quadrupole and magnetic coupling constants for RbK and RbCs and explore the hyperfine structure in the presence of electric and magnetic fields. For nonrotating states, the zero-field splittings are dominated by the electron-mediated part of the nuclear spin-spin coupling. They are a few kHz for RbK isotopologs …
We have systematically investigated the ground-state hyperfine structure for alkali-metal atoms ^{87}Rb, ^{133}Cs, ^{211}Fr and alkali-metal-like ions ^{135}Ba^+, ^{225}Ra^+, which are of particular interest for parity violation studies. The quantum electrodynamic one-loop radiative corrections have been rigorously evaluated within an extended Furry picture employing core-Hartree and Kohn-Sham atomic potentials. Moreover, the effect of the nuclear magnetization distribution on the hyperfine structure intervals has been studied in detail and its uncertainty has been estimated. Finally, the theo…
Simple and efficient "λ-method" and "λ/2-method" (λis the resonant wavelength of laser radiation) based on nanometric-thickness cell filled with rubidium are implemented to study the splitting of hyperfine transitions of 85Rb and 87Rb D_1 line in an external magnetic field in the range of B = 0.5 - 0.7 T. It is experimentally demonstrated from 20 (12) Zeeman transitions allowed at low B-field in 85Rb (87Rb) spectra in the case of σ+ polarized laser radiation, only 6 (4) remain at B > 0.5 T, caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Pasch…
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…
The low-lying n(=3,4,5)d $^2D_{5/2}$ states alkaline earth ions are of vital importance in a number of different physical applications. The hyperfine structure constants of these states are characterized by unusually strong electron correlation effects. Relativistic coupled-cluster theory has been employed to carry out {\it ab initio} calculations of these constants. The role of the all order core-polarization effects was found to be decisive in obtaining good agreement of the results of our calculations with accurate measurements. The present work is an apt demonstration of the power of the c…
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…
Measuring the hyperfine structure (HFS) of long-lived $^3P_2$ states of divalent atoms may offer the opportunity of extracting relatively unexplored nuclear magnetic octupole and electric hexadecapole moments. Here, using relativistic many-body methods of atomic structure and the nuclear shell model, we evaluate the effect of these higher nuclear moments on the hyperfine structure. We find that the sensitivity of HFS interval measurements in $^{87}$Sr needed to reveal the perturbation caused by the nuclear octupole moment is on the order of kHz. Results of similar analyses for $^{9}$Be, $^{25}…
We demonstrate that it is possible to efficiently control ultracold chemical reactions of alkali-metal atoms colliding with open-shell alkali-metal dimers in their metastable triplet states by choosing the internal hyperfine and rovibrational states of the reactants as well as by inducing magnetic Feshbach resonances with an external magnetic field. We base these conclusions on coupled-channel statistical calculations that include the effects of hyperfine contact and magnetic-field-induced Zeeman interactions on ultracold chemical reactions of hyperfine-resolved ground-state Na and the triplet…
In atomic systems, clock states feature a zero projection of the total angular momentum and thus a low sensitivity to magnetic fields. This makes them widely used for metrological applications like atomic fountains or gravimeters. Here, we show that a mixture of two such non-magnetic states still display magnetic dipole-dipole interactions. Using high resolution spectroscopy of a planar gas of $^{87}$Rb atoms with a controlled in-plane shape, we explore the effective isotropic and extensive character of these interactions and demonstrate their tunability. Our measurements set strong constraint…
We explore the feasibility of producing ultracold diatomic molecules with nonzero electric and magnetic dipole moments by magnetically associating two atoms, one with zero electron spin and one with nonzero spin. Feshbach resonances arise through the dependence of the hyperfine coupling on internuclear distance. We survey the Feshbach resonances in diatomic systems combining the nine stable alkali-metal isotopes with those of Yb, focussing on the illustrative examples of RbYb and CsYb. We show that the resonance widths may expressed as a product of physically comprehensible terms in the framew…
A relativistic version of the coupled-cluster single-double (CCSD) method is developed for atoms with a single valence electron. In earlier work, a linearized version of the CCSD method (with extensions to include a dominant class of triple excitations) led to accurate predictions for energies, transition amplitudes, hyperfine constants, and other properties of monovalent atoms. Further progress in high-precision atomic structure calculations for heavy atoms calls for improvement of the linearized coupled-cluster methodology. In the present work, equations for the single and double excitation …
We present a first-principles analysis of the noise spectra of alkali-metal-metal vapors in and out of the spin-exchange-relaxation-free (SERF) regime, and we predict non-intuitive features with a potential to further improve the sensitivity of SERF media, and which must be taken into account in their use in quantum optical applications. Studying the process of spin-noise spectroscopy (SNS), we derive analytic formulas for the observable noise spectra, and for the correlation functions among different hyperfine components, which give additional insight into the spin dynamics. The analytic resu…
The electric dipole polarizabilities evaluated at imaginary frequencies for hydrogen, the alkali-metal atoms, the alkaline earth atoms, and the inert gases are tabulated along with the resulting values of the atomic static polarizabilities, the atom-surface interaction constants, and the dispersion (or van der Waals) constants for the homonuclear and the heteronuclear diatomic combinations of the atoms.
