  At a finite temperature, the stable equilibrium states of a coupled
two-component superfluid with the same mass in both non-rotating and rotating
cases can be obtained by studying its real time dynamics via holography, the
equilibrium state is the final stable state that does not change in time
anymore in the evolution process . Without rotation, the spatial phase
separated states of the two components become more stable than the miscible
condensates state when the direct repulsive inter-component coupling constant
$\eta>\eta_c=0.05$ when the Josephson coupling $\epsilon$ is turned off. While
a finite $\epsilon$ will always prevent the two species to be separated
spatially. Under rotation, with vanishing $\epsilon$, the quantum fluid reveals
many equilibrium structures of vortex states by varying the $\eta$ from
negative to positive, the interlaced vortex lattices undergo a phase transition
to vortex sheets with each component made up of chains of single quantized
vortices.
