1. Department of Applied Physics and DIMES, Delft Univesity of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands
2. Permanent address: Service de Physique de l'Etat Condensé, CEA-Saclay, F-91191, Gif-sur-Yvette, France.

Correspondence to: Alexander van Oudenaarden¹ Correspondence and requests for materials should be addressed to A.v.O. (e-mail: Email: socrates@qt.tn.tudelft.nl).

Abstract

The quantum-mechanical phase of the wavefunction of an electron can be changed by electromagnetic potentials, as was predicted by Aharonov and Bohm¹ in 1959. Experiments on propagating electron waves in vacuum have revealed both the magnetic^{2, 3, 4} and electrostatic⁵ Aharonov–Bohm effect. Surprisingly, the magnetic effect was also observed in micrometre-sized metal rings^{6, 7, 8}, demonstrating that electrons keep their phase coherence in such samples despite their diffusive motion. The search for the electrostatic contribution to the electron phase in these metal rings⁹,¹⁰ was hindered by the high conductivity of metal, which makes it difficult to apply a well defined voltage difference across the ring. Here we report measurements of quantum interference of electrons in metal rings that are interrupted by two small tunnel junctions. In these systems, a well defined voltage difference between the two parts of the ring can beapplied. Using these rings we simultaneously explore the influence of magnetic and electrostatic potentials on the Aharonov–Bohm quantum-interference effect, and we demonstrate that these two potentials play interchangeable roles.