The transport properties of electronic devices are usually characteriz
ed on the basis of conductance measurements. Such measurements are ade
quate for devices in which transport occurs incoherently, but for very
small devices-such as quantum dots(1,2)-the wave nature of the electr
ons plays an important role(3), Because the phase of an electron's wav
efunction changes as it passes through such a device, phase measuremen
ts are required to characterize the transport properties fully, Here w
e report the results of a double-slit interference experiment which pe
rmits the measurement of the phase-shift of an electron traversing a q
uantum dot, This is accomplished by inserting the quantum dot into one
arm of an interferometer, thereby introducing a measurable phase shif
t between the arms, We find that the phase evolution within a resonanc
e of the quantum dot can be accounted for qualitatively by a model tha
t ignores the interactions between the electrons within the dot. Altho
ugh these electrons must interact strongly, such interactions apparent
ly have no observable effect on the phase. On the other hand, we also
find that the phase behaviour is identical for all resonances, and tha
t there is a sharp jump of the phase between successive resonance peak
s. Adequate explanation of these features may require a model that inc
ludes interactions between electrons.