Stability of a two-dimensional homogeneous spin-orbit-coupled boson system

We investigate the condensation of a two-dimensional homogeneous spin-orbit-coupled boson system at zero temperature. We prove that the condensate is stable although the spin-orbit coupling makes the momentum distribution of depletion more divergent in the infrared limit. The stability of the system depends solely on the infrared behavior of the density waves, while the spin waves play a nonessential role. The condensate fraction is a decreasing function of the ratio of spin-orbit coupling to the square root of the boson density. The peak of the momentum distribution of depletion stretches anisotropically when the strength of spin-orbit coupling increases.