  Tunneling and Coulomb drag are sensitive probes of spontaneous interlayer
phase coherence in bilayer two-dimensional electron systems at total Landau
level filling factor $\nu_T = 1$. We find that the phase boundary between the
interlayer phase coherent state and the weakly-coupled compressible phase moves
to larger layer separations as the electron density distribution in the bilayer
is imbalanced. The critical layer separation increases quadratically with layer
density difference.
