We present results of first-principles calculations of the frequency-dependent polarizabilities of all alkali atoms for light in the wavelength range 300-1600 nm, with particular attention to wavelengths of common infrared lasers. We parameterize our results so that they can be extended accurately to arbitrary wavelengths above 800 nm. This work is motivated by recent experiments involving simultaneous optical trapping of two different alkali species. Our data can be used to predict the oscillation frequencies of optically-trapped atoms, and particularly the ratios of frequencies of different species held in the same trap. We identify wavelengths at which two different alkali atoms have the same oscillation frequency.
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.
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.
Calculations of the static electric-dipole scalar and tensor polarizabilities are presented for two alkali atoms, Rb and Cs, for the $nS$, $nP_{1/2, 3/2}$, and $nD_{3/2, 5/2}$ states with large principal quantum numbers up to $n = 50$. The calculations are performed within an effective one-electron approximation, based on the Dirac-Fock Hamiltonian with a semi-empirical core-polarization potential. The obtained results are compared with those from a simpler semi-empirical approach and with available experimental data.
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.
The rapid development of experimental techniques to produce ultracold alkali molecules opens the ways to manipulate them and to control their dynamics using external electric fields. A prerequisite quantity for such studies is the knowledge of their static dipole polarizabilities. In this paper, we computed the variations with internuclear distance and with vibrational index of the static dipole polarizability components of all homonuclear alkali dimers including Fr$_2$, and of all heteronuclear alkali dimers involving Li to Cs, in their electronic ground state and in their lowest triplet stat…
We analyze the molecular electric dipole moments (PDMs) and static electric dipole polarizabilities of heteronuclear alkali dimers in their ground states by employing coupled-cluster theory, both in the non-relativistic and four-component relativistic frameworks. The roles of electron correlations as well as relativistic effects are demonstrated by studying them at different levels of theory, followed by a comprehensive treatment of error estimates. We compare our obtained values with the previous non-relativistic calculations, some of which include lower-order relativistic corrections, as wel…
Effective oscillator strength distributions are systematically generated and tabulated for the alkali atoms, the alkaline-earth atoms, the alkaline-earth ions, the rare gases and some miscellaneous atoms. These effective distributions are used to compute the dipole, quadrupole and octupole static polarizabilities, and are then applied to the calculation of the dynamic polarizabilities at imaginary frequencies. These polarizabilities can be used to determine the long-range $C_6$, $C_8$ and $C_{10}$ atom-atom interactions for the dimers formed from any of these atoms and ions, and we present tab…
We present a general approach within the relativistic coupled-cluster theory framework to calculate exactly the first order wave functions due to any rank perturbation operators. Using this method, we calculate the static dipole and quadrupole polarizabilities in some alkali atoms and alkaline earth-metal ions. This may be a good test of the present theory for different rank and parity interaction operators. This shows a wide range of applications including precise calculations of both parity and CP violating amplitudes due to rank zero and rank one weak interaction Hamiltonians. We also give …
We analyze the electric dipole moments (PDMs) and static electric dipole polarizabilities of the alkali--alkaline-earth (Alk-AlkE) dimers by employing finite-field coupled-cluster methods, both in the frameworks of non-relativistic and four-component spinfree relativistic theory. In order to carry out comparative analyses rigorously, we consider those Alk-AlkE molecules made out of the lightest to the medium-heavy constituent atoms (Alk: Li to Rb and AlkE: Be through Sr). We present behaviour of electron correlation effects as well as relativistic effects with the size of the molecules. Uncert…
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 scalar and tensor components of the electric quadrupole (E2) polarizabilities of the first two excited states of all the alkali-metal atoms are determined. To validate the calculations, we have evaluated the ground state E2 polarizabilities of these atoms and compared them with the literature values. We could not find the ground state E2 polarizability value for Fr in the literature to compare with our result. The dominant parts of these quantities are estimated by combining the precisely calculated E2 transition matrix elements of many low-lying transitions with the experimental energies,…
