Quantum Skyrmion Qudit in a Triangular-lattice magnet

TL;DR

This paper develops a comprehensive analytical model for quantum skyrmions in frustrated triangular magnets, revealing conditions under which they function as qubits or qudits, and demonstrating their potential for quantum information applications.

Contribution

It generalizes previous models to arbitrary electric fields, characterizes skyrmion states as qudits, and analyzes their coherence properties, advancing quantum skyrmionics and resource theory.

Findings

System's state transitions from qubit to qudit with increasing barrier.

The $l_1$ norm of coherence is significantly higher in skyrmion qudits.

Analytic solutions applicable for arbitrary electric field strengths.

Abstract

Since the pioneering work Lohani et. al., Phys. Rev. X 9, 041063 (2019), it became clear that quantum skyrmions have highly unusual properties as compared to the classical skyrmions and, due to their quantumness, cannot be described by continuous magnetic textures akin to the classical skyrmions. Competing nearest-neighbor and next-nearest-neighbor ferromagnetic and antiferromagnetic interactions in triangular spin-frustrated magnets lead to the formation of quantum skyrmion states. In frustrated magnets, skyrmions are characterized by the helical degree of freedom, which can store quantum information. In the limit of a weak electric field, the system can be described as a two-level system, i.e., a skyrmion qubit. Here, we propose a more general formulation of the problem and obtain general analytic solution of the model previously introduced in Psaroudaki et. al., Phys. Rev. Lett. 127, 067201 (2021). Our solution is valid not only for small barrier but for the arbitrary electric field. In the case of a significant barrier, we prove that the system's state is not a Skyrmion qubit as it was thought before, but a Skyrmion qudit. We constructed the density matrix of the Skyrmion qudit and studied its evolution in time. The obtained results suggest that the proposed model can be exploited further to meet the needs of quantum information theory and quantum skyrmionics. We showed that the $l_1$ norm of coherence of the skyrmion quantum qudit is a thousand times larger than the coherence of the skyrmion quantum qubit. The obtained result opens new perspectives for quantum skyrmion-based resource theory.