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arXiv:physics/0105030 · Physical Review Letters

Feasibility of Cooling and Trapping Metastable Alkaline-Earth Atoms

Andrei Derevianko

Published Jun 22, 2001• 69 citations
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Abstract

Metastability and long-range interactions of Mg, Ca, and Sr in the lowest-energy metastable $^{3}P_{2}$ state are investigated. The calculated lifetimes are 38 min for ${\mathrm{Mg}}^{*}$, 118 min for ${\mathrm{Ca}}^{*}$, and 17 min for ${\mathrm{Sr}}^{*}$, supporting feasibility of cooling and trapping experiments. The quadrupole-quadrupole long-range interactions of two metastable atoms are evaluated for various molecular symmetries. Hund's case (c) ${4}_{g}$ potential possesses a large 100--1000 K potential barrier. Therefore magnetic trap losses can possibly be reduced using cold metastable atoms in a stretched $M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ state. Calculations were performed in the framework of ab initio relativistic configuration interaction method coupled with the random-phase approximation.

DOI
10.1103/physrevlett.87.023002

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Metastability and long-range interactions of Mg, Ca, and Sr in the lowest-energy metastable 3P2^{3}P_{2}3P2​ state are investigated. The calculated lifetimes are 38 min for Mg∗{\mathrm{Mg}}^{*}Mg∗, 118 min for Ca∗{\mathrm{Ca}}^{*}Ca∗, and 17 min for Sr∗{\mathrm{Sr}}^{*}Sr∗, supporting feasibility of cooling and trapping experiments. The quadrupole-quadrupole long-range interactions of two metastable atoms are evaluated for various molecular symmetries. Hund's case (c) 4g{4}_{g}4g​ potential possesses a large 100--1000 K potential barrier. Therefore magnetic trap losses can possibly be reduced using cold metastable atoms in a stretched M=2M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2M=2 state. Calculations were performed in the framework of ab initio relativistic configuration interaction method coupled with the random-phase approximation.
Hyperfine quenching rates of the lowest-energy metastable 3P0^{3}P_{0}3P0​ and 3P2^{3}P_{2}3P2​ states of Mg, Ca, Sr, and Yb atoms are computed. The calculations are carried out using ab initio relativistic many-body methods. The computed lifetimes may be useful for designing novel ultraprecise optical clocks and trapping experiments with the 3P2^{3}P_{2}3P2​ fermionic isotopes. The resulting natural widths of the $^{3}P_{0}\ensuremath{-}^{1}S_{0}$ clock transition are 0.44mHz0.44\phantom{\rule{0.3em}{0ex}}\text{mHz}0.44mHz for 25Mg^{25}\mathrm{Mg}25Mg, 2.2mHz2.2\phantom{\rule{0.3em}{0ex}}\text{mHz}2.2mHz for 43Ca^{43}\mathrm{Ca}43Ca, 7.6mHz7.6\phantom{\rule{0.3em}{0ex}}\text{mHz}7.6mHz for 87Sr^{87}\mathrm{Sr}87Sr, 43.5mHz43.5\phantom{\rule{0.3em}{0ex}}\text{mHz}43.5mHz for 171Yb^{171}\mathrm{Yb}171Yb, and 38.5mHz38.5\phantom{\rule{0.3em}{0ex}}\text{mHz}38.5mHz for 173Yb^{173}\mathrm{Yb}173Yb. Compared to the bosonic isotopes, the lifetime of the 3P2^{3}P_{2}3P2​ states in fermionic isotopes is noticeably shortened by the hyperfine quenching but still remains long enough for trapping experiments.
Alkaline-earth-metal atoms in their lowest (nsnp)(\mathrm{nsnp})(nsnp) 3P2{}^{3}{P}_{2}3P2​ state are exceptionally long lived and can be trapped magnetically. The nonspherical atomic structure leads to anisotropic long-range interactions between two metastable alkaline-earth-metal atoms. The anisotropy affects the rotational motion of the diatomic system and couples states of different rotational quantum numbers. This paper develops a tensorial decomposition of the most important long-range interaction operators, and a systematic inclusion of molecular rotations, in the presence of an external magnetic field. This analysis illuminates the nature of the coupling between the various degrees of freedom. The consequences are illustrated by application to a system of practical interest: metastable 88Sr.{}^{88}\mathrm{Sr}.88Sr. Using atomic parameters determined in a nearly ab initio calculation, we compute adiabatic potential-energy curves. The anisotropic interatomic interaction, in combination with the applied magnetic field, is demonstrated to induce the formation of a long-range molecular potential well. This curve correlates to two fully polarized, low-field seeking atoms in a rotational s-wave state. The coupling among molecular rotational states controls the existence of the potential well, and its properties vary as a function of magnetic-field strength, thus allowing the scattering length in this state to be tuned. The scattering length of metastable 88Sr{}^{88}\mathrm{Sr}88Sr displays a resonance at a field of 339 G.
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.
Ultracold collisions of spin-polarized 24Mg, 40Ca, and 88Sr in the metastable 3P2 excited state are investigated based on molecular potentials obtained from ab initio calculations. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 mT. A loss-rate model shows that losses should be smallest near zero magnetic field and for fields slightly larger than the resonance field, where the scattering length is also positive.
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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 C6C_6C6​ and three-dipole C9C_9C9​ dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The C6C_6C6​ and C9C_9C9​ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated C6C_6C6​ coefficients for the considered alkaline-earth atoms among themselves are compared with the previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the C6C_6C6​ coefficients for alkaline-earth atoms with alkaline-earth ions and the C9C_9C9​ coefficients, we have performed separate fitting calculations and compared. Our calculations match in an excellent manner with the fitting calculations. We have also reported the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth ions, i.e., Mg+^++, Ca+^++, Sr+^++, and Ba+^++ as well as the alkaline-earth atoms, i.e., Mg, Ca, Sr, and Ba. These, when compared with the available experimental results, show good agreement.