  We study the ground-state behavior of a Bose-Einstein Condensate (BEC) in a
Raman-laser-assisted one-dimensional (1D) optical lattice potential forming a
multilayer system. We find that, such system can be described by an effective
model with spin-orbit coupling (SOC) of pseudospin $(N-1)/2$, where $N$ is the
number of layers. Due to the intricate interplay between atomic interactions,
SOC and laser-assisted tunnelings, the ground-state phase diagrams generally
consist of three phases -- a stripe, a plane wave and a normal phase with
zero-momentum, touching at a quantum tricritical point. More important, even
though the single-particle states only minimize at zero-momentum for odd $N$,
the many-body ground states may still develop finite momenta. The underlying
mechanisms are elucidated. Our results provide an alternative way to realize an
effective spin-orbit coupling of Bose gas with the Raman-laser-assisted optical
lattice, and would also be beneficial to the studies on SOC effects in spinor
Bose systems with large spin.
