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We theoretically present an economical and convenient way to study ground-state properties of a strongly interacting superfluid Fermi gas. Our strategy is that complicated strong-coupling calculations are used only to evaluate quantum fluctuation corrections to the chemical potential µ.Then, without any further strong-coupling calculations, we calculate the compressibility, sound velocity, internal energy, pressure, and Tan's contact, from the calculated µ without loss of accuracy, by using exact thermodynamic identities. Using a recent precise measurement of µ in a superfluid 6 Li Fermi gas, we show that an extended T -matrix approximation (ETMA) is suitable for our purpose, especially in the BCS-unitary regime, where our results indicate that many-body corrections are dominated by superfluid fluctuations. Since precise determinations of physical quantities are not always easy in cold Fermi gas physics, our approach would greatly reduce experimental and theoretical efforts toward the understanding of ground-state properties of this strongly interacting Fermi system.

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We propose a novel mechanism for a nonequilibrium phase transition in a U (1)-broken phase of an electron-hole-photon system, from a Bose-Einstein condensate of polaritons to a photon laser, induced by the non-Hermitian nature of the condensate. We show that a (uniform) steady state of the condensate can always be classified into two types, namely, arising either from lower or upperbranch polaritons. We prove (for a general model) and demonstrate (for a particular model of polaritons) that an exceptional point where the two types coalesce marks the endpoint of a firstorder-like phase boundary between the two types, similar to a critical point in a liquid-gas phase transition. Since the phase transition found in this paper is not in general triggered by population inversion, our result implies that the second threshold observed in experiments is not necessarily a strong-to-weak-coupling transition, contrary to the widely-believed understanding. Although our calculation mainly aims to clarify polariton physics, our discussion is applicable to general drivendissipative condensates composed of two complex fields.