Stark-induced electric dipole amplitudes between states of the same nominal parity can be important in experiments to observe parity nonconservation in atoms. The Stark-induced E1 amplitudes are expressed in terms of an irreducible spherical-tensor decomposition. This formalism is applied to the specific case of transitions between hyperfine sublevels of a single atomic state. It is shown that in the ground states of alkali atoms, such transitions are suppressed by many orders of magnitude relative to naive expectations.
We investigate the energetics of reactions involving pairs of alkali metal dimers. Atom exchange reactions to form homonuclear dimers are energetically allowed for some but not all of the heteronuclear dimers. We carry out high-level electronic structure calculations on the potential energy surfaces of all the heteronuclear alkali metal trimers and show that trimer formation reactions are always energetically forbidden for low-lying singlet states of the dimers. The results have important implications for the stability of quantum gases of alkali metal dimers.
We have performed high-precision calculations of the hyperfine structure for n 2S_1/2 and n 2P_1/2 states of the alkali-metal atoms Rb, Cs, and Fr across principal quantum number n, and studied the trend in the size of the correlations. Our calculations were performed in the all-orders correlation potential method. We demonstrate that the relative correlation corrections fall off quickly with n and tend towards constant and non-zero values for highly-excited states. This trend is supported by experiment, and we utilize the smooth dependence on n to make high-accuracy predictions of the hyperfi…
Alkali-metal atomic magnetometers suffer from heading errors in geomagnetic fields as the measured magnetic field depends on the orientation of the sensor with respect to the field. In addition to the nonlinear Zeeman splitting, the difference between Zeeman resonances in the two hyperfine ground states can also generate heading errors depending on initial spin polarization. We examine heading errors in an all-optical scalar magnetometer that uses free precession of polarized $^{87}\text{Rb}$ atoms by varying the direction and magnitude of the magnetic field at different spin polarization regi…
This article deals with the general implementation of 4-component spinor relativistic extended coupled cluster (ECC) method to calculate first order property of atoms and molecules in their open-shell ground state configuration. The implemented relativistic ECC is employed to calculate hyperfine structure (HFS) constant of alkali metals (Li, Na, K, Rb and Cs), singly charged alkaline earth metal atoms (Be+, Mg+, Ca+ and Sr+) and molecules (BeH, MgF and CaH). We have compared our ECC results with the calculations based on restricted active space configuration interaction (RAS-CI) method. Our re…
The retarded long-range potentials for hydrogen and alkali-metal atoms in their ground states and a perfectly conducting wall are calculated. The potentials are given over a wide range of atom-wall distances and the validity of the approximations used is established.
We consider the long-range states expected for complexes formed from an alkali-metal diatomic molecule in a singlet state and an alkali-metal atom. We explore the structure of the Hamiltonian for such systems, and the couplings between the six angular momenta that are present. We consider the patterns and densities of the long-range states, and the terms in the Hamiltonian that can cause Feshbach resonances when the states cross threshold as a function of magnetic field. We present a case study of $^{40}$K$^{87}$Rb+$^{87}$Rb. We show multiple types of resonance due to long-range states with ro…
A finite-field scaling method is applied to evaluate the Lennard-Jones interaction constant C_3 for alkali-metal atoms. The calculations are based on the relativistic single-double (SD) approximation in which single and double excitations of Dirac-Hartree-Fock wave functions are included to all orders in perturbation theory.
