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arXiv:physics/0310121 · Physical Review A

Multiplet structure of Feshbach resonances in nonzero partial waves

Christopher Ticknor, Cindy A. Regal, D. S. Jin, John L. Bohn

Published Apr 16, 2004• 246 citations
arXivHTMLPDF

Abstract

We report a unique feature of magnetic-field Feshbach resonances in which atoms collide with nonzero orbital angular momentum. $p$-wave $(l=1)$ Feshbach resonances are split into two components depending on the magnitude of the resonant state's projection of orbital angular momentum onto the field axis. This splitting is due to the magnetic dipole-dipole interaction between the atoms and it offers a means to tune anisotropic interactions of an ultracold gas of atoms. Furthermore this splitting in the $p$-wave Feshbach resonance has been experimentally observed and is reported. A parametrization of the $p$-wave resonance in terms of an effective-range expansion is given.

DOI
10.1103/physreva.69.042712

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We report a unique feature of magnetic-field Feshbach resonances in which atoms collide with nonzero orbital angular momentum. ppp-wave (l=1)(l=1)(l=1) Feshbach resonances are split into two components depending on the magnitude of the resonant state's projection of orbital angular momentum onto the field axis. This splitting is due to the magnetic dipole-dipole interaction between the atoms and it offers a means to tune anisotropic interactions of an ultracold gas of atoms. Furthermore this splitting in the ppp-wave Feshbach resonance has been experimentally observed and is reported. A parametrization of the ppp-wave resonance in terms of an effective-range expansion is given.
can be tuned using an external magnetic field. When the energy of the quasi-bound state is magnetically tuned into degeneracy with the energy of the free atomic pair, a resonant scattering process occurs in which the s-wave scattering length diverges and both elastic and inelastic collision cross sections are dramatically enhanced. When the collision involves two distinct atoms, the underlying molecular states can possess an electric dipole moment. In this case, the application of an external electric field can couple the bound molecular states mixing their orbital character and leading to level repulsion which breaks the degeneracy for dierent orbital angular momentum projections. The result is that the electric field shifts the positions of intrinsic magnetic Feshbach resonances, generates copies of resonances previously restricted to a particular partial-wave collision to other partial-wave channels, and splits Feshbach resonances into multiple resonances for states of nonzero angular momenta. This latter phenomenon oers a way to produce and tune an anisotropic interaction in atomic mixtures and to produce p-wave molecules of particular orbital angular momenta projections (1). In this talk, we discuss recent theoretical work and experimental progress on the realization and study of these phenomena associated with electric field dressing of magnetically tunable Feshbach resonances.
High partial-wave Feshbach resonances in an ultracold 6^66Li-133^{133}133Cs mixture
We measure higher partial wave Feshbach resonances in an ultracold mixture of fermionic 6^66Li and bosonic 133^{133}133Cs by magnetic field dependent atom-loss spectroscopy. For the ppp-wave Feshbach resonances we observe triplet structures corresponding to different projections of the pair rotation angular momentum onto the external magnetic field axis. We attribute the splittings to the spin-spin and spin-rotation couplings by modelling the observation using a full coupled-channel calculation. Comparison with an oversimplified model, estimating the spin-rotation coupling by describing the weakly bound close-channel molecular state with the perturbative multipole expansion, reveals the significant contribution of the molecular wavefunction at short internuclear distances. Our findings highlight the potential of Feshbach resonances in providing precise information on short- and intermediate-range molecular couplings and wavefunctions. The observed ddd-wave Feshbach resonances allow us to refine the LiCs singlet and triplet ground-state molecular potential curves at large internuclear separations.
We report evidence for spin-rotation coupling in ppp-wave Feshbach resonances in an ultracold mixture of fermionic 6^66Li and bosonic 133^{133}133Cs lifting the commonly observed degeneracy of states with equal absolute value of orbital-angular-momentum projection on the external magnetic field. By employing magnetic field dependent atom-loss spectroscopy we find triplet structures in ppp-wave resonances. Comparison with coupled-channel calculations, including contributions from both spin-spin and spin-rotation interactions, yields a spin-rotation coupling parameter ∣γ∣=0.566(50)×10−3|γ|=0.566(50)\times10^{-3}∣γ∣=0.566(50)×10−3. Our findings highlight the potential of Feshbach resonances in revealing subtle molecular couplings and providing precise information on electronic and nuclear wavefunctions, especially at short internuclear distance. The existence of a non-negligible spin-rotation splitting may have consequences for future classifications of ppp-wave superfluid phases in spin-polarized fermions.
The effects of combined external electric and magnetic fields on elastic collisions in ultracold Li-Rb mixtures are studied using recently obtained experimentally verified potentials. Our analysis provides both quantitative predictions for and a detailed physical interpretation of the phenomena arising from electric-field-induced interactions. It is shown that the electric field shifts the positions of intrinsic magnetic Feshbach resonances, generates copies of resonances previously restricted to a particular partial-wave collision to other partial-wave channels, and splits Feshbach resonances into multiple resonances for states of nonzero angular momenta. It was recently observed that the magnetic dipole-dipole interaction can also lift the degeneracy of a ppp-wave state splitting of the associated ppp-wave Feshbach resonance into two distinct resonances at different magnetic fields. Our work shows that the splitting of the resonances produced by an applied electric field is more than 1 order of magnitude larger. This phenomenon offers a complementary way to produce and tune an anisotropic interaction and to study its effect on the many-body physics of heteronuclear atomic gases.
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.
In a recent experiment [Peng et al., Phys. Rev. A 97, 012702 (2018)], it has been shown that the ppp-wave Feshbach resonance can be shifted toward the sss-wave Feshbach resonance by a laser field. Based on this experiment, we study the universal relations and the normal-state properties in an ultracold Fermi gas with coexisting sss- and ppp-wave interactions under optical control of a ppp-wave magnetic Feshbach resonance. Within the operator-product expansion, we derive the high-momentum tail of various observable quantities in terms of contacts. We find that the high-momentum tail becomes anisotropic. Adopting the quantum virial expansion, we calculate the normal-state contacts with and without a laser field for 40K^{40}\mathrm{K}40K atoms using typical experimental parameters. We show that the contacts are dependent on the laser dressing. We also reveal the interplay of laser dressing and different partial-wave interactions on various contacts. In particular, we demonstrate that the impact of the laser dressing in the ppp-wave channel can be probed by measuring the sss-wave contacts, which is a direct manifestation of few-body effects on the many-body level. Our results can be readily checked experimentally.