The scattering amplitude of ultracold atoms near the p-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 $f_1(k)$ is given by , where $k$ is the incident momentum, and $\mathcal{V}$ and $\mathcal{R}$ 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. 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 p-wave scattering amplitude in the presence of PMFR takes the form $f_1(k)=-1/[ik+1/(\mathcal{V}^{\mathrm{eff}}k^2)+1/(\mathcal{S}^{\mathrm{eff}%}k)+1/\mathcal{R}^{\mathrm{eff}}]$ where ${\mathcal{V}}^{\mathrm{eff}},$ and ${\mathcal{R}}^{\mathrm{eff}}$ 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.

13 pages, 3 figs

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• Experimental Determination of p-wave Scattering Parameters in ultracold 6Li atoms
• Renormalization in the Three-body Problem with Resonant P-wave Interactions
• Analytic description of atomic interaction at ultracold temperatures II: Scattering around a magnetic Feshbach resonance
• Quantitative analysis of $p$-wave three-body losses via cascade process
• Three-body losses of a polarized Fermi gas near a p-wave Feshbach resonance in effective field theory
• Probing open- and closed-channel p-wave resonances
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• Universal relations and normal phase of an ultracold Fermi gas with coexisting $s$- and $p$-wave interactions
• Three-body bound states in atomic mixtures with resonant p-wave interaction
• Universal Feature in Optical Control of a p-wave Feshbach Resonance
• Quantum Monte Carlo study of the role of p-wave interactions in ultracold repulsive Fermi gases
• Optical Feshbach resonances through a molecular dark state: Efficient manipulation of $p$-wave resonances in fermionic ${}^{171}$Yb atoms
• Universality in s-wave and higher partial wave Feshbach resonances: an illustration with a single atom near two scattering centers
• Universal relations and normal-state properties of a Fermi gas with laser-dressed mixed-partial-wave interactions
• Temperature-Dependent Contact of Weakly Interacting Single-Component Fermi Gases and Loss Rate of Degenerate Polar Molecules
• Three-body universality in ultracold $p$-wave resonant mixtures
• Studies of Single Component Fermi Gas near a $P$-wave Resonance with Lowest Order Constrained Variational Method
• Elastic collision rates of spin-polarized fermions in two dimensions