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arXiv:physics/0312006 · Physical Review A

Hyperfine quenching of the metastable P0,23 states in divalent atoms

S. G. Porsev, Andrei Derevianko

Published Apr 7, 2004• 117 citations

Abstract

Hyperfine quenching rates of the lowest-energy metastable $^{3}P_{0}$ and $^{3}P_{2}$ 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 $^{3}P_{2}$ fermionic isotopes. The resulting natural widths of the $^{3}P_{0}\ensuremath{-}^{1}S_{0}$ clock transition are $0.44\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{25}\mathrm{Mg}$, $2.2\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{43}\mathrm{Ca}$, $7.6\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{87}\mathrm{Sr}$, $43.5\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{171}\mathrm{Yb}$, and $38.5\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{173}\mathrm{Yb}$. Compared to the bosonic isotopes, the lifetime of the $^{3}P_{2}$ states in fermionic isotopes is noticeably shortened by the hyperfine quenching but still remains long enough for trapping experiments.

DOI: 10.1103/physreva.69.042506

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Hyperfine quenching rates of the lowest-energy metastable

^{3}P_{0}

and

^{3}P_{2}

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

^{3}P_{2}

fermionic isotopes. The resulting natural widths of the

^{3}P_{0}\ensuremath{-}^{1}S_{0}

clock transition are

0.44\phantom{\rule{0.3em}{0ex}}\text{mHz}

for

^{25}\mathrm{Mg}

,

2.2\phantom{\rule{0.3em}{0ex}}\text{mHz}

for

^{43}\mathrm{Ca}

,

7.6\phantom{\rule{0.3em}{0ex}}\text{mHz}

for

^{87}\mathrm{Sr}

,

43.5\phantom{\rule{0.3em}{0ex}}\text{mHz}

for

^{171}\mathrm{Yb}

, and

38.5\phantom{\rule{0.3em}{0ex}}\text{mHz}

for

^{173}\mathrm{Yb}

. Compared to the bosonic isotopes, the lifetime of the

^{3}P_{2}

states in fermionic isotopes is noticeably shortened by the hyperfine quenching but still remains long enough for trapping experiments.

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.

We report the first experimental determination of the hyperfine quenching rate of the $6{s}^{2}\text{ }^{1}{S}_{0}(F=1/2)\ensuremath{-}6s6p\text{ }^{3}{P}_{0}(F=1/2)$ transition in

^{171}\mathrm{Yb}

with nuclear spin

I=1/2

. This rate determines the natural linewidth and the Rabi frequency of the clock transition of a Yb optical frequency standard. Our technique involves spectrally resolved fluorescence decay measurements of the lowest lying

^{3}{P}_{0,1}

levels of neutral Yb atoms embedded in a solid Ne matrix. The solid Ne provides a simple way to trap a large number of atoms as well as an efficient mechanism for populating

^{3}{P}_{0}

. The decay rates in solid Ne are modified by medium effects including the index-of-refraction dependence. We find the

^{3}{P}_{0}

hyperfine quenching rate to be $(4.42\ifmmode\pm\else\textpm\fi{}0.35)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}2}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for free

^{171}\mathrm{Yb}

, which agrees with recent ab initio calculations.

We report magnetic trapping of Yb in the excited

{}^{3}{P}_{2}

state. This state, with a lifetime of 15 s, could play an important role in studies ranging from optical clocks and quantum computation to the search for a permanent electric dipole moment. Yb atoms are first cooled and trapped in the ground state in a 399-nm magneto-optic trap. The cold atoms are then pumped into the excited state by driving the ${}^{1}{S}_{0}\ensuremath{\rightarrow}{}^{3}{P}_{1}\ensuremath{\rightarrow}{}^{3}{S}_{1}$ transition. Atoms in the

{}^{3}{P}_{2}

state are magnetically trapped in a spherical quadrupole field with an axial gradient of 110 G/cm. We trap up to

{10}^{6}

atoms with a lifetime of 1.5 s.

Hyperfine quenching rates of

nsnp\,^3P_0-ns^2\,^1S_0

transition in

^{25}

Mg,

^{87}

Sr and

^{113}

Cd

Magic wavelengths for laser trapping of boson isotopes of alkaline-earth metal atoms Sr, Ca, and Mg are investigated while considering terahertz clock transitions between the

{}^{3}{P}_{0}

,

{}^{3}{P}_{1}

, and

{}^{3}{P}_{2}

metastable triplet states. Our calculation shows that magic wavelengths for laser trapping do exist. This result is important because those metastable states have already been used to make accurate clocks in the terahertz frequency domain. Detailed discussions for magic wavelengths for terahertz clock transitions are given in this article.

The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the

^{3}P_{1}

state into the long-living metastable state

^{3}P_{0}

, thus enabling the strictly forbidden $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ ``clock'' transition in even isotopes of alkaline-earth-metal-like atoms, without a change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the linewidth of the clock transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional ``state-mixing'' wave, including estimations of the ``magic'' wavelengths, Rabi frequencies for the clock and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.