# Squeezed Dirac and Topological Magnons in a Bosonic Honeycomb Optical Lattice

## TL;DR

This paper explores the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice, revealing control mechanisms via anisotropy and phase-dependent noise modulation, with implications for quantum information storage.

## Contribution

It introduces a novel analysis of magnon squeezing in a honeycomb lattice with spin-orbit interaction, linking optical lattice models to solid-state magnetic systems.

## Key findings

- Magnons can be controlled by Z2 anisotropy.
- System noise is periodically modulated in different magnetic phases.
- Results are applicable to solid-state honeycomb magnetic insulators.

## Abstract

Quantum information storage using charge-neutral quasiparticles are expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-$1/2$ XYZ Heisenberg model on the honeycomb lattice with discrete Z$_2$ symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z$_2$ anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators.