  We study an atomic chain in the presence of modulated charge potential and
modulated Rashba spin-orbit coupling (RSOC) of equal period. We show that for
commensurate periodicities $\lambda=4 n$ with integer $n$, the
three-dimensional synthetic space obtained by sliding the two phases of the
charge potential and RSOC features a topological nodal line semimetal protected
by an antiunitary particle-hole symmetry. The location and shape of the nodal
lines strongly depend on the relative amplitude between the charge potential
and RSOC.
