  Measuring phase in coherent electron systems (mesoscopic systems) provides
ample information not easily revealed by conductance measurements. Phase
measurements in relatively large quantum dots (QDs) recently demonstrated a
universal like phase evolution independent of dot size, shape, and occupancy.
Explicitly, in Coulomb blockaded QDs the transmission phase increased
monotonically by pi throughout each conductance peak, thereafter, in the
conductance valleys the phase returned sharply to its base value. Expected
mesoscopic features in the phase, related to spin degeneracy or to exchange
effects, were never observed. Presently, there is no satisfactory full
explanation for the observed phase universality. Unfortunately, the phase in a
few-electron QDs, where it can be better understood was never measured. Here we
report on such measurements on a small QD that occupy only 1-20 electrons. Such
dot was embedded in one arm of a two path electron interferometer, with an
electron counter near the dot. Unlike the repetitive behavior found in larger
dots we found now mesoscopic features for dot occupation of less than some 10
electrons. An unexpected feature in this regime is a clear observation of the
occupation of two different orbital states by the first two electrons -
contrary to the recent publications. As the occupation increased the phase
evolved and turned universal like for some 14 electrons and higher. The present
measurements allowed us to determine level occupancy and parity. More
importantly, they suggest that QDs go through a phase transition, from
mesoscopic to universal like behavior, as the occupancy increases. These
measurements help in singling out potential few theoretical models among the
many proposed.
