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Physical Review A

Determination of quadrupolar dispersion coefficients of the alkali-metal atoms interacting with different material media

Harpreet Kaur, Vipul Badhan, Bindiya Arora, B. K. Sahoo

Published Oct 20, 2022• 2 citations
Publisher

Abstract

In the present work, we determine the ${C}_{5}$ coefficients along with their uncertainties due to quadrupole polarization effects of all the alkali atoms interacting with a metal (Au), a semiconductor (Si), and four dielectric materials (${\mathrm{SiO}}_{2}, {\mathrm{SiN}}_{x}$, yttrium aluminum garnet, and sapphire). The required dynamic electric quadrupole ($E2$) polarizabilities are evaluated by calculating $E2$ matrix elements of a large number of transitions in the alkali atoms by employing a relativistic coupled-cluster method. A significant contribution towards the long-range van der Waals potential is made by the quadrupole polarization effects. Our finding shows that contributions from the ${C}_{5}$ coefficients to the atom-wall interaction potentials are pronounced at short distances (1--10 nm). The ${C}_{3}$ coefficients of a Fr atom interacting with the above material media are also reported. These results could be useful in understanding the interactions of alkali atoms trapped in different material bodies during high-precision measurements.

DOI
10.1103/physreva.106.042813

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In the present work, we determine the C5{C}_{5}C5​ coefficients along with their uncertainties due to quadrupole polarization effects of all the alkali atoms interacting with a metal (Au), a semiconductor (Si), and four dielectric materials (SiO2,SiNx{\mathrm{SiO}}_{2}, {\mathrm{SiN}}_{x}SiO2​,SiNx​, yttrium aluminum garnet, and sapphire). The required dynamic electric quadrupole (E2E2E2) polarizabilities are evaluated by calculating E2E2E2 matrix elements of a large number of transitions in the alkali atoms by employing a relativistic coupled-cluster method. A significant contribution towards the long-range van der Waals potential is made by the quadrupole polarization effects. Our finding shows that contributions from the C5{C}_{5}C5​ coefficients to the atom-wall interaction potentials are pronounced at short distances (1--10 nm). The C3{C}_{3}C3​ coefficients of a Fr atom interacting with the above material media are also reported. These results could be useful in understanding the interactions of alkali atoms trapped in different material bodies during high-precision measurements.
The C3{C}_{3}C3​ coefficients and their ratios for the alkali-metal atoms are determined very accurately by taking into account the optical properties of the atoms and four distinct types of trapping materials such as Au (metal), Si (semiconductor), vitreous SiO2{\text{SiO}}_{2}SiO2​ (dielectric), and SiNx{\text{SiN}}_{x}SiNx​ (dielectric). Dynamic dipole polarizabilities are calculated precisely for the alkali-metal atoms that produce C3{C}_{3}C3​ coefficients in a perfectly conducting medium within 0.2% accuracy. Thus, uncertainties from the atomic polarizabilities in the evaluation of the material-dependent C3{C}_{3}C3​ coefficients are small and accuracies of these C3{C}_{3}C3​ values mainly rely on the used optical data which are not taken into account in the present work. Our findings are in very good agreement with the available measurements, but they differ by around 10% from the previously reported high-precision calculations in heavy atoms for the perfect conductors. We also revisit the dispersion coefficients for the alkali-metal dimers and evaluate them using the above dynamic dipole polarizabilities which provide slightly different error bars than the other reported precise results. These coefficients are fitted into a ready-to-use functional form to aid the experimentalists in finding out the interaction potential only with the knowledge of atom-wall distance.
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 studies of magnetic field induced Feshbach resonances in ultracold collisions of Na and of Rb atoms. For Cs we provide critically needed data for ultracold collision studies.
Accurate knowledge of interaction potentials among the alkali-metal 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-metal atoms with the Ca+{\mathrm{Ca}}^{+}Ca+, Ba+{\mathrm{Ba}}^{+}Ba+, Sr+{\mathrm{Sr}}^{+}Sr+, and Ra+{\mathrm{Ra}}^{+}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 RRR. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above-mentioned systems, which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random-phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representations of the dispersion coefficients versus RRR are given among all the alkaline ions with Rb.
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 RRR. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus RRR are given among all the considered atoms and ions.
The scalar and tensor dynamic polarizabilities of the first excited 2P1∕2,3∕2^{2}P_{1∕2,3∕2}2P1∕2,3∕2​ states of the alkali-metal atoms Na\mathrm{Na}Na, K\mathrm{K}K, and Rb\mathrm{Rb}Rb are calculated using relativistic many-body perturbation theory. Comparison with experimental measurements of the static polarizabilities suggests that the errors in the theoretical predictions do not exceed 1%. The dynamic polarizabilities at imaginary frequencies are employed to calculate the long-range van der Waals coefficients for the interaction of ground-state helium atoms with the excited alkali-metal atoms to a probable error of less than 2%.
The van der Waals coefficients, C6,C8,{C}_{6},{C}_{8},C6​,C8​, and C10{C}_{10}C10​ for the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient, D8{D}_{8}D8​ and the three-body coefficient, C9{C}_{9}C9​ are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.