Universal Properties in a $P$-Wave Fermi Gas with a Resonant Interaction

We are interested in universal properties in a resonant regime where the effective interatomic interaction is very strong. The regime is quantitatively characterized by inequalities, $$a \gtrsim d \sim \lambda \gg r_\mathrm{int}. $$ Here, $a$ is a scattering length, which determines the effective strength of the interaction (or more precisely, low-energy scattering cross section), $d$ is the average interparticle distance, $\lambda$ is the thermal de Broglie length, and $r_\mathrm{int}$ is the range of the interaction. In previous studies (S. Tan, Ann. Whys., 2008), it has been pointed out that, in the unitary regime of the BCS-BEC crossover, anomalously large correlations build up in short-range/-time regimes, and that they also determine macroscopic properties such as thermodynamics. They are universal relations which bridge short- and long-range behavior. They hold true quite generally, at any temperature, with any number of particles, in a superfluid or normal fluid phase, and so on. Afterward, they are extended to other s-wave interacting systems such as Bose gases and lower dimensions, and are established as a fundamental property of the resonant gases.

Recently, we have found similar universal relations in a $p$-wave interacting Fermi gas. We showed for the first time the existence of universal relations in other universality classes than those of $s$-wave type. We also showed the anisotropy of the $p$-wave interaction brings a nontrivial structure in the universal relations, which is not seen in the $s$-wave system because the s-wave interaction is isotropic.

  1. S.M.Y. and M. Ueda, "Universal High-Momentum Asymptote and Thermodynamic Relations in a Spinless Fermi Gas with a Resonant $p$-Wave Interaction", Phys. Rev. Lett. 115, 135303 (2015).
  2. S.M.Y. and Masahito Ueda, "$p$-wave contact tensor: Universal properties of axisymmetry-broken $p$-wave Fermi gases", Phys. Rev. A 94, 033611 (2016).