  In this paper we study thermodynamic properties of dense cold $SU(2)$ QCD
within lattice simulation with dynamical rooted staggered quarks which in the
continuum limit correspond to $N_f=2$ quark flavours. We calculate baryon
density, renormalized chiral and diquark condensates for various baryon
chemical potentials in the region $\mu \in (0,\,2000)$ MeV. It is found, that
in the region $\mu \in (0,\,540)$ MeV the system is well described by the ChPT
predictions. In the region $\mu > 540$ MeV the system becomes sufficiently
dense and ChPT is no longer applicable to describe lattice data. For chemical
potentials $\mu > 900$ MeV we observe formation of the Fermi sphere, and the
system is similar to the one described by the Bardeen-Cooper-Schrieffer theory
where the the diquarks play a role of Cooper pairs. In order to study how
nonzero baryon density influences the gluon background we calculate
chromoelectric and chromomagnetic fields, as well as the topological
susceptibility. We find that the chromoelectric field and the topological
susceptibility decrease, whereas the chromomagnetic field increases with rising
of baryon chemical potential. Finally we study the equation of state of dense
two-color quark matter.