Intensity modulated optical lattice potentials can change sign for an alkali metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO$_2$ laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential seen by the Rydberg atom can be made to vanish for atoms in \targeted" Rydberg states. Such state selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices.…
Apropos to the growing interest in the study of long-range interactions which for their applications in cold atom physics, we have performed theoretical calculation for the two-dipole $C_6$ and three-dipole $C_9$ dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The $C_6$ and $C_9$ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated $C_6$ coefficients for the considered alkaline-earth atoms among themselves are compared with the previously …
We report the dispersion coefficients for the interacting inert gas atoms with the alkali ions, alkaline earth ions and alkali atoms with their singly charged ions. We use our relativistic coupled-cluster method to determine dynamic dipole and quadrupole polarizabilities of the alkali atoms and singly ionized alkaline earth atoms, whereas a relativistic random phase approximation approach has been adopted to evaluate these quantities for the closed-shell configured inert gas atoms and the singly and doubly ionized alkali and alkaline earth atoms, respectively. Accuracies of these results are a…
We evaluate separation dependent van der Waal dispersion ($C_3$) coefficients for the interactions of the Li, Na, K and Rb alkali atoms with a graphene layer and with a single walled carbon nanotube (CNT) using the hydrodynamic and Dirac models. The results from both the models are evaluated using accurate values of the dynamic polarizabilities of the above atoms. Accountability of these accurate values of dynamical polarizabilities of the alkali atoms in determination of the above $C_3$ coefficients are accentuated by comparing them with the coefficients evaluated using the dynamic dipole pol…
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…
Using the orbitals generated by the van Leeuwen-Baerends potential, we calculate frequency dependent response properties of noble gas atoms of He, Ne and Ar and alkaline earth atoms Be and Mg, with particlar emphasis on their nonlinear polarizabilities. For this we employ time-dependent Kohn-Sham formalism with adiabatic local-density aproximation (ALDA) for exchange and correlation. We show that results thus obtained for frequency dependent polarizabilities of the inert gas atoms are highly acurate. On the other hand, polarizabilities of the alkaline earths are not given with the same accurac…
We present revised measurements of the static electric dipole polarizabilities of K, Rb, and Cs based on atom interferometer experiments presented in [Phys. Rev. A 2015, 92, 052513] but now re-analyzed with new calibrations for the magnitude and geometry of the applied electric field gradient. The resulting polarizability values did not change, but the uncertainties were significantly reduced. Then we interpret several measurements of alkali metal atomic polarizabilities in terms of atomic oscillator strengths $f_{ik}$, Einstein coefficients $A_{ik}$, state lifetimes $τ_{k}$, transition dipole…
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 attractive branch of the interaction potentials with the surface of gold have been computed for a large variety of atomic systems: the hydrogen atom, noble gases (He, Ne, Ar, Kr, Xe), alkali atoms (Li, Na, K, Rb, Cs) and alkaline atoms (Be, Mg, Ca, Sr, Ba). The results include highly accurate dynamic polarizabilities for the helium atom calculated using a variational method and explicitly correlated wavefunctions. For other atoms considered we used the data available in the literature. The interaction potentials include both the effects of retardation of the electromagnetic interactions an…
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…
Largely motivated by a number of applications, the van der Waals dispersion coefficients ($C_3$s) of the alkali ions (Li$^+$, Na$^+$, K$^+$ and Rb$^+$), the alkaline-earth ions (Ca$^+$, Sr$^+$, Ba$^+$ and Ra$^+$) and the inert gas atoms (He, Ne, Ar and Kr) with a graphene layer are determined precisely within the framework of Dirac model. For these calculations, we have evaluated the dynamic polarizabilities of the above atomic systems very accurately by evaluating the transition matrix elements employing relativistic many-body methods and using the experimental values of the excitation energi…
The random-phase approximation with exchange (RPAE) is used with a $B$-spline basis to compute dynamic dipole polarizabilities of noble-gas atoms and several other closed-shell atoms (Be, Mg, Ca, Zn, Sr, Cd, and Ba). From these, values of the van der Waals $C_6$ constants for positronium interactions with these atoms are determined and compared with existing data. Our best predictions of $C_6$ for Ps--noble-gas pairs are expected to be accurate to within 1%, and to within a few per cent for the alkaline earths. We also used accurate dynamic dipole polarizabilities from the literature to comput…
