What does the Josephson effect tell us about the superconducting state of the cuprates
We review the recent measurements of the current-phase relation in cuprate Josephson junctions. Special attention is paid to 45 degree grain boundary junctions and to c-axis junctions between YBCO and Nb. It is shown that the anomalous properties of such junctions which have been found experimentally (large second harmonic of the current phase relation, sign change of the first harmonic as a function of temperature) are qualitatively consistent with the d-wave symmetry of pairing in the cuprates. It is argued that in order to describe the data quantitatively, quantum fluctuations of the order parameter need to be taken into account. It is pointed out that the Josephson effect is an ideal tool for measuring the reduced phase stiffness in the cuprates.