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Physica Scripta

Elastic collision properties of ultracold calcium atoms

Jicai Zhang, Jinfeng Sun, Zunlue Zhu, Yufang Liu

Published Jan 31, 2013• 3 citations
Publisher

Abstract

The s-wave scattering lengths are obtained for all stable isotope combinations of Ca atoms and those values are very sensitive to small changes of the reduced mass. These results rely on a recent measurement of the 40 Ca– 40 Ca scattering length in a Bose condensate of 40 Ca and making small corrections to a Born–Oppenheimer potential that reproduces all known spectroscopic data. We find that the 42 Ca isotope has a scattering length of 417.5 a 0 and, thus, can be Bose condensed. The large interisotope scattering length between 43 Ca and 42 Ca indicates that sympathetic cooling of 43 Ca by 42 Ca atoms will be effective, and 43 Ca– 42 Ca can also be used to study isotopic Bose–Fermi mixtures. We also predict a d-wave shape resonance for collisions of fermionic 43 Ca atoms in different spin components.

DOI
10.1088/0031-8949/87/02/025302

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The s-wave scattering lengths are obtained for all stable isotope combinations of Ca atoms and those values are very sensitive to small changes of the reduced mass. These results rely on a recent measurement of the 40 Ca– 40 Ca scattering length in a Bose condensate of 40 Ca and making small corrections to a Born–Oppenheimer potential that reproduces all known spectroscopic data. We find that the 42 Ca isotope has a scattering length of 417.5 a 0 and, thus, can be Bose condensed. The large interisotope scattering length between 43 Ca and 42 Ca indicates that sympathetic cooling of 43 Ca by 42 Ca atoms will be effective, and 43 Ca– 42 Ca can also be used to study isotopic Bose–Fermi mixtures. We also predict a d-wave shape resonance for collisions of fermionic 43 Ca atoms in different spin components.
We investigate the elastic scattering properties of strontium atoms at ultracold temperatures. The scattering parameters, such as s-wave scattering lengths, effective ranges and p-wave scattering lengths, are calculated for all stable isotope combinations of Sr atoms by the quantal method and semiclassical method, respectively. Good agreements are obtained. The scattering parameters are very sensitive to small changes of the reduced mass. Due to the repulsive interisotope and intraisotope s-wave scattering length and large elastic cross sections, 84 Sr— 86 Sr mixture is a good candidate to realize Bose—Bose quantum degenerate atomic gases.
We have calculated the sss-wave scattering length of all the even isotopes of calcium (Ca) and barium (Ba) in order to investigate the prospect of Bose-Einstein condensation (BEC). For Ca we have used an accurate molecular potential based on detailed spectroscopic data. Our calculations show that Ca does not provide other isotopes alternative to the recently Bose condensed 40{}^{40}40Ca that suffers strong losses because of a very large scattering length. For Ba we show by using a model potential that the even isotopes cover a broad range of scattering lengths, opening the possibility of BEC for at least one of the isotopes.
We determine the interspecies sss-wave triplet scattering length a3{a}_{3}a3​ for all K-Rb isotopic mixtures by measuring the elastic cross section for collisions between 41K^{\mathrm{41}}\mathrm{K}41K and 87Rb^{87}\mathrm{R}\mathrm{b}87Rb in different temperature regimes. The positive value ${a}_{3}=+{163}_{\ensuremath{-}12}^{+57}{a}_{0}$ ensures the stability against collapse of binary $^{41}\mathrm{K}\ensuremath{-}^{87}\mathrm{R}\mathrm{b}$ Bose-Einstein condensates. For the fermion-boson mixture $^{40}\mathrm{K}\ensuremath{-}^{87}\mathrm{R}\mathrm{b}$, we obtain a large and negative scattering length which implies an efficient sympathetic cooling of the fermionic species down to the degenerate regime.
We have determined the scattering lengths for collisions between the different isotopes of two potassium atoms in singlet and triplet molecular states of K2{\mathrm{K}}_{2}K2​. We show that for the two bosonic species 39K{}^{39}\mathrm{K}39K and 41K{}^{41}\mathrm{K}41K the scattering lengths are positive, hence, leading to stable condensates. The fermionic isotope 40K{}^{40}\mathrm{K}40K also has positive scattering lengths, but the triplet value is nearly zero, hence, a quasi-non-interacting fermionic gas. We also give results for the interspecies collisions. We conclude that double condensates of 39K{}^{39}\mathrm{K}39K and 41K{}^{41}\mathrm{K}41K are possible for purely spin-polarized atoms, and sympathetic cooling between the bosonic 39K{}^{39}\mathrm{K}39K and the fermionic 40K{}^{40}\mathrm{K}40K will be efficient due to low spin-flip rates and a sizable interspecies scattering length.
The hyperfine-state-selected scattering properties of potassium atoms at ultralow temperatures are calculated using interaction potentials gleaned from an analysis of recent photoassociation data. We predict that the small, probably negative value of the 39K{}^{39}\mathrm{K}39K triplet scattering length will hamper efforts to produce a Bose-Einstein condensate, unless experiments utilize a broad, accessible magnetic Feshbach resonance. The large positive value calculated for the 41K{}^{41}\mathrm{K}41K triplet scattering length makes it a better candidate for condensation at zero magnetic field. The fermionic isotope 40K{}^{40}\mathrm{K}40K is also predicted to have a large, positive scattering length for elastic collisions between spin states of experimental interest, implying that it can be efficiently evaporatively cooled to the quantum degenerate regime. In addition, certain spin states possess Feshbach resonances that may enable tuning of its interatomic interactions, possibly leading to the formation of Cooper pairs.