Using accurate dynamic polarizabilities of Li, Na, K and, Rb atoms, we scrutinize the thermal Casimir-Polder interactions of these atoms with a single layered graphene. Considering the modified Lifshitz theory for material interactions, we reanalyze the dispersion coefficients ($C_3$s) of the above atoms with graphene as functions of separation distance, gap parameter and temperature among which some of them were earlier studied by estimating dynamic polarizabilities of the above atoms from the single oscillator model approximation. All these $C_3$ coefficients have been evaluated in the frame…
A relativistic description of the structure of heavy alkali atoms and alkali-like ions using S-spinors and L-spinors has been developed. The core wavefunction is defined by a Dirac-Fock calculation using an S-spinors basis. The S-spinor basis is then supplemented by a large set of L-spinors for the calculation of the valence wavefunction in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a $Z=60$ hydrogenic ion. The approach is then appli…
The damping coefficients for the alkali atoms are determined very accurately by taking into account the optical properties of the atoms and three distinct types of trapping materials such as Au (metal), Si (semi-conductor) and vitreous SiO2 (dielectric). Dynamic dipole polarizabilities are calculated precisely for the alkali atoms that reproduce the damping coefficients in the perfect conducting medium within 0.2% accuracy. Upon the consideration of the available optical data of the above wall materials, the damping coefficients are found to be substantially different than those of the ideal c…
Using first-principles calculations, we identify "magic-zero" optical wavelengths, λ_zero, for which the ground-state frequency-dependent polarizabilities of alkali-metal atoms vanish. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. We discuss the use of magic-zero wavelengths for sympathetic cooling in two-species mixtures of alkalis with group-II and other elements of interest. Special cases in which these wavelengths coincide with s…
The van der Waals coefficients and the separation dependent retardation functions of the interactions between the atomically thin films of the multi-layered transition metal molybdenum disulfide (MoS$_2$) dichalcogenides with the alkali atoms are investigated. First, we determine the frequency-dependent dielectric permittivity and intrinsic carrier density values for different layers of MoS$_2$ by adopting various fitting models to the recently measured optical data reported by Yu and co-workers [Sci. Rep. {\bf 5}, 16996 (2015)] using spectroscopy ellipsometry. Then, dynamic electric dipole po…
The properties of the electronic ground state of the polar and paramagnetic europium-$S$-state-atom molecules have been investigated. Ab initio techniques have been applied to compute the potential energy curves for the europium-alkali-metal-atom, Eu$X$ ($X$=Li, Na, K, Rb, Cs), europium-alkaline-earth-metal-atom, Eu$Y$ ($Y$=Be, Mg, Ca, Sr, Ba), and europium-ytterbium, EuYb, molecules in the Born-Oppenheimer approximation for the high-spin electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), w…
Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency stan…
We present the derivation of the frequency dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the 87Rb atom 5s ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the 5s ground state sub-levels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far-detuned from the atomic resonance and the total electronic angular momentu…
Diatomic molecular anions of alkali-metal and alkaline-earth-metal atoms
University of Monastir（莫纳斯提尔大学）；University of Warsaw（华沙大学）；University of Sousse（苏塞大学）；Higher Institute of Applied Sciences and Technology of Sousse（苏塞高等应用科学与技术学院）；American University of Ras Al Khaimah（拉斯海马美国大学）
We attempt to provide physical interpretations of light-induced desorption phenomena that have recently been observed for alkali atoms on glass surfaces of alkali vapor cells used in atomic physics experiments. We find that the observed desorption phenomena are closely related to recent studies in surface science, and can probably be understood in the context of these results. If classified in terms of the photon-energy dependence, the coverage and the bonding state of the alkali adsorbates, the phenomena fall into two categories: It appears very likely that the neutralization of isolated ioni…
The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the $7s~^2S_{1/2}$, $7p~^2P_{1/2, 3/2}$ and $8s~^{2}S_{1/2}$ levels of the $7s~^{2}S_{1/2}-7p~^{2}P_{1/2,3/2}$ and $7s~^{2}S_{1/2}-8s~^{2}S_{1/2}$ transitions, respectively. Wavelengths in the ultraviolet, visible and near infrared region is identified that are suitable for cooling and trapping. Magic wavelengths between 600-700~nm and 700…
We analyze several possibilities for precisely measuring electronic transitions in atomic helium by the direct use of phase-stabilized femtosecond frequency combs. Because the comb is self-calibrating and can be shifted into the ultraviolet spectral region via harmonic generation, it offers the prospect of greatly improved accuracy for UV and far-UV transitions. To take advantage of this accuracy an ultracold helium sample is needed. For measurements of the triplet spectrum a magneto-optical trap (MOT) can be used to cool and trap metastable 2^3S state atoms. We analyze schemes for measuring t…
