Engineered Crystal Systems for Erbium Quantum Hardware

Abstract

Rare-earth ions in solid-state hosts are a compelling hardware platform for quantum networking due to their exceptional optical, and long-lived spin transitions.

Erbium's transitions couple to photons in the Telecom-C band, making it compatible with fibre, and has demonstrated high coherence and low spectral diffusion in a range of materials. However, it has a low optical dipole moment, leading to low light-matter coupling. This limits the rate at which operations performed within a network.

Despite decades of research, Er transitions remain poorly understood. Hosts are chosen based on convention, convenience, and (well-informed) heuristics, since calculations of the properties of lanthanide 4f shell are prohibitively difficult. This thesis addresses the challenge of this weak dipole through two complementary approaches; both of which constitute engineering the erbium-crystal system.

Firstly, we engineer the emitter itself, from the bottom up. We seek an optimal crystal site for ions, which maintains coherence but increases transition strength. To this end, we have characterised four Er sites in CaF2 to understand how the crystal field affects ion properties. We identify sites with dipole moments as high as 1.63x10^-32 Cm despite lifetimes in excess of 10 ms, and coherence of up to 43.9 µs. This informs our next steps, in selecting an optimal site for single ion addressing, and our long-term goal of designing sites for high dipole moments.

In the second approach, we engineer the crystal from the top down, fabricating whispering gallery mode resonators in calcium fluoride. I have fabricated five high Q resonators in doped and undoped CaF2, and commenced their characterisation. We have prototyped a coupler for use of these devices in a cryostat with no free-space optical access.

This engineered crystal system - a high dipole erbium site coupled to a high Q resonator - provides a path toward competitive optical cooperativity for single erbium ions in the solid state.