  Recent experimental realization of one-dimensional (1D) spin-orbit coupling
(SOC) for ultracold alkaline-earth(-like) atoms in optical lattice clocks opens
a new avenue for exploring exotic quantum matter because of the strongly
suppressed heating of atoms from lasers comparing with alkaline atoms. Here we
propose a scheme to realize two-dimensional (2D) Rashba and three-dimensional
(3D) Weyl types of SOC in a 3D optical lattice clock and explore their
topological phases. With 3D Weyl SOC, the system can support topological phases
with various numbers as well as types (I or II) of Weyl points. The spin
textures of such topological bands for 2D Rashba and 3D Weyl SOC can be
detected using suitably designed spectroscopic sequences. Our proposal may pave
the way for the experimental realization of robust topological quantum matters
and their exotic quasiparticle excitations in ultracold atomic gases.
