Nonreciprocal effects in Josephson junction arrays*

We investigate nonreciprocal effects in arrays of Josephson junctions, where a Zeeman field induces an anomalous phase shift in the current-phase relation. We show that in square-symmetry 2D-arrays nonreciprocity is given by ratchet-like deformation of the egg-crate potential which pins Josephson vortices. A simple analysis reveals that second-nearest neighbor coupling between the array islands is necessary to break the symmetry. In experiments, the nonreciprocal effect is demonstrated by measuring both the critical current and the array inductance-versus-current asymmetry. For dilute vortices, the experimental results match what is expected from simple models. For finite frustration, measurements show a similar nonreciprocity for all major commensurate fractions, but with an intriguing exception: for f=1/3, the nonreciprocity changes sign. Our results open a new research direction in the field of Josephson junction arrays, namely, the possibility to control the real-space shape and symmetry of vortices and of their potential by an external Zeeman field.