Abstract
We study a three-component superfluid Fermi gas in a spherically symmetric harmonic trap using the Bogoliubov–deGennes method. We predict a coexistence phase in which two pairing field order parameters are simultaneously non-zero, in stark contrast to studies performed for trapped gases using local density approximation. We also discuss the role of atom number conservation in the context of a homogeneous system.
Highlights
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Ultracold Fermi gases have opened up a way to explore multi-component gases experimentally
Optical lattices are interesting due to the rich phase diagram: theoretical investigations have found that color superconductivity competes with normal phase and formation of trions [9,10,11,12,13,14,15]
Summary
The general mean-field Hamiltonian for a three-component system in the contact interaction potential approximation is (up to a constant). Analogous to the SU(3) symmetric case, the total pairing field is a two-dimensional (2D) vector = [ 12, 23]T, and in the symmetric case, where components |1 and |3 are identical, it is preserved under spin rotations of the hyperfine states |1 and |3. This symmetry implies that the ground state is degenerate with respect to the orientation of the total pairing field vector. The degeneracy is lifted by changing masses, chemical potentials or interaction strengths and, as we will soon show, by imposing boundary conditions, such as fixing the number of atoms in different components.
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