  We investigate the superfluid phases of a Rashba spin-orbit coupled
Bose-Einstein condensate residing on a two dimensional square optical lattice
in the presence of an effective Zeeman field $\Omega$. At a critical value
$\Omega=\Omega_c$, the single-particle spectrum $ E_k $ changes from having a
set of four degenerate minima to a single minimum at $k=0$, corresponding to
condensation at finite or zero momentum, respectively. We describe this quantum
phase transition and the symmetry breaking of the condensate phases. We use the
Bogoliubov theory to treat the superfluid phases and determine the phase
diagram, the excitation spectrum and the sound velocity of the phonon
excitations. A novel dynamically unstable superfluid regime occurring when
$\Omega$ is close to $\Omega_c$ is analytically identified and the behavior of
the condensate quantum depletion is discussed. Moreover, we show that there are
two types of roton excitations occurring in the $\Omega<\Omega_c$ regime and
obtain explicit values for the corresponding energy gaps.
