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The symmetry properties of the Cooper pairing problem for multi-componentultra-cold dipolar molecular systems are investigated. The dipolar anisotropyprovides a natural and robust mechanism for both triplet and singlet Cooperpairing to first order in the interaction strength. With a purely dipolarinteraction, the triplet $p_z$-like polar pairing is the most dominant. Ashort-range attractive interaction can enhance the singlet pairing to be nearlydegenerate with the triplet pairing. We point out that these two pairingchannels can mix by developing a relative phase of $\pm\frac{\pi}{2}$, thusspontaneously breaking time-reversal symmetry. We also suggest the possibilityof such mixing of triplet and singlet pairing in other systems.

Mixed triplet and singlet pairing in multicomponent ultracold fermion systems with dipolar interactions