Universal one-dimensional atomic gases near odd-wave resonance

Abstract

We show the renormalization of the contact interaction for odd-wave scattering in one-dimension (1D). Based on the renormalized interaction, we exactly solve the two-body problem in a harmonic trap and further explore the universal properties of spin-polarized fermions near odd-wave resonance by using the operator-product-expansion method. It is found that the high-momentum distribution behaves as $C/{k}^{2}$, with $C$ being the odd-wave contact. Various universal relations are derived. Our work suggests a universal system emergent in 1D with large odd-wave scattering length.