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arXiv:2302.14687 · Physical Review Research

Tunable Feshbach resonances in collisions of ultracold molecules in 2Σ states with alkali-metal atoms

Robert C. Bird, Michael R. Tarbutt, Jeremy M. Hutson

Published Jun 23, 2023• 5 citations
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Abstract

We consider the magnetically tunable Feshbach resonances that may exist in ultracold mixtures of molecules in ${}^{2}\mathrm{\ensuremath{\Sigma}}$ states and alkali-metal atoms. We focus on $\mathrm{Rb}+\mathrm{CaF}$ as a prototype system. There are likely to be Feshbach resonances analogous to those between pairs of alkali-metal atoms. We investigate the patterns of near-threshold states and the resonances that they cause, using coupled-channel calculations of the bound states and low-energy scattering on model interaction potentials. We explore the dependence of the properties on as-yet-unknown potential parameters. There is a high probability that resonances will exist at magnetic fields below 1000 G, and that these will be broad enough to control collisions and form triatomic molecules by magnetoassociation. We consider the effects of CaF rotation and anisotropy of the interaction potential, and conclude that they may produce additional resonances but should not affect the existence of rotation-free resonances.

DOI
10.1103/physrevresearch.5.023184

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We consider the magnetically tunable Feshbach resonances that may exist in ultracold mixtures of molecules in 2\ensuremathΣ{}^{2}\mathrm{\ensuremath{\Sigma}}2\ensuremathΣ states and alkali-metal atoms. We focus on Rb+CaF\mathrm{Rb}+\mathrm{CaF}Rb+CaF as a prototype system. There are likely to be Feshbach resonances analogous to those between pairs of alkali-metal atoms. We investigate the patterns of near-threshold states and the resonances that they cause, using coupled-channel calculations of the bound states and low-energy scattering on model interaction potentials. We explore the dependence of the properties on as-yet-unknown potential parameters. There is a high probability that resonances will exist at magnetic fields below 1000 G, and that these will be broad enough to control collisions and form triatomic molecules by magnetoassociation. We consider the effects of CaF rotation and anisotropy of the interaction potential, and conclude that they may produce additional resonances but should not affect the existence of rotation-free resonances.
We investigate the interactions between ultracold alkali-metal atoms and closed-shell atoms using electronic structure calculations on the prototype system Rb+Sr. There are molecular bound states that can be tuned across atomic thresholds with a magnetic field and previously neglected terms in the collision Hamiltonian that can produce zero-energy Feshbach resonances with significant widths. The largest effect comes from the interaction-induced variation of the Rb hyperfine coupling. The resonances may be used to form paramagnetic polar molecules if the magnetic field can be controlled precisely enough.
We have investigated magnetically tunable Feshbach resonances in ultracold collisions of Rb with Yb in its metastable 3P2{}^{3}{P}_{2}3P2​ and 3P0{}^{3}{P}_{0}3P0​ states, using coupled-channel scattering and bound-state calculations. For the 3P2{}^{3}{P}_{2}3P2​ state, we find sharp resonances when both atoms are in their lowest Zeeman sublevels. However, these resonances are decayed by inelastic processes that produce Yb atoms in 3P1{}^{3}{P}_{1}3P1​ and 3P0{}^{3}{P}_{0}3P0​ states. The molecules that might be produced by magnetoassociation at the 3P2{}^{3}{P}_{2}3P2​ thresholds can decay by similar pathways and would have lifetimes no more than a few microseconds. For the 3P0{}^{3}{P}_{0}3P0​ state, by contrast, there are resonances that are promising for magnetoassociation. There are resonances due to both rotating and nonrotating molecular states that are significantly stronger than the analogous resonances for Yb(1S\mathrm{Yb}{(}^{1}SYb(1S). The ones due to rotating states are denser in magnetic field; in contrast to Yb(1S\mathrm{Yb}{(}^{1}SYb(1S), they exist even for bosonic isotopes of Yb(3P0\mathrm{Yb}{(}^{3}{P}_{0}Yb(3P0​).
