Critical Zeeman Splitting of Fermi Superfluidity at Infinite Scattering Length

We determine the critical Zeeman energy splitting for Fermi superfluidity at infinite s-wave scattering length according to the Monte Carlo and experimental results of the equations of state. Based on the universality hypothesis, we show that there exist two critical fields $H_{c1}$ and $H_{c2}$, between which a superfluid-normal mixed phase is energetically favored, and model-independent formulae for $H_{c1}$, $H_{c2}$ and the critical population imbalance $P_c$ are derived. Using recent Monte Carlo and experimental results of $P_c$, $H_{c1}$ and $H_{c2}$ are determined. It is found $H_{c1}=0.41\epsilon_{\text F}$ and $H_{c2}=0.50\epsilon_{\text F}$, with $\epsilon_{\text F}$ being the Fermi energy of non-interacting gas.