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Journal of Physics B Atomic Molecular and Optical Physics

Scattering lengths for spin-polarized metastable helium-3 and helium-4

A S Dickinson, Florent Xavier Gadéa, Thierry Leininger

Published Jan 20, 2004• 22 citations
Publisher

Abstract

Upper and lower bounds are estimated for the scattering length, a , for the various isotopes of spin-polarized metastable helium. From a previous study involving various large basis sets and two ab initio approaches, and paying special attention to combine them with the accurate long-range potential, we get, for 4 He*– 4 He* collisions (in Bohr) 152 < 4−4 a < 230 and for 3 He*– 3 He* collisions 94 < 3−3 a < 113, while a surprising result arises for mixed collisions, 3 He*– 4 He*, 3−4 a < −488 and 3−4 a > 865. Indeed, the scattering length for this species is very close to the divergence occurring at the binding of a 14th vibrational level. Within these limits, our approach suggests that the values for 4−4 a and 3−3 a are closer to their upper bounds than to their lower bounds, and that the value for 3−4 a is negative and very large (>500) in magnitude. Sympathetic cooling could therefore be very efficient for the mixed species. Cooling-rate coefficients are also evaluated: they are large, of order 10 −9 cm 3 s −1 at mK temperatures for all combinations.

DOI
10.1088/0953-4075/37/3/005

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Upper and lower bounds are estimated for the scattering length, a , for the various isotopes of spin-polarized metastable helium. From a previous study involving various large basis sets and two ab initio approaches, and paying special attention to combine them with the accurate long-range potential, we get, for 4 He*– 4 He* collisions (in Bohr) 152 < 4−4 a < 230 and for 3 He*– 3 He* collisions 94 < 3−3 a < 113, while a surprising result arises for mixed collisions, 3 He*– 4 He*, 3−4 a < −488 and 3−4 a > 865. Indeed, the scattering length for this species is very close to the divergence occurring at the binding of a 14th vibrational level. Within these limits, our approach suggests that the values for 4−4 a and 3−3 a are closer to their upper bounds than to their lower bounds, and that the value for 3−4 a is negative and very large (>500) in magnitude. Sympathetic cooling could therefore be very efficient for the mixed species. Cooling-rate coefficients are also evaluated: they are large, of order 10 −9 cm 3 s −1 at mK temperatures for all combinations.
A theoretical study is performed to re-evaluate the scattering length for spin-polarized metastable helium. The Σ5g+ potential is calculated with three huge basis sets, as well as one previously proposed, using two ab initio approaches: a large configuration interaction method and a coupled-cluster method. The influence of a dummy basis set is analyzed and shown to yield spurious behavior in the energy decrease, roughly Gaussian with changing separation of the dummy basis from the molecule. The scattering length is found to be extremely sensitive here even to tiny details of the potential because the potential is very close to supporting a fifteenth rotationless vibrational level. This behavior can be rationalized using semiclassical methods. From this study we conclude that there are certainly 15 vibrational levels and that the dissociation energy is most probably 1045.2±1 cm−1, while our final result for the scattering length, a=291 a0, is best considered as an upper limit.
We developed a series of correlation-consistent, polarized multiple zeta basis sets optimized specifically for the energy of the 2 3S state of helium atom. These basis sets were subsequently augmented with diffuse functions optimized for the van der Waals constants C6 through C14 which determine the asymptotic behavior of the second-order dispersion interaction between 2 3S helium atoms at large interatomic separation R. The resulting bases were applied to compute the Born-Oppenheimer (BO) potential for the lowest 5Sigmag+ state of the helium dimer. The coupled cluster and the full configuration-interaction techniques were employed to account for the electron correlation effects. The cardinal number extrapolation technique was used to obtain the complete-basis-set limit V(R) for the interaction potential and to find its lower VL(R) and upper VU(R) bounds. The resulting potentials were fitted to an analytical function containing accurate van der Waals constants C6 through C12 (including C11). We found that the complete-basis-set BO potential has a well depth De=1048.24+/-0.36 cm-1. The