arXiv:1307.2654

Long range interactions of ytterbium in mixed quantum gases

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko, Charles W. Clark

Published Jul 10, 2013• 0 citations

Abstract

We present methods for accurate evaluation of van der Waals coefficients of dimers with excited atoms that have a strong decay channel. We calculate C_6 coefficients for the Yb-Yb 1S_0+ 3P_{0,1}, 3P_0+3P_0 and Yb-Rb 3P_1+5s, 1S_0+ 5p_{1/2} dimers and C_8 coefficients for the Yb-Yb 1S_0+1S_0, 1S_0+3P_1 and Yb-Rb 1S_0+5s dimers. We evaluate uncertainties of all properties.

DOI: 10.48550/arxiv.1307.2654

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arXiv:1307.2654

Long range interactions of ytterbium in mixed quantum gases

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko, Charles W. Clark

Published Jul 10, 2013• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.1307.2654

Related papers

Long-range interaction coefficients for ytterbium dimers

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko +1 more

We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the $6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}$ , $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$ , and $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the ${C}_{6}$ coefficients for the Yb-Yb ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}$ and ${}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$ dimers and ${C}_{8}$ coefficients for the ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ and ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ dimers.We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the $6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}$, $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$, and $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the ${C}_{6}$ coefficients for the Yb-Yb ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}$ and ${}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$ dimers and ${C}_{8}$ coefficients for the ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ and ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ dimers.

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The long-range part of the interatomic interactions plays a substantial role in the collisional dynamics of ultracold gases. Here, we report on the calculation of the isotropic and anisotropic ${C}_{6}$ coefficients characterizing the van der Waals interaction between dysprosium or erbium atoms in the two lowest energy levels and the ground-state alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba) atoms. The calculations are done using the integral of dynamic dipole polarizabilities at so-called imaginary frequencies of the two interacting atoms. For all atom pairs, we find that the isotropic ${C}_{6}$ coefficients are two or three orders of magnitude larger than the anisotropic ones. Those coefficients are essential for modeling collisional properties of heteronuclear quantum mixtures containing highly magnetic dysprosium or erbium atoms and alkali-metal or alkaline-earth-metal atoms.The long-range part of the interatomic interactions plays a substantial role in the collisional dynamics of ultracold gases. Here, we report on the calculation of the isotropic and anisotropic ${C}_{6}$ coefficients characterizing the van der Waals interaction between dysprosium or erbium atoms in the two lowest energy levels and the ground-state alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba) atoms. The calculations are done using the integral of dynamic dipole polarizabilities at so-called imaginary frequencies of the two interacting atoms. For all atom pairs, we find that the isotropic ${C}_{6}$ coefficients are two or three orders of magnitude larger than the anisotropic ones. Those coefficients are essential for modeling collisional properties of heteronuclear quantum mixtures containing highly magnetic dysprosium or erbium atoms and alkali-metal or alkaline-earth-metal atoms.

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We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the

6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}

6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}

, and

6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the

{C}_{6}

coefficients for the Yb-Yb

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}

and

{}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}

dimers and

{C}_{8}

coefficients for the

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}

and

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

dimers.

We derive the relativistic formulas for the van der Waals coefficients of Yb--alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate

{C}_{6}

and

{C}_{8}

coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the

{C}_{8}

coefficient of heteronuclear

A+B

dimers in terms of the

{C}_{6}

and

{C}_{8}

coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states

A

and

B

. We report results of calculation of the

{C}_{6}

coefficients for the Yb-Rb

{}^{3}{P}_{1}^{o}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

and

{}^{1}{S}_{0}+5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}^{o}

dimers, and the

{C}_{8}

coefficients for the Yb-Li

{}^{1}{S}_{0}+2s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

and Yb-Rb

{}^{1}{S}_{0}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

dimers. Uncertainties are estimated for all predicted properties.

We present semiempirical calculations of long-range van der Waals interactions for two interacting metastable rare-gas atoms Ne through Xe. Dispersion coefficients

{C}_{6}

are obtained for homonuclear molecular potentials asymptotically connecting to the

{\mathrm{ns}(3/2)}_{2}{+ns(3/2)}_{2}

atomic states. The estimated uncertainty of the calculated

{C}_{6}

dispersion coefficients is 4%.

The long-range part of the interatomic interactions plays a substantial role in the collisional dynamics of ultracold gases. Here, we report on the calculation of the isotropic and anisotropic

{C}_{6}

coefficients characterizing the van der Waals interaction between dysprosium or erbium atoms in the two lowest energy levels and the ground-state alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba) atoms. The calculations are done using the integral of dynamic dipole polarizabilities at so-called imaginary frequencies of the two interacting atoms. For all atom pairs, we find that the isotropic

{C}_{6}

coefficients are two or three orders of magnitude larger than the anisotropic ones. Those coefficients are essential for modeling collisional properties of heteronuclear quantum mixtures containing highly magnetic dysprosium or erbium atoms and alkali-metal or alkaline-earth-metal atoms.