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arXiv:1806.02800 · Physical Review A

Magnetically tunable Feshbach resonances in ultracold gases of europium atoms and mixtures of europium and alkali-metal atoms

Klaudia Zaremba-Kopczyk, Piotr Szymon Żuchowski, Michał Tomza

Published Sep 14, 2018• 14 citations
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Abstract

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 $^{153}\mathrm{Eu}+^{153}\mathrm{Eu}$ and heteronuclear $^{151}\mathrm{Eu}+^{153}\mathrm{Eu}$ systems are studied. Calculations for mixtures of europium and alkali-metal atoms are carried out for prototype systems of $^{153}\mathrm{Eu}+^{87}\mathrm{Rb}$ and $^{153}\mathrm{Eu}+^{7}\mathrm{Li}$. 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 $1000\phantom{\rule{0.28em}{0ex}}\mathrm{G}$ 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 $200\phantom{\rule{0.28em}{0ex}}\mathrm{G}$ 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.

DOI
10.1103/physreva.98.032704

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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 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.
This thesis reports on calculations of the scattering properties of a variety of ultracold alkali-metal mixtures. In particular, we have calculated the scattering properties of homonuclear mixtures of 85Rb, in a variety of incoming channels, and we have calculated the properties of heteronuclear mixtures of the isotopologues of Rb and Cs, and K and Cs. In general, we are interested in the location and character of Feshbach resonances in these mixtures with a view towards ultracold molecule formation. In 85Rb there is a rich Feshbach structure and potential uses for the resonances that we find, in the scattering lengths of the various incoming channels, are discussed. In 85RbCs there is a rich Feshbach structure and the prospects for ultracold molecule formation using this system are detailed. Similarly, we detail the Feshbach resonances of 87RbCs and discuss our results in the context of the successful formation of ultracold ground-state molecules. In the isotopologues of KCs each system has a rich Feshbach structure and we detail the location and width of the resonances, as well as the potential for ultracold molecule formation using each of the isotopes of potassium. In addition to scattering calculations, we have also calculated the location and character of the highest-lying bound states of each system. We have investigated the energy dependence of the scattering length using accurate coupled-channel calculations on 6Li, 39K and 133Cs to explore the behaviour of the effective range in the vicinity of both broad and narrow Feshbach resonances. We present an alternative parametrization of the effective range and further demonstrate that an analytical form of an energy and magnetic field-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length. Lastly, we examine the effect of additional external fields on alkali-metal collisions and discuss how external fields can be used to manipulate the interaction properties of a system.
We investigate Feshbach resonances in collisions of high-spin atoms such as Er and Dy with closed-shell atoms such as Sr and Yb, using coupled-channel scattering and bound-state calculations.We consider both low-anisotropy and high-anisotropy limits.In both regimes, we find many resonances with a wide variety of widths.The wider resonances are suitable for tuning interatomic interactions, while some of the narrower resonances are highly suitable for magnetoassociation to form high-spin molecules.These molecules might be transferred to short-range states, where they would have large magnetic moments and electric dipole moments that can be induced with very low electric fields.The results offer the opportunity to study mixed quantum gases where one species is dipolar and the other is not and open up important prospects for a new field of ultracold high-spin polar molecules.
We study ultracold gases of alkali-metal atoms in the quantum degenerate regime. The interatomic interactions in these type of systems can be tuned using resonances induced by magnetic or electric fields. The tunability of the interactions, together with the possibility of confining the atoms with several kinds of external potentials, allows for a completely novel approach to study basic problems in many-body physics, and moreover, allows to enter regimes which have never been accessible in condensed matter or nuclear physics. For example, this has led to the experimental demonstration of an intimate relation between two types of superfluidity: the crossover from Bose-Einstein condensation of tightly bound molecules to the superfluid behavior related to weakly bound BCS-like pairs. Another experimental landmark was reached when the existence of universal Efimov three-body bound states was proven in experiments with ultracold bosonic cesium atoms. In this thesis, we study several aspects of these strongly interacting and ultracold atomic gases. We develop an analytical model that encapsulates all of the relevant scattering physics in atomic systems where open-channel shape resonances and closedchannel Feshbach resonances give rise to complicated and non-trivial scattering properties. This model provides lots of physical insight and is shown to describe important quantities, such as the molecular energies and scattering phase shifts, with a high level of accuracy. The model is compared to full numerical coupled-channel calculations in two atomic systems: rubidium and lithium. We study the BCS-BEC crossover using a many-body description of the ultracold gas that includes the non-trivial energy dependence of the scattering model. We show that it gives rise to superfluid behavior associated with the formation of BCS-like pairs while the low-energy interactions are repulsive in character. The energy dependence of the interactions is crucial, as it gives rise to attractive interactions at the Fermi energy, necessary for the formation of Cooper pairs. We demonstrate new ways of controlling the interatomic interactions using a combination of magnetic and electric fields. This leads to experimental control of, for instance, the three-body parameter in the context of Efimov physics and of non-universal behavior in the BCS-BEC crossover in fermionic gases. Using a four-body method based on first principles, we solve the molecule-molecule scattering problem to calculate several important properties of bosonic and fermionic Summary 145 molecules that consist of light and heavy atoms. These type of molecules are of current experimental interest, and we predict several exciting relations between three- and four-body observables in these type of systems.
This thesis presents the investigation of the two-body scattering properties of cold atoms in \nsodium and lithium-sodium mixtures and their effects on the many body dynamics. Since both \nspecies are alkali atoms, the combined spin of both unpaired electrons can be either zero or one, \nproviding two different scattering channels. \nThe coupling of bound molecular states in these channels with the free atoms asymptote \ngives rise to the rich field of Feshbach resonance physics, where the interaction between the \nparticles can be controlled as an easily accessible experimental parameter. We have investigated \nthe Feshbach spectrum in the bosonic 7LiNa mixture and could confirm predictions based on \n6LiNa measurements, with a shift of the predicted spectrum by about 50 G. Also, the prospects \nof interaction tuning via Feshbach resonances were examined. \nThe difference of the scattering lengths of the electronic potentials also causes a coupling \nof atomic collisional channels, which can enable a spin exchange between the atoms. In this \nthesis, spin exchange processes have been studied in coherent oscillations in a thermal gas and \na Bose-Einstein condensate of sodium, as well as the evolution of this spinor gas into its ground \nstate. Preliminary studies of the heteronuclear spin exchange process in both the bosonic 7LiNa \nand in the fermionic-bosonic mixture 6LiNa are presented as well.
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.