We present additional magic wavelengths ($λ_{\rm{magic}}$) for the clock transitions in the alkaline-earth metal ions considering circular polarized light aside from our previously reported values in [J. Kaur et al., Phys. Rev. A {\bf 92}, 031402(R) (2015)] for the linearly polarized light. Contributions from the vector component to the dynamic dipole polarizabilities ($α_d(ω)$) of the atomic states associated with the clock transitions play major roles in the evaluation of these $λ_{\rm{magic}}$, hence facilitating in choosing circular polarization of lasers in the experiments. Moreover, the …
A fully classical explanation of the nonhydrogenic ionization threshold for low angular momentum Rydberg states of Alkali-metal atoms in a linearly polarized low frequency monochromatic microwave field is given: the classical equivalent to the quantum rate-limiting step, which is responsible for the n^(-5) scaling and which according to the literature initiates what then continues as essentially classical diffusion, is found.
We demonstrate a novel way to form and deplete a vapor-cell magneto-optic trap (MOT) using a reversible, solid-state alkali-metal source (AMS) via an applied polarized voltage. Using ~100 mW of electrical power, a trapped-atom number of 5x10^6 has been achieved starting from near zero and the timescales of the MOT formation and depletion of ~1 s. This fast, reversible, and low power alkali-atom source is desirable in both tabletop and portable cold-atom systems. The core technology of this device should translate readily to other alkali and alkaline-earth elements that could find a wide range …
Extensive calculations of the electric-dipole matrix elements in alkali-metal atoms are conducted using the relativistic all-order method. This approach is a linearized version of the coupled-cluster method, which sums infinite sets of many-body perturbation theory terms. All allowed transitions between the lowest ns, np_1/2, np_3/2 states and a large number of excited states are considered in these calculations and their accuracy is evaluated. The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of the excited states…
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…
Weak interactions within a nucleus generate a nuclear spin dependent parity violating electromagnetic moment; the anapole moment. In heavy nuclei, the anapole moment is the dominant contribution to spin-dependent atomic parity violation. We analyze a method to measure the nuclear anapole moment through the electric dipole transition it induces between hyperfine states of the ground level. The method requires tight confinement of the atoms to position them at the anti-node of a standing wave driving the anapole-induced E1 transiton. We explore the necessary limits in the number of atoms, excita…
Dispersion coefficients between the alkali metal atoms (Li-Rb) and alkaline-earth metal atoms (Be-Sr) are evaluated using matrix elements computed from frozen core configuration interaction calculations. Besides dispersion coefficients with both atoms in their respective ground states, dispersion coefficients are also given for the case where one atom is in its ground state and the other atom is in a low lying excited state.
The influence of negative-energy states (NES) on forbidden magnetic-dipole $ns_{1/2}-(n+1)s_{1/2}$ transitions in alkali-metal atoms is investigated. We find that the NES contributions are significant in almost all cases and for rubidium reduce the transition rate by a factor of 8. We tabulate magnetic-dipole (M_1) transition amplitudes for the alkalis. Our M_1 value for cesium, where accurate measurements are available, differs from experiment by 16%. We briefly discuss the feasibility of an experimental test of NES effects.
We have developed an improved scheme for loading atoms into a magneto-optical trap (MOT) from a directed alkali metal dispenser in < 10^-10 torr ultra-high vacuum conditions. A current-driven dispenser was surrounded with a cold absorbing "shroud" held at < 0 C, pumping rubidium atoms not directed into the MOT. This nearly eliminates background alkali atoms and reduces the detrimental rise in pressure normally associated with these devices. The system can be well-described as a current-controlled, rapidly-switched, two-temperature thermal beam, and was used to load a MOT with 3 x 10^8 atoms.
We use the perturbed relativistic coupled-cluster theory to compute the static electric dipole polarizabilities of the singly ionized alkali atoms, namely, Na$^+$, $^+$, Rb$^+$, Cs$^+$ and Fr$^+$. The computations use the Dirac-Coulomb-Breit Hamiltonian with the no-virual-pair approximation and we also estimate the correction to the static electric dipole polarizability arising from the Breit interaction.
