1. Département de Physique de la Matière Condensée, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Genève 4, Switzerland
   
2. Physikinstitut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
   
3. Laboratoire de Physique des Solides, Bat 510, Université Paris-Sud 11, Centre d'Orsay, 91405 Orsay Cedex, France
   
4. Experimental Physics VI, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany

Correspondence to: A. D. Caviglia¹ Correspondence and requests for materials should be addressed to A.D.C. (Email: andrea.caviglia@unige.ch.).

Interfaces between complex oxides are emerging as one of the most interesting systems in condensed matter physics¹. In this special setting, in which translational symmetry is artificially broken, a variety of new and unusual electronic phases can be promoted². Theoretical studies predict complex phase diagrams and suggest the key role of the charge carrier density in determining the systems' ground states. A particularly fascinating system is the conducting interface between the band insulators LaAlO₃ and SrTiO₃ (ref. 3). Recently two possible ground states have been experimentally identified: a magnetic state⁴ and a two-dimensional superconducting condensate⁵. Here we use the electric field effect to explore the phase diagram of the system. The electrostatic tuning of the carrier density allows an on/off switching of superconductivity and drives a quantum phase transition^{6, 7, 8} between a two-dimensional superconducting state and an insulating state. Analyses of the magnetotransport properties in the insulating state are consistent with weak localization and do not provide evidence for magnetism. The electric field control of superconductivity demonstrated here opens the way to the development of new mesoscopic superconducting circuits.