  We report experiments on a quantum electron interferometer fabricated from
high mobility, low density GaAs/AlGaAs heterostructure material. In this
device, a nearly circular electron island is defined by four front gates
deposited in etched trenches. The island is separated from the 2D electron bulk
by two nearly open constrictions. In the quantum Hall regime, two
counterpropagating edge channels are coupled by tunneling in the constrictions,
thus forming a closed electron interference path.For several fixed front gate
voltages, we observe periodic Aharonov-Bohm interference oscillations in
four-terminal resistance as a function of the enclosed flux. The oscillation
period DeltaB gives the area of the interference path S via quantization
condition S=h/eDeltaB. We experimentally determine the dependence of S on the
front gate voltage, and find that the Aharonov-Bohm quantization condition does
not require significant corrections due to the confining potential. These
results can be interpreted as a constant integrated compressibility of the
island with respect to the front gates. We also analyze experimental results
using two classical electrostatics models: one modeling the 2D electron density
due to depletion from an etch trench, and another modeling the gate voltage
dependence of the electron density profile in the island.
