  In this paper, we study two-color, two-flavor QCD using chiral perturbation
theory at next-to-leading order when the diquark chemical potential ($\mu_{B}$)
is equal to the isospin chemical potential ($\mu_{I}$). For chemical potentials
larger than the physical pion mass, the system is in a multicomponent
superfluid phase with both pions and diquarks. We construct the one-loop
effective potential using $\chi$PT in the presence of an external
multicomponent superfluid source and use the effective potential to calculate
the chiral condensate, the multicomponent superfluid condensate and the
(multicomponent) superfluid density. We also find the critical chemical
potential and the order of the phase transition from the normal phase to the
multicomponent condensed phase at next-to-leading order. The phase transition
remains second order (as at tree-level) and the critical chemical potential is
equal to the one-loop renormalized diquark (or pion) mass.
