  We investigate chemical-potential (\mu) dependence of static-quark free
energies in both the real and imaginary \mu regions, performing lattice QCD
simulations at imaginary \mu and extrapolating the results to the real \mu
region with analytic continuation. Lattice QCD calculations are done on a
16^{3}\times 4 lattice with the clover-improved two-flavor Wilson fermion
action and the renormalization-group improved Iwasaki gauge action.
Static-quark potential is evaluated from the Polyakov-loop correlation
functions in the deconfinement phase. As the analytic continuation, the
potential calculated at imaginary \mu=i\mu_{\rm I} is expanded into a
Taylor-expansion series of i\mu_{\rm I}/T up to 4th order and the pure
imaginary variable i\mu_{\rm I}/T is replaced by the real one \mu_{\rm R}/T. At
real \mu, the 4th-order term weakens \mu dependence of the potential sizably.
At long distance, all of the color singlet and non-singlet potentials tend to
twice the single-quark free energy, indicating that the interactions between
heavy quarks are fully color-screened for finite \mu. For both real and
imaginary \mu, the color-singlet q{\bar q} and the color-antitriplet qq
interaction are attractive, whereas the color-octet q{\bar q} and the
color-sextet qq interaction are repulsive. The attractive interactions have
stronger \mu/T dependence than the repulsive interactions. The color-Debye
screening mass is extracted from the color-singlet potential at imaginary \mu,
and the mass is extrapolated to real \mu by analytic continuation. The
screening mass thus obtained has stronger \mu dependence than the prediction of
the leading-order thermal perturbation theory at both real and imaginary \mu.
