14
possibility of P-wave superfluidity [17]. Over the past two years or so, a flurry of theo-
retical activities in resonant population imbalanced Fermi gas has been stimulated by the
experiments carried out in the Hulet’s group at Rice [18] and Ketterle’s group at MIT
[19]. Nevertheless, there are still many open questions concerning, for instance, the impor-
tance of finite-size effects and the Stabifity of exotic non-BCS pairing state remaining to be
answered. In particular, finite-size effects are considered to be the leading candidate that
accounts for the discrepancies in experimental observation between the two groups, but a
detailed exploration is still lacking. The main discrepancies concern the breakdown of the
local density approximation (LDA) which is apparent in Rice data but not in MIT ones and
the existance of the Chandrasekhar-Clogston (CC) limit [20] which is observed at MIT but
not at Rice.
To shed light on these important questions, we have started a systematic investigation
by solving Self-Consistently the Bogoliubov-de Gennes (BdG) equations which describe the
mean-field properties of two-component Fermi gases and the ground state inhomogeneity
effects are readily incorporated. In our calculation, the interaction strength (i.e., the ,s-
wave scattering length a between the two components) is a controllable parameter. In this
thesis, however, we restrict our discussion to the unitarity limit (i.e., a —> inf) with a
divergent scattering length since this is the regime explored by the experiments [18, 19].
To simulate the Rice experiment, we consider a 3D system in an anisotropic traps with
cylindrical symmetry, the external potential is taken to be: Vext(r) = mω2(Λ2p2 ÷ z2)∕2 with
p2 = x2 + y2. The parameter Л represents the trap aspect ratio. We can take advantage of the