Stability of Majorana zero modes with quantum optical lattices

TL;DR

This paper explores how Majorana zero modes can emerge in a one-dimensional ultracold fermionic system within a quantum optical lattice, revealing conditions for their formation and potential for topological quantum computing.

Contribution

It demonstrates the emergence of Majorana zero modes in a quantum optical lattice with long-range interactions, analyzed through exact diagonalization and singular value decomposition.

Findings

Majorana zero modes appear under specific conditions.

MZM are topologically protected and resemble Kitaev chain behavior.

Potential applications in quantum information processing.

Abstract

I analyze the emergence of Majorana zero modes (MZM) in a one dimensional ultracold fermionic system confined by an optical lattice inside a high-Q cavity. This forms a quantum optical lattice due to the cavity backaction, with emergent long range interactions controlled by the light pumped into the system and thus long range pairing. I investigate the possibility of formation and emergence of edge modes using exact diagonalization and singular value decomposition of the Hamiltonian in the Majorana representation, while computing the mass gap of the MZM. I find that under certain conditions MZM appear distinctively. This MZM have potential applications for quantum information as they are topologically protected analogous to the behaviour of the Kitaev chain.