highest rotationless vibrational level is bound by D14=90.2+/-4.7 MHz, much stronger than the previous most accurate estimation of 15.2 MHz. The error bounds for De and D14 were obtained using the VL(R) and VU(R) potentials. The S-wave scattering length computed using the VL(R), V(R), and VU(R) potentials (assuming atomic masses) is aL=7.41 nm, a=7.54 nm, and aU=7.69 nm, respectively. We also computed the adiabatic, relativistic, and quantum electrodynamics (QED) corrections to the BO potential. When these corrections are taken into account the values of D14 and of a (both computed assuming nuclear masses) are 87.4+/-6.7 MHz and 7.64+/-0.20 nm; the error bounds reflect now also the uncertainty of the included adiabatic, relativistic, and QED corrections. The value of the scattering length resulting from our investigation lies outside the error bounds of all experimental determinations based on the properties of Bose-Einstein condensate of spin-polarized helium atoms.
We present a new measurement of the sss-wave scattering length aaa of spin-polarized helium atoms in the 2 3S12\text{ }^{3}S_{1}2 3S1​ metastable state. Using two-photon photoassociation spectroscopy and dark resonances, we measure the energy ${E}_{v=14}=\ensuremath{-}91.35\ifmmode\pm\else\textpm\fi{}0.06\text{ }\text{ }\mathrm{MHz}$ of the least-bound state v=14v=14v=14 in the interaction potential of the two atoms. We deduce a value of $a=7.512\ifmmode\pm\else\textpm\fi{}0.005\text{ }\text{ }\mathrm{nm}$, which is at least 100 times more precise than the best previous determinations and is in disagreement with some of them. This experiment also demonstrates the possibility to create exotic molecules binding two metastable atoms with a lifetime of the order of $1\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$.
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.
In this paper we investigate the effective scattering length a of spin-polarized Ne∗.{\mathrm{Ne}}^{*}.Ne∗. Due to its anisotropic electrostatic interaction, its scattering length is determined by five interaction potentials instead of one, even in the spin-polarized case, a unique property among the Bose condensed species and candidates. Because the interaction potentials of Ne∗{\mathrm{Ne}}^{*}Ne∗ are not known accurately enough to predict the value of the scattering length, we investigate the behavior of a as a function of the five phase integrals ${\ensuremath{\Phi}}_{\ensuremath{\Omega}}$ corresponding to the five interaction potentials. We find that the scattering length has five resonances instead of only one and cannot be described by a simple gas-kinetic approach or the degenerate internal state (DIS) approximation. However, the probability for finding a positive or large value of the scattering length is not enhanced compared to the single-potential case. We find that the induced dipole-dipole interaction enables strong coupling between the different $|J\ensuremath{\Omega}{\mathrm{PM}}_{P}〉$ states, resulting in an inhomogeneous shift of the resonance positions and widths in the quantum-mechanical calculation as compared to the DIS approach. The dependence of the resonance positions and widths on the input potentials turns out to be rather straightforward. The existence of two bosonic isotopes of Ne∗{\mathrm{Ne}}^{*}Ne∗ enables us to choose the isotope with the most favorable scattering length for efficient evaporative cooling towards the Bose-Einstein condensation transition, greatly enhancing the feasibility to reach this transition.
We investigate heteronuclear collisions in isotope mixtures of laser-cooled metastable (3P2{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2}3P2​) neon. Experiments are performed with spin-polarized atoms in a magnetic trap for all two-isotope combinations of the stable neon isotopes 20{}^{20}20Ne, 21{}^{21}21Ne, and 22{}^{22}22Ne. We determine the rate coefficients for heteronuclear ionizing collisions to ${\ensuremath{\beta}}_{21,20}=(3.9\ifmmode\pm\else\textpm\fi{}2.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ cm3{}^{3}3/s, ${\ensuremath{\beta}}_{22,20}=(2.6\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ cm3{}^{3}3/s, and ${\ensuremath{\beta}}_{21,22}=(3.9\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ cm3{}^{3}3/s. We also study heteronuclear elastic collision processes and give upper bounds for heteronuclear thermal relaxation cross sections. This work significantly extends the limited available experimental data on heteronuclear ionizing collisions for laser-cooled atoms involving one or more rare gas atoms in a metastable state.