In this paper, we investigate the Feshbach resonances of high partial waves and the influence of spin-spin (S-S) interaction on ultracold scattering processes. Taking the Na23- Rb87 system as an example, we plot the variations of weakly bound state energy and elastic scattering cross section with magnetic field and with collision energy. We find that the number of splittings in high partial wave Feshbach resonances does not strictly conform to the expected l + 1 (l is rotational angular momentum), and the deviation is attributed to the influence of bound states in other channels coupled by S-S interaction. For different ml (the projection of l on the external magnetic field direction), the effects of S-S interaction lead to different scattering patterns in the incident channels. These results reveal the complex features of ultracold scattering processes in high partial waves caused by S-S interaction.
In this paper, we investigate the Feshbach resonances of high partial waves and the influence of spin-spin (S-S) interaction on ultracold scattering processes. Taking the Na23- Rb87 system as an example, we plot the variations of weakly bound state energy and elastic scattering cross section with magnetic field and with collision energy. We find that the number of splittings in high partial wave Feshbach resonances does not strictly conform to the expected l + 1 (l is rotational angular momentum), and the deviation is attributed to the influence of bound states in other channels coupled by S-S interaction. For different ml (the projection of l on the external magnetic field direction), the effects of S-S interaction lead to different scattering patterns in the incident channels. These results reveal the complex features of ultracold scattering processes in high partial waves caused by S-S interaction.
Abstract Taking the ultracold 85 Rb– 87 Rb collision system as an example, we investigated the Feshbach resonances of nonzero partial waves above the threshold. The self-energy at the threshold, which represents the coupling strength between open and closed channels, is considered a critical parameter to quantitatively describe the properties of Feshbach resonances. The total elastic and inelastic cross sections are calculated as functions of the magnetic field B and collision energy E col , ranging from 0.1 to 600 μ K. For a large absolute value of the self-energy at the threshold, the resonance decays rapidly with increasing collision energy, and narrow resonances of nonzero partial waves can be clearly resolved in the contour plot of the inelastic cross section versus the collision energy and magnetic field. It was found that the resonance tail appeared at the given magnetic field when the cross section decreased from the maximal value of the resonance peak to the minimum value, where a long resonance tail indicates an appreciable resonance in a relatively large region of collision energy. This relationship between the self-energy and the properties of Feshbach resonances still exists in the thermally averaged inelastic rate coefficient. The bound-state energies for nonzero partial waves split owing to the spin–spin interaction, which results in multiple nearly-overlapping resonances. Both the spin–spin and second-order spin–orbit effects are included. However, multiple nearly-overlapping resonances for nonzero partial waves are difficult to resolve in thermally averaged rate coefficients.
The ultracold mixture of 23Na and 87Rb atoms has become an important system for investigating physics in Bose-Bose atomic mixtures and for forming ultracold ground-state polar molecules. In this work, we provide an improved characterization of the most commonly used Feshbach resonance near 347.64 G between 23Na and 87Rb in their absolute ground states. We form Feshbach molecules using this resonance and measure their binding energies by dissociating them via magnetic-field modulation. We use the binding energies to refine the singlet and triplet potential-energy curves, using coupled-channel bound-state calculations. We then use coupled-channel scattering calculations on the resulting potentials to produce a high-precision mapping between magnetic field and scattering length. We also observe ten additional s-wave Feshbach resonances for 23Na and 87Rb in different combinations of Zeeman sublevels of the F=1 hyperfine states. Some of the resonances show two-body inelastic decay due to spin exchange. We compare the resonance properties with coupled-channel scattering calculations that full take account of inelastic properties.
High partial-wave Feshbach resonances in an ultracold 6Li-133Cs mixture
We measure higher partial wave Feshbach resonances in an ultracold mixture of fermionic 6Li and bosonic 133Cs by magnetic field dependent atom-loss spectroscopy. For the p-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 d-wave Feshbach resonances allow us to refine the LiCs singlet and triplet ground-state molecular potential curves at large internuclear separations.
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.
Abstract We discuss s-wave scattering in an atomic binary collision with two coupled channels, tunable by an external magnetic field, one channel open and the other closed for the incident energies considered. The analysis is performed with a stylized model of square-well potentials. This simplification allows for a pedagogically thorough discussion of the different scattering resonances that appear in coupled channels. One of them, the potential resonances at vanishing energy, occurs as a bound state of the coupled system emerges, in turn, tuned at a very precise value of the external field. The other resonances, described by Feshbach theory, occur when the incident energy is near a bound state of the closed channel, as if it were decoupled from the open channel. These resonances exist for values of the external field above a particular threshold value. Besides the potential intrinsic value of this study in a quantum mechanics course, as the analysis can be performed with minor numerical calculations, it is also an aid for the understanding of current research advances in the exciting field of ultracold gases.
Ultracold Cs2 Feshbach Spectroscopy
We have observed and located more than 60 magnetic field-induced Feshbach resonances in ultracold collisions of ground-state 133Cs atoms. These resonances are associated with molecular states with up to four units of rotational angular momentum, and are detected through variations in the elastic, inelastic, and radiative collision cross sections. These observations allow us to greatly improve upon the interaction potentials between two cesium atoms and to reproduce the positions of most resonances to accuracies better than 0.5%. Based on the relevant coupling scheme between the electron spin, nuclear spin, and orbital angular momenta of the nuclei, quantum numbers and energy structure of the molecular states beneath the dissociation continuum are revealed. Finally, we predict the relevant collision properties for cesium Bose-Einstein condensation experiments.