We study the superradiant phase transition of a mesoscopic Fermi gas comprising between a few tens and a few thousand
6Li atoms in a high-finesse cavity across a wide range of densities. We observe a non-monotonic variation of the superradiant threshold as a function of density, with a minimum reached when the Fermi and recoil wavevectors are comparable. The minimum corresponds to a crossover between Fermi pressure-assisted ordering and Pauli blocking of photon scattering, in good agreement with theory. This interpretation is confirmed by a study of the atom-number dependence of the ordering threshold and photon number scaling. Our system opens the perspective of studying few-fermion systems with strong and coherent light-matter coupling.
By numerically calculating the time-evolved Wigner functions, we investigate the dynamics of a few-photon superposed (e.g., up to two ones) state in a dissipating cavity. It is shown that, the negativity of the Wigner function of the photonic state unquestionably vanishes with the cavity's dissipation. As a consequence, the nonclassical effects related to the negativity of the Wigner function should be weakened gradually. However, it is found that the value of the second-order correlation function
g(2)(0) (which serves usually as the standard criterion of a typical nonclassical effect, i.e.,
g(2)(0)<1 implies that the photon is anti-bunching) is a dynamical invariant during the dissipative process of the cavity. This feature is also proven analytically and suggests that
g(2)(0) might not be a good physical parameter to describe the photonic decays. Alternatively, we find that the anti-normal-order correlation function
g(2A)(0) changes with the cavity's dissipation and thus is more suitable to describe the dissipative-dependent cavity. Finally, we propose an experimental approach to test the above arguments with a practically-existing cavity QED system.