# High-cooperativity coupling of a rare-earth spin ensemble to a superconducting resonator using yttrium orthosilicate as a substrate

## TL;DR

This study demonstrates that yttrium orthosilicate (Y$_2$SiO$_5$) is an effective substrate for superconducting resonators, achieving high cooperativity coupling with rare-earth spins, suitable for quantum memory and microwave-optical conversion applications.

## Contribution

We show that Y$_2$SiO$_5$ can host high-Q superconducting resonators with strong coupling to rare-earth spins, offering an alternative to traditional substrates like sapphire.

## Key findings

- Resonator on Y$_2$SiO$_5$ exhibits a quality factor of approximately 400,000.
- Coupling strength with Nd$^{145}$ spins reaches high cooperativity ($C=30$).
- Dielectric loss tangent comparable to sapphire, indicating low loss.

## Abstract

Yttrium orthosilicate (Y$_2$SiO$_5$, or YSO) has proved to be a convenient host for rare-earth ions used in demonstrations of microwave quantum memories and optical memories with microwave interfaces, and shows promise for coherent microwave--optical conversion owing to its favourable optical and spin properties. The strong coupling required by such microwave applications could be achieved using superconducting resonators patterned directly on Y$_2$SiO$_5$, and hence we investigate here the use of Y$_2$SiO$_5$ as an alternative to sapphire or silicon substrates for superconducting hybrid device fabrication. A NbN resonator with frequency 6.008 GHz and low power quality factor $Q \approx 400000$ was fabricated on a Y$_2$SiO$_5$ substrate doped with isotopically enriched Nd$^{145}$. Measurements of dielectric loss yield a loss-tangent $\tan\delta = 4 \times 10^{-6}$, comparable to sapphire. Electron spin resonance (ESR) measurements performed using the resonator show the characteristic angular dependence expected from the anisotropic Nd$^{145}$ spin, and the coupling strength between resonator and electron spins is in the high cooperativity regime ($C = 30$). These results demonstrate Y$_2$SiO$_5$ as an excellent substrate for low-loss, high-Q microwave resonators, especially in applications for coupling to optically-accessible rare earth spins.