arXiv:2211.07557 · Physical Review Research

Magnetic Feshbach resonances between atoms in S2 and P03 states: Mechanisms and dependence on atomic properties

Bijit Mukherjee, Matthew D. Frye, Jeremy M. Hutson

Published Feb 13, 2023• 2 citations

Abstract

Magnetically tunable Feshbach resonances exist in ultracold collisions between atoms in $^{2}\mathrm{S}$ and ${}^{3}{\mathrm{P}}_{0}$ 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 ${}^{3}{\mathrm{P}}_{1}$ 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 ${}^{3}{\mathrm{P}}_{0}$ 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 $^{87}\mathrm{Rb}+\mathrm{Yb}$, $\mathrm{Cs}+\mathrm{Yb}$, and $^{85}\mathrm{Rb}+\mathrm{Sr}$ are particularly promising combinations.

DOI: 10.1103/physrevresearch.5.013102

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arXiv:2211.07557 · Physical Review Research

Magnetic Feshbach resonances between atoms in S2 and P03 states: Mechanisms and dependence on atomic properties

Bijit Mukherjee, Matthew D. Frye, Jeremy M. Hutson

Published Feb 13, 2023• 2 citations

arXiv HTML PDF

Abstract

Magnetically tunable Feshbach resonances exist in ultracold collisions between atoms in

^{2}\mathrm{S}

and

{}^{3}{\mathrm{P}}_{0}

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

{}^{3}{\mathrm{P}}_{1}

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

{}^{3}{\mathrm{P}}_{0}

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

^{87}\mathrm{Rb}+\mathrm{Yb}

\mathrm{Cs}+\mathrm{Yb}

, and

^{85}\mathrm{Rb}+\mathrm{Sr}

are particularly promising combinations.

DOI: 10.1103/physrevresearch.5.013102

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Magnetic Feshbach resonances in collisions of closed-shell $^1\Sigma$ moleculesMagnetic Feshbach resonances in collisions of closed-shell $^1\Sigma$ molecules

Alisdair O. G. Wallis, Roman V. Krems

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 $^1\Sigma$ state. Unlike alkali metal atoms, $^1\Sigma$ 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 $^1\Sigma$ 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 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 $^1\Sigma$ state. Unlike alkali metal atoms, $^1\Sigma$ 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 $^1\Sigma$ molecules may exceed 1 milliGauss, rendering such resonances experimentally detectable. We hope that this work will stimulate the experimental search of these resonances.

Sep 6, 20120 citations

Magnetically tunable Feshbach resonances exist in ultracold collisions between atoms in

^{2}\mathrm{S}

and

{}^{3}{\mathrm{P}}_{0}

{}^{3}{\mathrm{P}}_{1}

{}^{3}{\mathrm{P}}_{0}

^{87}\mathrm{Rb}+\mathrm{Yb}

\mathrm{Cs}+\mathrm{Yb}

, and

^{85}\mathrm{Rb}+\mathrm{Sr}

are particularly promising combinations.

We have investigated magnetically tunable Feshbach resonances in ultracold collisions of Rb with Yb in its metastable

{}^{3}{P}_{2}

and

{}^{3}{P}_{0}

states, using coupled-channel scattering and bound-state calculations. For the

{}^{3}{P}_{2}

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

{}^{3}{P}_{1}

and

{}^{3}{P}_{0}

states. The molecules that might be produced by magnetoassociation at the

{}^{3}{P}_{2}

thresholds can decay by similar pathways and would have lifetimes no more than a few microseconds. For the

{}^{3}{P}_{0}

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

\mathrm{Yb}{(}^{1}S

). The ones due to rotating states are denser in magnetic field; in contrast to

\mathrm{Yb}{(}^{1}S

), they exist even for bosonic isotopes of

\mathrm{Yb}{(}^{3}{P}_{0}

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.

We have investigated magnetically tunable Feshbach resonances arising from the interaction of Li(

{}^{2}S

) with metastable Yb(

{}^{3}{P}_{2}

) and (

{}^{3}{P}_{0}

). For Yb(

{}^{3}{P}_{2}

), all the resonance features are strongly suppressed by inelastic collisions that produce Yb in its lower-lying

{}^{3}{P}_{1}

and

{}^{3}{P}_{0}

states. For Yb(

{}^{3}{P}_{0}

), sharp resonances exist but they are extremely narrow (widths less than 1 mG).

Magnetic Feshbach resonances in collisions of closed-shell

^1\Sigma

molecules

^1\Sigma

state. Unlike alkali metal atoms,

^1\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\Sigma

molecules may exceed 1 milliGauss, rendering such resonances experimentally detectable. We hope that this work will stimulate the experimental search of these resonances.