Simulation of the Majorana equation in circuit QED

TL;DR

This paper presents a method to simulate the 1D Majorana equation using circuit QED with Cooper pair boxes and a transmission line resonator, enabling experimental verification of Majorana wave functions.

Contribution

It introduces a novel circuit QED setup for simulating the Majorana equation and proposes a measurement scheme for verifying the wave function.

Findings

Strong coupling can be achieved in the setup.

Different interactions can be engineered for simulation.

Measurement of pseudo-helicity is feasible with current technology.

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.