Simulation of the Majorana equation in circuit QED

Abstract

We propose a scheme to simulate the 1D Majorana equation with two Cooper pair boxes coupled to a 1D superconducting transmission line resonator, where strong coupling limit can be achieved. With proper chosen of systematic parameters, we are able to engineer different kinds of interaction, which is indispensable in simulating the Majorana equation in an enlarged real Hilbert space. Measurement of the conserved observable of pseudo-helicity via transmission spectrum of the cavity field can verify the simulated Majorana wave function. The measurement results are experimentally resolvable based on our estimation with conservative parameters.