We investigate magnetically tunable Feshbach resonances between ultracold europium atoms and between europium and alkali-metal atoms using multichannel quantum scattering calculations. For ultracold gases of europium atoms both homonuclear 153Eu+153Eu^{153}\mathrm{Eu}+^{153}\mathrm{Eu}153Eu+153Eu and heteronuclear 151Eu+153Eu^{151}\mathrm{Eu}+^{153}\mathrm{Eu}151Eu+153Eu systems are studied. Calculations for mixtures of europium and alkali-metal atoms are carried out for prototype systems of 153Eu+87Rb^{153}\mathrm{Eu}+^{87}\mathrm{Rb}153Eu+87Rb and 153Eu+7Li^{153}\mathrm{Eu}+^{7}\mathrm{Li}153Eu+7Li. We analyze the prospects for the control of scattering properties, observation of quantum chaotic behavior, and magnetoassociation into ultracold polar and paramagnetic molecules. We show that favorable resonances can be expected at experimentally feasible magnetic-field strengths below 1000G1000\phantom{\rule{0.28em}{0ex}}\mathrm{G}1000G for all investigated atomic combinations. For Eu atoms, a rich spectrum of resonances is expected as a result of the competition between relatively weak short-range spin-exchange and strong long-range magnetic dipole-dipole interactions, where the dipolar interaction induces measurable resonances. A high density of resonances is expected at magnetic-field strengths below 200G200\phantom{\rule{0.28em}{0ex}}\mathrm{G}200G without pronounced quantum chaos signatures. The present results may be useful for the realization and application of dipolar atomic and molecular quantum gases based on europium atoms in many-body physics.
We consider the long-range states expected for complexes formed from an alkali-metal diatomic molecule in a singlet state and an alkali-metal atom. We explore the structure of the Hamiltonian for such systems, and the couplings between the six angular momenta that are present. We consider the patterns and densities of the long-range states, and the terms in the Hamiltonian that can cause Feshbach resonances when the states cross threshold as a function of magnetic field. We present a case study of 40K87Rb+87Rb^{40}\mathrm{K}^{87}\mathrm{Rb}+^{87}\mathrm{Rb}40K87Rb+87Rb. We show multiple types of resonance due to long-range states with rotational and/or hyperfine excitation, and consider the likelihood of them existing at low to moderate magnetic fields.
We consider the long-range states expected for complexes formed from an alkali-metal diatomic molecule in a singlet state and an alkali-metal atom. We explore the structure of the Hamiltonian for such systems, and the couplings between the six angular momenta that are present. We consider the patterns and densities of the long-range states, and the terms in the Hamiltonian that can cause Feshbach resonances when the states cross threshold as a function of magnetic field. We present a case study of 40^{40}40K87^{87}87Rb+87^{87}87Rb. We show multiple types of resonance due to long-range states with rotational and/or hyperfine excitation, and consider the likelihood of them existing at low to moderate magnetic fields.
Magnetically tunable Feshbach resonances exist in ultracold collisions between atoms in 2S^{2}\mathrm{S}2S and 3P0{}^{3}{\mathrm{P}}_{0}3P0​ states, such as an alkali-metal atom colliding with Yb or Sr in a clock state. We investigate the mechanisms of these resonances and identify the terms in the collision Hamiltonian responsible for them. They involve indirect coupling between the open and closed channels, via intermediate channels involving atoms in 3P1{}^{3}{\mathrm{P}}_{1}3P1​ states. The resonance widths are generally proportional to the square of the magnetic field and are strongly enhanced when the magnitude of the background scattering length is large. For any given pair of atoms, the scattering length can be tuned discretely by choosing different isotopes of the 3P0{}^{3}{\mathrm{P}}_{0}3P0​ atom. For each combination of an alkali-metal atom and either Yb or Sr, we consider the prospects of finding an isotopic combination that has both a large background scattering length and resonances at a high but experimentally accessible field. We conclude that 87Rb+Yb^{87}\mathrm{Rb}+\mathrm{Yb}87Rb+Yb, Cs+Yb\mathrm{Cs}+\mathrm{Yb}Cs+Yb, and 85Rb+Sr^{85}\mathrm{Rb}+\mathrm{Sr}85Rb+Sr are particularly promising combinations.