Exact Solution for 1D Spin-Polarized Fermions with Resonant Interactions

Using the asymptotic Bethe ansatz, we obtain an exact solution of the many-body problem for 1D spin-polarized fermions with resonant p-wave interactions, taking into account the effects of both scattering volume and effective range. Under typical experimental conditions, accounting for the effective range, the properties of the system are significantly modified due to the existence of shape resonances. The excitation spectrum of the considered model has unexpected features, such as the inverted position of the particle-and holelike branches at small momenta, and rotonlike minima. We find that the frequency of the breathing mode in the harmonic trap provides an unambiguous signature of the effective range.