  We study ultracold bosons in three dimensions with an anisotropic
Rashba-Dresselhaus spin-orbit coupling. We first carry out the exact summation
of ladder diagrams for the two-boson t-matrix at zero energy. Then, with the
t-matrix as the effective interaction, we find the ground-state phase diagrams
of bosons in mean field as a function of the spin-orbit coupling, the
anisotropy, and the scattering lengths between particles in the same and in
different pseudospin states. The resulting phase diagrams have much richer
structures than those obtained using mean-field couplings, exhibiting three
different phases: a plane-wave condensate, a striped condensate, and an
unstable phase. The differences between the present approach using the t-matrix
compared to using mean-field couplings is significant for large scattering
lengths, large spin-orbit-coupling strength, or small anisotropy.

Quantum Gases