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arXiv:1808.03917 · Physical Review A

Broad Feshbach resonances in ultracold alkali-metal systems

Yue Cui, Min Deng, Li You, Bo Gao, Meng Khoon Tey

Published Oct 24, 2018• 24 citations
arXivHTMLPDF

Abstract

A comprehensive search for broad Feshbach resonances (FRs) in all possible combinations of stable alkali-metal atoms is carried out, using a multichannel quantum-defect theory assisted by the analytic wave functions for a long-range van der Waals potential. A number of broad $s$-, $p$-, and $d$-wave FRs in the lowest-energy scattering channels, which are stable against two-body dipolar spin-flip loss, are predicted and characterized. Our results also show that broad FRs of $p$- or $d$-wave type that are free of two-body loss do not exist between fermionic alkali-metal atoms for a magnetic field up to 1000 G. These findings constitute helpful guidance on efforts towards the experimental study of high-partial-wave coupling-induced many-body physics.

DOI
10.1103/physreva.98.042708

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Acta Physica Sinica•Jan 1, 2025•0 citations
A comprehensive search for broad Feshbach resonances (FRs) in all possible combinations of stable alkali-metal atoms is carried out, using a multichannel quantum-defect theory assisted by the analytic wave functions for a long-range van der Waals potential. A number of broad sss-, ppp-, and ddd-wave FRs in the lowest-energy scattering channels, which are stable against two-body dipolar spin-flip loss, are predicted and characterized. Our results also show that broad FRs of ppp- or ddd-wave type that are free of two-body loss do not exist between fermionic alkali-metal atoms for a magnetic field up to 1000 G. These findings constitute helpful guidance on efforts towards the experimental study of high-partial-wave coupling-induced many-body physics.
In the ultracold gases of alkali-earth-metal-like atoms, a new type of Feshbach resonance, i.e., the orbital Feshbach resonance (OFR), has been proposed and experimentally observed in ultracold 173Yb^{173}\mathrm{Yb}173Yb atoms [R. Zhang et al., Phys. Rev. Lett. 115, 135301 (2015)]. When the OFR of the 173Yb^{173}\mathrm{Yb}173Yb atoms occurs, the energy gap between the open and closed channels is smaller by two orders of magnitude than the van der Waals energy. As a result, quantitative accurate results for the low-energy two-body problems can be obtained via multichannel quantum defect theory (MQDT), which is based on the exact solution of the Schr\"odinger equation with the van der Waals potential. In this paper we use MQDT to calculate the two-atom scattering length, effective range, and binding energy of two-body bound states for the systems with OFR. With these results we further study the clock-transition spectrum for the two-body bound states, which can be used to experimentally measure the binding energy. Our results are helpful for the quantitative theoretical and experimental research for the ultracold gases of alkali-earth-metal-like atoms with OFR.
High partial-wave (l≥2) Feshbach resonance (FR) in an ultracold mixture of ^{85}Rb-^{87}Rb atoms is investigated experimentally aided by a partial-wave insensitive analytic multichannel quantum-defect theory. Two "broad" resonances from coupling between d waves in both the open and closed channels are observed and characterized. One of them shows a fully resolved triplet structure with a splitting ratio well explained by the perturbation to the closed channel due to interatomic spin-spin interaction. These tunable "broad" d-wave resonances, especially the one in the lowest-energy open channel, could find important applications in simulating d-wave coupling dominated many-body systems. In addition, we find that there is generally a time and temperature requirement, associated with tunneling through the angular momentum barrier, to establish and observe resonant coupling in nonzero partial waves.
We have developed a model of Feshbach resonances in gases of ultracold alkali-metal atoms using the ideas of multichannel quantum-defect theory. Our model requires just three parameters describing the interactions---the singlet and triplet scattering lengths, and the long-range van der Waals coefficient---in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to 6Li-40K^{6}\text{L}\text{i-}^{40}\text{K}6Li-40K and $^{40}\text{K}\text{\ensuremath{-}}^{87}\text{R}\text{b}$ scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique.
Abstract We report the new observation of several high partial-wave (HPW) magnetic Feshbach resonances (FRs) in 39K atoms of the hyperfine substate | F = 1 , m F = − 1 ⟩ . These resonances locate at the region between two broad s-wave FRs from 32.6 G to 162.8 G, in which Bose–Einstein condensates can be produced with tunable positive scattering length obtained by magnetic FRs. These HPW FRs are induced by the dipolar spin–spin interaction with s-wave in the open channel and HPW in the closed channel. Therefore, these HPW FRs have distinct characteristics in temperature dependence and loss line shape from that induced by spin–exchange interaction with HPWs in both open and closed channels. Among these resonances, one d-wave and two g-wave FRs are confirmed by the multichannel quantum-defect theory calculation. The HPW FRs have significant applications in many-body physics dominated by HPW pairing.
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.
Feshbach resonance is a fundamental phenomenon in cold atomic physics, where interatomic interactions can be precisely changed into a scattering resonance by varying an external magnetic field. This effect plays a crucial role in ultracold atomic experiments, enabling the control of interaction strength, the formation of molecular bound states, and the realization of strongly correlated quantum systems. With the rapid development of cold atom experiments, numerous Feshbach resonances corresponding to different partial waves, such as s-wave, p-wave, and even higher partial wave ones, have been experimentally identified. While s-wave resonances have been widely utilized due to their isotropic nature and strong coupling, and higher partial-wave resonances (including p-wave and d-wave resonances), provide unique opportunities for exploring anisotropic interactions and novel quantum phases. In this study, by using the multichannel quantum defect theory (MQDT), we predict that two d-wave Feshbach resonances are existent in 7Li at 1039.24 G and 1055.64 G, repectively. Physical properties of the two resonances are presented, such as the resonance width and closed channel dimer energy. In addition, we optimize the computational parameters by using the Nelder-Mead algorithm and investigate the possible resonance splitting induced by dipole-dipole interactions in higher partial waves. The presence of these d-wave resonances at high magnetic fields provides a new platform for investigating the interplay between higher-order partial wave interactions and quantum many-body effects. Our results provide opportunities for investigating the effects of higher partial wave Feshbach resonances in high magnetic fields. Our theoretical predictions thus serve as a useful reference for future experimental studies of higher-order resonance phenomena in lithium and other atomic species.