Extending the search for the magic wavelengths using the circularly polarized light in rubidium [Phys. Rev. A 86, 033416 (2012)], we pursue here to look for the magic wavelengths in the $ns-np_{1/2,3/2}$ transitions of Li, Na and K alkali atoms. These wavelengths for all possible sub-levels are given and compared with the corresponding wavelengths due to the linearly polarized light. We have also mentioned explicitly the dynamic polarizabilities at few important wave lengths. The present study suggests that it is possible to carry out state insensitive trapping of different alkali atoms using …
The structure of the Cooper minima in the transition probabilities and photoionization cross-sections for low-excited and Rydberg nS, nP, nD and nF states of alkali-metal atoms has been studied using a Coulomb approximation and a quasiclassical model. The range of applicability of the quasiclassical model has been defined from comparison with available experimental and theoretical data on dipole moments, oscillator strengths, and photoionization cross-sections. A new Cooper minimum for transitions between rubidium Rydberg states has been found.
The first three electronically excited states in the alkaline-earth-metal atoms magnesium, calcium, and strontium comprise the (nsnp) triplet P^o_J (J=0,1,2) fine-structure manifold. All three states are metastable and are of interest for optical atomic clocks as well as for cold-collision physics. An efficient technique--based on a physically motivated potential that models the presence of the ionic core--is employed to solve the Schroedinger equation for the two-electron valence shell. In this way, radiative lifetimes, laser-induced clock shifts, and long-range interaction parameters are cal…
The van der Waals coefficients for the alkali-metal atoms from Na to Fr interacting in their ground states, are calculated using relativistic ab initio methods. The accuracy of the calculations is estimated by also evaluating atomic static electric dipole polarizabilities and coefficients for the interaction of the atoms with a perfectly conducting wall. The results are in excellent agreement with the latest data from ultra-cold collisions and from studies of magnetic field induced Feshbach resonances in Na and Rb. For Cs we provide critically needed data for ultra-cold collision studies.
We explore the properties of 3-atom complexes of alkali-metal diatomic molecules with alkali-metal atoms, which may be formed in ultracold collisions. We estimate the densities of vibrational states at the energy of atom-diatom collisions, and find values ranging from 2.2 to 350~K$^{-1}$. However, this density does not account for electronic near-degeneracy or electron and nuclear spins. We consider the fine and hyperfine structure expected for such complexes. The Fermi contact interaction between electron and nuclear spins can cause spin exchange between atomic and molecular spins. It can dri…
Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca$^+$, Ba$^+$, Sr$^+$, and Ra$^+$ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation $R$. Both the dispersion and induction components of these interactions are determined accura…
Spin noise sets fundamental limits to the precision of measurements using spin-polarized atomic vapors, such as performed with sensitive atomic magnetometers. Spin squeezing offers the possibility to extend the measurement precision beyond the standard quantum limit of uncorrelated atoms. Contrary to the current understanding, we show that even in the presence of spin relaxation, spin squeezing can lead to a significant reduction of spin noise, and hence an increase in magnetometric sensitivity, for a long measurement time. This is the case when correlated spin relaxation due to binary alkali-…
We consider long-range interactions between two alkali-metal atoms in their respective ground states. We extend the previous relativistic many-body calculations of C_6 dispersion coefficients [Phys.Rev. Lett. {\bf 82}, 3589 (1999)] to higher-multipole coefficients C_8 and C_10. A special attention is paid to usually omitted contribution of core-excited states. We calculate this contribution within relativistic random-phase approximation and demonstrate that for heavy atoms core excitations contribute as much as 10% to the dispersion coefficients. We tabulate results for both homonuclear and he…
Alkaline-earth-like transition-metal atoms such as Zn and Cd are promising candidates for precision measurements and quantum many-body physics experiments. Here, we theoretically investigate the properties of diatomic molecules containing these closed-shell atoms. We calculate potential energy curves, permanent electric dipole moments, and spectroscopic constants for molecules consisting of either a Zn or Cd atom interacting with an alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atom. We use the ab initio electronic structure coupled cluster method with s…
