  Recently three dimensional topological quantum materials with gapless energy
spectra have attracted considerable interests in many branches of physics.
Besides the celebrated example, Dirac and Weyl points which possess gapless
point structures in the underlying energy dispersion, the topologically
protected gapless spectrum can also occur along a ring, named Dirac and Weyl
nodal rings. Ultra-cold atomic gases provide an ideal platform for exploring
new topological materials with designed symmetries. However, whether Dirac and
Weyl rings can exist in the single-particle spectrum of cold atoms remains
elusive. Here we propose a realistic model for realizing Dirac and Weyl rings
in the single-particle band dispersion of a cold atom optical lattice. Our
scheme is based on previously experimentally already implemented Raman coupling
setup for realizing spin-orbit coupling. Without the Zeeman field, the model
preserves both pseudo-time-reversal and inversion symmetries, allowing Dirac
rings. The Dirac rings split into Weyl rings with a Zeeman field that breaks
the pseudo-time-reversal symmetry. We examine the superfluidity of attractive
Fermi gases in this model and also find Dirac and Weyl rings in the
quasiparticle spectrum.
