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Physical Review Research

Long-range states and Feshbach resonances in collisions between ultracold alkali-metal diatomic molecules and atoms

Matthew D. Frye, Jeremy M. Hutson

Published Apr 3, 2023• 7 citations
Publisher

Abstract

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 $^{40}\mathrm{K}^{87}\mathrm{Rb}+^{87}\mathrm{Rb}$. 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.

DOI
10.1103/physrevresearch.5.023001

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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.
Abstract We present measurements of more than 80 magnetic Feshbach resonances in collisions of ultracold23Na40K with40K. We assign quantum numbers to a group of low-field resonances and show that they are probably due to long-range states of the triatomic complex in which the quantum numbers of the separated atom and molecule are approximately preserved. The resonant states are not members of chaotic bath of short-range states. Similar resonances are expected to be a common feature of alkali-metal diatom + atom systems.
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 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.
Magnetic Feshbach resonances in collisions of closed-shell 1Σ^1\Sigma1Σ molecules
Magnetic Feshbach resonances play a central role in experimental research of atomic gases at ultracold temperatures, as they allow one to control the microscopic interactions between ultracold atoms by tuning an applied magnetic field. These resonances arise due to strong hyperfine interactions between the unpaired electron and the nuclear magnetic moment of the alkali metal atoms. A major thrust of current research is to create an ultracold gas of diatomic alkali-metal molecules in the ground rovibrational state of the ground electronic 1Σ^1\Sigma1Σ state. Unlike alkali metal atoms, 1Σ^1\Sigma1Σ diatomic molecules have no unpaired electrons. However, the hyperfine interactions of molecules may give rise to magnetic Feshbach resonances. We use quantum scattering calculations to study the possible width of these resonances. Our results show that the widths of magnetic Feshbach resonances in ultracold molecule-molecule collisions for 1Σ^1\Sigma1Σ molecules may exceed 1 milliGauss, rendering such resonances experimentally detectable. We hope that this work will stimulate the experimental search of these resonances.
Magnetic Feshbach resonances play a central role in experimental research on atomic gases at ultracold temperatures, as they allow one to control the microscopic interactions between ultracold atoms by tuning an applied magnetic field. These resonances arise due to strong hyperfine interactions between the unpaired electron and the nuclear magnetic moment of the alkali metal atoms. A major thrust of current research is to create an ultracold gas of diatomic alkali metal molecules in the ground rovibrational state of the ground electronic ${}^{1}\ensuremath{\Sigma}$ state. Unlike alkali metal atoms, ${}^{1}\ensuremath{\Sigma}$ diatomic molecules have no unpaired electrons. However, the hyperfine interactions of molecules may give rise to magnetic Feshbach resonances. We use quantum scattering calculations to study the possible width of these resonances. Our results show that the widths of magnetic Feshbach resonances in ultracold molecule-molecule collisions for ${}^{1}\ensuremath{\Sigma}$ molecules may exceed 1 mG, rendering such resonances experimentally detectable. We hope that this work will stimulate the experimental search of these resonances.