  The chemical potential ($\mu$) dependence of the topological susceptibility
with two-color two-flavor QCD is studied. We find that at temperature $T
\approx T_c /2$, where $T_c$ denotes the critical temperature at zero chemical
potential, the topological susceptibility is almost constant throughout $0 \leq
a\mu \lesssim 1.0$, while at $T\approx T_c$, it decreases significantly from
the $\mu=0$ value in a high $\mu$ regime.
  In this work, we perform the simulation for $\mu/T \le 16$, which covers even
the low temperature and the high chemical potential regime. In this regime, we
introduce a diquark source term, which is characterized by $j$, into the
action. We also show our results for the phase diagram in a low temperature
regime ($T\approx T_c/2$), which is obtained after taking the $j \to 0$ limit
of the diquark condensate and the Polyakov loop.
