Quasiparticle Spectrum of Quantum Degenerate Fermi Gas in the Presence of Self—Consistent Magnetization Field

In this paper, we develop a systematic and simple method to derive quasiparticle spectrum of the quantum degenerate Fermi gases within the framework of Hartree–Fock–Bogoliubov theory which turns a general nonlinear two-body interaction Hamiltonian into a bilinear Hamiltonian by introducing certain self-consistent mean fields. Applying the approach, we obtain the quasi-particle spectrum of the model describing the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas in the presence of the magnetization fields and . When the gap parameter Δ is smaller than one or both of the magnetization fields, the spectrum manifests roton-type structure dramatically different from the spectrum in the absence of the magnetization fields.