Analytic descriptions of magnetic Feshbach resonances in nonzero partial waves

Christopher Ticknor, Cindy A. Regal

Constantinos Makrides, Bo Gao

We present a multichannel quantum-defect theory for magnetic Feshbach resonances in the interaction of two heteronuclear group-I atoms. The theory provides a unified and a uniform description of resonances in all partial waves and enables the characterization of a large number of resonances in terms of very few parameters. For the sample system of $^{6}\mathrm{Li} ^{40}\mathrm{K}$, we present descriptions of all resonances in $aa$, $ab$, and $ba$ channels, in partial waves $s$ ($l=0$) through $h$ ($l=5$), and in a magnetic field of 0--1000 G. All resonances, including those in nonzero partial waves, are fully characterized using the newly developed parametrization of Gao [Phys. Rev. A 84, 022706 (2011)].

Bo Gao

Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave $l$ and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances of arbitrary $l$, is presented for ultracold atomic scattering around a Feshbach resonance. Other related issues addressed include (a) the parametrization of a magnetic Feshbach resonance of arbitrary $l$, (b) rigorous definitions of ``broad'' and ``narrow'' resonances of arbitrary $l$ and their different scattering characteristics, and (c) the tuning of the effective range and the generalized effective range by a magnetic field.

Raffaele Carlone, M. Correggi, D. Finco +1 more

Zhong-Bo Chen, Jing-Lun Li, Shu‐Lin Cong

Li-Hang Li, Yang Hai, Bing-Kuan Lyu +2 more

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.