Scattering amplitude of ultracold atoms near thep-wave magnetic Feshbach resonance

Abstract

Most of the current theories on the p-wave superfluid in cold atomic gases are based on the effective-range theory for the two-body scattering, where the low energy p-wave scattering amplitude f1(k) is given by f1(k) = −1/[ik + 1/(Vk 2 ) + 1/R], where k is the incident momentum, and V and R are the k-independent scattering volume and effective-range, respectively. However, due to the long-range nature of the van der Waals interaction between two colliding ultracold atoms, the p-wave scattering amplitude of the two atoms is not described by the effective-range theory [1, 2]. In this paper we provide an explicit calculation for the p-wave scattering of two ultracold atoms near the p-wave magnetic Feshbach resonance (PMFR). We show that the low energy pwave scattering amplitude in the presence of PMFR takes the form f1(where V eff , S eff and R eff are k-dependent parameters. Based on this result, we show sufficient conditions for the effective range theory to be a good approximation of the exact scattering amplitude. Using these conditions we show that the effective-range theory is a good approximation for the p-wave scattering in the ultracold gases of 6 Li and 40 K when the scattering volume is enhanced by the resonance.

Experimental determination ofp-wave scattering parameters in ultracold6Li atoms

“…From the fitting, we find V bg ∆B = −2. [32]. The measured magnetic field dependence of the scattering volume is also consistent with the calculation by Lysebo et al [33].…”

Analytic description of atomic interaction at ultracold temperatures. II. Scattering around a magnetic Feshbach resonance

“…(21) at a bgl = ∞, and the corresponding failure of Eqs. (18) and (19) at K c0 bgl = 0, is a necessary sacrifice for using B 0l , which has a more direct physical interpretation than theB 0l parameter of Appendix B but does not exist for a bgl = ∞. Its failure at a bgl = 0 is the price we pay for using the parameter Bl .…”

“…Such understandings, which have been mostly limited to the s wave [12,13], are not only of interest by themselves, they are also prerequisites for understanding atomic interaction in an optical lattice [16] and behaviors of quantum few-atom and many-atom systems around a Feshbach resonance. For nonzero partial waves, the theory here is a necessity as ERT fails [7,8,17,18]. Even for the s wave, it offers much improved analytic description, especially for narrow resonances around which the energy dependence of the scattering amplitude can * bo.gao@utoledo.edu; http://bgaowww.physics.utoledo.edu become so significant that it has to be incorporated into the corresponding few-body [19] and many-body theories (See, e.g., Refs.…”

Universal relations and normal phase of an ultracold Fermi gas with coexistings- andp-wave interactions

“…Close to resonance, |a s | r s,0 , the second virial coefficient for s-wave scattering can then be written as [34,35] In the case of p-wave scattering [40][41][42] …”