Realizing Majorana zero modes using Josephson Junction arrays

We design a 1-D array of Josephson junctions that features Majorana zero modes (MZM) at its edges. This analog quantum circuit is described by the quantum Sine-Gordan (qSG) model, a prototypical example of an integrable system exhibiting Symmetry Protected Topological (SPT) phases. By tuning various parameters in the circuit, one can probe the qSG model in both the semi-classical regime and quantum regime where the qSG corresponds to the Massive Thirring (MT) model. In the quantum regime, the phase accumulations correspond to genuine quantum numbers associated with Majorana zero modes (MZM) which are protected by the symmetries of the system. By virtue of its tunability, the system also provides a platform to investigate the stability of the MZM in the face of integrability-breaking perturbations.