The efficiency of optical trapping is determined by the atomic dynamic dipole polarizability, whose real and imaginary parts are associated with the potential energy and photon-scattering rate, respectively. In this article we develop a formalism to calculate analytically the real and imaginary parts of the scalar, vector, and tensor polarizabilities of lanthanide atoms. We assume that the sum-over-state formula comprises only transitions involving electrons in the valence orbitals like $6s,\phantom{\rule{0.16em}{0ex}}5d,\phantom{\rule{0.16em}{0ex}}6p$ , and $7s$ , while transitions involving $4f$ core electrons are neglected. Applying this formalism to the ground level of configuration $4{f}^{q}6{s}^{2}$ , we restrict the sum to transitions implying the $4{f}^{q}6s6p$ configuration, which yields polarizabilities depending on two parameters: an effective transition energy and an effective transition dipole moment. Then, by introducing configuration-interaction mixing between $4{f}^{q}6s6p$ and other configurations, we demonstrate that the imaginary part of the scalar, vector, and tensor polarizabilities is very sensitive to configuration-interaction coefficients, whereas the real part is not. The magnitude and anisotropy of the photon-scattering rate are thus strongly related to the details of the atomic electronic structure. Those analytical results agree with our detailed electronic-structure calculations of the energy levels, Land\'e $g$ factors, transition probabilities, polarizabilities, and van der Waals ${C}_{6}$ coefficients, previously performed on erbium and dysprosium and presently performed on holmium. Our results show that, although the density of states decreases with increasing $q$ , the configuration interaction between $4{f}^{q}6s6p,\phantom{\rule{0.16em}{0ex}}4{f}^{q\ensuremath{-}1}5d6{s}^{2}$, and $4{f}^{q\ensuremath{-}1}5{d}^{2}6s$ is surprisingly stronger in erbium ( $q=12$ ) than in holmium ( $q=11$ ), itself stronger than in dysprosium ( $q=10$ ).The efficiency of optical trapping is determined by the atomic dynamic dipole polarizability, whose real and imaginary parts are associated with the potential energy and photon-scattering rate, respectively. In this article we develop a formalism to calculate analytically the real and imaginary parts of the scalar, vector, and tensor polarizabilities of lanthanide atoms. We assume that the sum-over-state formula comprises only transitions involving electrons in the valence orbitals like $6s,\phantom{\rule{0.16em}{0ex}}5d,\phantom{\rule{0.16em}{0ex}}6p$, and $7s$, while transitions involving $4f$ core electrons are neglected. Applying this formalism to the ground level of configuration $4{f}^{q}6{s}^{2}$, we restrict the sum to transitions implying the $4{f}^{q}6s6p$ configuration, which yields polarizabilities depending on two parameters: an effective transition energy and an effective transition dipole moment. Then, by introducing configuration-interaction mixing between $4{f}^{q}6s6p$ and other configurations, we demonstrate that the imaginary part of the scalar, vector, and tensor polarizabilities is very sensitive to configuration-interaction coefficients, whereas the real part is not. The magnitude and anisotropy of the photon-scattering rate are thus strongly related to the details of the atomic electronic structure. Those analytical results agree with our detailed electronic-structure calculations of the energy levels, Land\'e $g$ factors, transition probabilities, polarizabilities, and van der Waals ${C}_{6}$ coefficients, previously performed on erbium and dysprosium and presently performed on holmium. Our results show that, although the density of states decreases with increasing $q$, the configuration interaction between $4{f}^{q}6s6p,\phantom{\rule{0.16em}{0ex}}4{f}^{q\ensuremath{-}1}5d6{s}^{2}$, and $4{f}^{q\ensuremath{-}1}5{d}^{2}6s$ is surprisingly stronger in erbium ($q=12$) than in holmium ($q=11$), itself stronger than in dysprosium ($q=10$).

arXiv:1704.04134Physical Review AJun 26, 201729 citations

Magneto-optical trapping of holmium atoms

Jinlu Miao, James Hostetter, Georgios Stratis +1 more

We demonstrate sub-Doppler laser cooling and magneto-optical trapping of the rare earth element Holmium. Atoms are loaded from an atomic beam source and captured in six-beam $σ_+ - σ_-$ molasses using a strong $J=15/2 \leftrightarrow J=17/2$ cycling transition at $λ=410.5 \rm nm$ . Due to the small difference in hyperfine splittings and Landé $g$ -factors in the lower and upper levels of the cooling transition the MOT is self-repumped without additional repump light, and deep sub-Doppler cooling is achieved with the magnetic trap turned on. We measure the leakage out of the cycling transition to metastable states and find a branching ratio $\sim 10^{-5}$ which is adequate for state resolved measurements on hyperfine encoded qubits.We demonstrate sub-Doppler laser cooling and magneto-optical trapping of the rare earth element Holmium. Atoms are loaded from an atomic beam source and captured in six-beam $σ_+ - σ_-$ molasses using a strong $J=15/2 \leftrightarrow J=17/2$ cycling transition at $λ=410.5 \rm nm$. Due to the small difference in hyperfine splittings and Landé $g$-factors in the lower and upper levels of the cooling transition the MOT is self-repumped without additional repump light, and deep sub-Doppler cooling is achieved with the magnetic trap turned on. We measure the leakage out of the cycling transition to metastable states and find a branching ratio $\sim 10^{-5}$ which is adequate for state resolved measurements on hyperfine encoded qubits.

arXiv:1401.4156Physical Review AApr 3, 201487 citations

6s,\phantom{\rule{0.16em}{0ex}}5d,\phantom{\rule{0.16em}{0ex}}6p

, and

7s

, while transitions involving

4f

core electrons are neglected. Applying this formalism to the ground level of configuration

4{f}^{q}6{s}^{2}

, we restrict the sum to transitions implying the

4{f}^{q}6s6p

configuration, which yields polarizabilities depending on two parameters: an effective transition energy and an effective transition dipole moment. Then, by introducing configuration-interaction mixing between

4{f}^{q}6s6p

and other configurations, we demonstrate that the imaginary part of the scalar, vector, and tensor polarizabilities is very sensitive to configuration-interaction coefficients, whereas the real part is not. The magnitude and anisotropy of the photon-scattering rate are thus strongly related to the details of the atomic electronic structure. Those analytical results agree with our detailed electronic-structure calculations of the energy levels, Land\'e

g

factors, transition probabilities, polarizabilities, and van der Waals

{C}_{6}

coefficients, previously performed on erbium and dysprosium and presently performed on holmium. Our results show that, although the density of states decreases with increasing

q

, the configuration interaction between $4{f}^{q}6s6p,\phantom{\rule{0.16em}{0ex}}4{f}^{q\ensuremath{-}1}5d6{s}^{2}$, and $4{f}^{q\ensuremath{-}1}5{d}^{2}6s$ is surprisingly stronger in erbium (

q=12

) than in holmium (

q=11

), itself stronger than in dysprosium (

q=10

We demonstrate sub-Doppler laser cooling and magneto-optical trapping of the rare earth element Holmium. Atoms are loaded from an atomic beam source and captured in six-beam

σ_+ - σ_-

molasses using a strong

J=15/2 \leftrightarrow J=17/2

cycling transition at

λ=410.5 \rm nm

. Due to the small difference in hyperfine splittings and Landé

g

-factors in the lower and upper levels of the cooling transition the MOT is self-repumped without additional repump light, and deep sub-Doppler cooling is achieved with the magnetic trap turned on. We measure the leakage out of the cycling transition to metastable states and find a branching ratio

\sim 10^{-5}

which is adequate for state resolved measurements on hyperfine encoded qubits.