  We investigate the quantum phase transitions of a two-dimensional
Bose-Hubbard model in the presence of a Rashba spin-orbit coupling with and
without thermal fluctuations. The interplay of single-particle hopping,
strength of spin-orbit coupling, and interspin interaction leads to superfluid
phases with distinct properties. With interspin interactions weaker than
intraspin interactions, the spin-orbit coupling induces two finite-momentum
superfluid phases. One of them is a phase-twisted superfluid that exists at low
hopping strengths and reduces the domain of insulating phases. At comparatively
higher hopping strengths, there is a transition from the phase-twisted to a
finite momenta stripe superfluid. With interspin interactions stronger than the
intraspin interactions, the system exhibits phase-twisted to ferromagnetic
phase transition. At finite temperatures, the thermal fluctuations destroy the
phase-twisted superfluidity and lead to a wide region of normal-fluid states.
These findings can be observed in recent quantum gas experiments with
spin-orbit coupling in optical lattices.
