Pairing and coherence order parameters in a three-component ultracold Fermi gas

Abstract

We investigate the mean-field ground state of a homogeneous three-component attractive Fermi gas at zero temperature. This is achieved by deriving a set of Bogoliubov--de Gennes (BdG) equations of the three-component system, including pairing both order parameters ${\ensuremath{\Delta}}_{\mathit{ij}}$ and coherence order parameters $\ensuremath{\langle}{\ensuremath{\psi}}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{\ensuremath{\psi}}_{j}\ensuremath{\rangle}$ ($i\ensuremath{\ne}j$), where ${\ensuremath{\psi}}_{j}$ is the field operator for spin level $j$. Ward-Takahashi identities are obtained to constrain these order parameters. In addition, we present an explicit analytic mean-field solution for symmetric systems and verify that the quasiparticle excitations consist of both gapped and gapless spectra, which correspond to the excitations of paired and unpaired atoms. We further point out that the omission of $\ensuremath{\langle}{\ensuremath{\psi}}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{\ensuremath{\psi}}_{j}\ensuremath{\rangle}$ in BdG equations could lead to an overestimation of ${\ensuremath{\Delta}}_{\mathit{ij}}$ in the strong coupling regime.