  Topological nodal rings as the simplest topological nodal lines recently have
been extensively studied in optical lattices. However, the realization of
complex nodal line structures like nodal chains in this system remains a
crucial challenge. Here we propose an experimental scheme to realize and detect
topological nodal chains in optical Raman lattices. Specifically, we construct
a three-dimensional optical Raman lattice which supports next nearest-neighbor
spin-orbit couplings and hosts topological nodal chains in its energy spectra.
Interestingly, the realized nodal chains are protected by mirror symmetry and
could be tuned into a large variety of shapes, including the inner and outer
nodal chains. We also demonstrate that the shapes of the nodal chains could be
detected by measuring spin polarizations. Our study opens up the possibility of
exploring topological nodal-chain semimetal phases in optical lattices.
