  For pseudospin-half bosons with inter-spin attraction and intra-spin
repulsion, normal phase and Bose condensed phase can coexist at finite
temperature. The homogeneous system is unstable against the spinodal
decomposition within a medium density interval, and consequently, a
normal-superfluid phase separation takes place. The isothermal
equation-of-state shows a characteristic plateau in the P-V (pressure-volume)
diagram, which is reminiscent of a classical gas-liquid transition, although,
unlike the latter, the coexistence lines never terminate at a critical point as
temperature increases. In a harmonic trap, the phase separation can be revealed
by the density profile of the atomic cloud, which exhibits a sudden jump across
the phase boundary.
