Quasiparticle Spectrum of Quantum Degenerate Fermi Gas in the Presence of Self-Consistent Magnetization Field**The project supported by National Natural Fundamental Research Program of China under Grant No. 2001CB309310, National Natural Science Foundation of China under Grant Nos. 90103026, 60078023, and 10125419, and The Chinese Academy of Sciences under 100 Talents Project

Abstract

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.