  Spin singlet superconductors with quasi-two dimensional multilayer structure
are studied in high magnetic fields. Specifically we concentrate on bi- and
tri-layer systems whose layers by symmetry are subject Rashba-type spin-orbit
coupling. The combination of magnetic field and spin-orbit coupling leads to a
first order phase transition between different states of layer-dependent
superconducting order parameters upon rising the magnetic field. In this
context we distinguish the low-field Bardeen-Cooper-Schrieffer state where all
layers have order parameters of the same sign and the high-field pair-density
wave state where the layer-dependent order parameters change the sign at the
center layer. We also show that progressive paramagnetic limiting effects yield
additional features in the H-T phase diagram. As possible realizations of such
unusual superconducting phases we consider artificial superlattices of
CeCoIn_5, as well as some multilayer high-T_c cuprates.
