Measurement of the Thulium Ion Spin Hamiltonian Within a Yttrium Gallium Garnet Host Crystal

We characterize the magnetic effects present for thulium ions in a Y₃Ga₅O₁₂ (Tm:YGG) lattice. In this work we measure hyperfine tensors for the ground, ³H₆, and excited, ³H₄, states using a combination of spectral hole burning and optically detected nuclear magnetic resonance (ODNMR). From these techniques we measure and fit the orientation dependence of the Tm³⁺ ion's spin-Hamiltonian by rotating the sample through a series of angles with an external magnetic field. Independent measurements of the level splittings and optical transition shifts at a fixed external field orientation show good agreement with the measured tensor parameters. Using this measured spin-Hamiltonian we propose a set of orientations based on the ZEFOZ technique, [1], to improve optical coherence, and spin level in-homogeneous broadening, both of which are desirable for light-matter interaction and quantum information applications in this material.

[1] E. Fraval, M. J. Sellars, and J. J. Longdell. Method of extending hyperfine coherence times in Pr³⁺:Y₂SIO₅ .Phys. Rev. Lett., 92:077601, Feb 2004.