New experiments are presented on the transmission of electron waves through a 2DEG (2 dimensional electron gas) ring with a gate on top of one of the branches. Magnetoconductance oscillations are observed, and the phase of the Aharanov-Bohm signal alternates between 0 and π as the gate voltage is scanned. A Fourier transform of the data reveals a dominant period in the voltage which corresponds to the energy spacing between successive transverse modes. A theoretical model including random phase shifts between successive modes reproduces the essential features of the experiment. PACS number: 73.40.-c Typeset using REVTEX 1 The Aharonov–Bohm (AB) effect has proven to be an invaluable tool for quantifying interference phenomena in mesoscopic physics. Early experiments on long metal cylinders  revealed that an electron accumulates a phase ∫ A.dl as it is scattered elastically by impurities while traveling around the loop: when the magnetic flux is varied, an oscillator
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