Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields

TL;DR

This paper investigates spin-orbit qubits in rare-earth ions, focusing on how their Rabi frequency varies with magnetic field orientation and magnitude, revealing anisotropic behaviors and hyperfine effects in a specific crystal system.

Contribution

It provides a detailed experimental and analytical study of Rabi frequency variations in rare-earth spin-orbit qubits, highlighting hyperfine splitting effects and potential for qubit control.

Findings

Rabi frequency varies anisotropically with magnetic field orientation.

Hyperfine interactions split Rabi frequency curves into eight distinct patterns.

The study opens pathways for decoherence analysis and qubit addressing in rare-earth systems.

Abstract

Contrary to the well known spin qubits, rare-earth qubits are characterized by a strong influence of crystal field due to large spin-orbit coupling. At low temperature and in the presence of resonance microwaves, it is the magnetic moment of the crystal-field ground-state which nutates (for several $\mu$s) and the Rabi frequency $\Omega_R$ is anisotropic. Here, we present a study of the variations of $\Omega_R(\vec{H}_{0})$ with the magnitude and direction of the static magnetic field $\vec{H_{0}}$ for the odd $^{167}$Er isotope in a single crystal CaWO$_4$:Er$^{3+}$. The hyperfine interactions split the $\Omega_R(\vec{H}_{0})$ curve into eight different curves which are fitted numerically and described analytically. These "spin-orbit qubits" should allow detailed studies of decoherence mechanisms which become relevant at high temperature and open new ways for qubit addressing using properly oriented magnetic fields.