Quantum phase transitions in two dimensions: Experiments in Josephson-junction arrays

We have studied two-dimensional superconducting networks coupled by Josephson junctions in the regime where the Josephson coupling energy is comparable in magnitude to the capacitive energy of charging an island with a Cooper pair. We have mapped out the dependence of quantum phase transitions on the ratio of these two energies (for different values of the applied magnetic field) and on the applied field for arrays both with square and triangular cells. Our experimental results are compared with existing theoretical predictions.