Dynamics of a Majorana trijunction in a microwave cavity

TL;DR

This paper investigates the dynamics of Majorana bound states in a trijunction embedded in a microwave cavity, revealing how braiding operations influence observable quantum states and photon properties, including the Berry phase effects.

Contribution

It extends previous models by computing the full time evolution of the system's density matrix, incorporating relaxation channels and Floquet formalism for periodic driving, to analyze braiding in a cavity.

Findings

Stationary state observables depend on ground state parity and Berry phase.

Photon number and coherence functions reveal the non-Abelian Berry phase.

The model captures the impact of braiding on quantum and photonic properties.

Abstract

A trijunction made of three topological semiconducting wires, each supporting a Majorana bound state at its two extremities, appears as one of the simplest geometry in order to perform braiding of Majorana fermions. By embedding the trijunction into a microwave cavity allows to study the intricate dynamics of the low-energy Majorana bound states (MBSs) coupled to the cavity electric field under a braiding operation. Extending a previous work (Phys. Rev. Lett. 2019, 122, 236803), the full time evolution of the density matrix of the low-energy states, including various relaxation channels, is computed both in the adiabatic regime, as well as within the Floquet formalism in the case of periodic driving. It turns out that in the stationary state the observables of the system depend on both the parity of the ground state and on the non-Abelian Berry phase acquired during braiding. The average photon number and the second order photon coherence function $g^{(2)}(0)$ are explicitly evaluated and reveal the accumulated non-Abelian Berry phase during the braiding process.