Many-body stabilization of a resonant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-wave Fermi gas in one dimension

Abstract

Using the asymptotic Bethe ansatz, we study the stabilization problem of the one-dimensional spin-polarized Fermi gas confined in a hard-wall potential with a tunable $p$-wave scattering length and finite effective range. We find that the interplay of two factors, i.e., the finite interaction range and the hard-wall potential, will stabilize the system near resonance. The stabilization occurs even on the positive scattering length side, where the system undergoes a many-body collapse if any of the factors is absent. At $p$-wave resonance, the fermion system is found to feature ``quasiparticle condensation'' for any value of effective range, which is stabilized if the range is above twice the mean particle distance. Slightly away from resonance, the correction to the stability condition linearly depends on the inverse scattering length. Finally, a global picture is presented for the energetics and stability properties of fermions from the weakly attractive to deep bound-state regime. Our results raise the possibility of achieving stable $p$-wave superfluidity in quasi-one-dimensional (1D) atomic systems, and meanwhile shed light on the intriguing $s$- and $p$-wave physics in 1D that violate the Bose-Fermi duality.