  We present a phase diagram for a two-dimensional electron system with two
populated subbands. Using a gated GaAs/AlGaAs single quantum well, we have
mapped out the phases of various quantum Hall states in the density-magnetic
filed plane. The experimental phase diagram shows a very different topology
from the conventional Landau fan diagram. We find regions of negative
differential Hall resistance which are interpreted as preliminary evidence of
the long sought reentrant quantum Hall transitions. We discuss the origins of
the anomalous topology and the negative differential Hall resistance in terms
of the Landau level and subband mixing.
