Phonon-bottlenecked spin relaxation of Er$^{3+}$:CaWO$_4$ at milliKelvin temperatures

TL;DR

This study investigates the spin-lattice relaxation times of Er$^{3+}$ ions in CaWO$_4$ at millikelvin temperatures, revealing phonon-bottleneck effects relevant for quantum technology applications.

Contribution

It provides experimental evidence of phonon-bottlenecked spin relaxation in Er$^{3+}$:CaWO$_4$ at ultra-low temperatures, highlighting its impact on quantum coherence.

Findings

Relaxation times increase with spin-excitations at high magnetic fields.

Observed a unique $[ anh (rac{ ext{hbar} imes ext{omega}_0}{k_B T})]^2$ temperature dependence.

Results suggest phonon-bottleneck effects dominate spin relaxation at millikelvin temperatures.

Abstract

We study spin-lattice relaxation times of electron spins in Er$^{3+}$:CaWO$_4$ at millikelvin temperature, detected via their coupling to a low-mode volume superconducting resonator. At large magnetic field supporting strong phonon-emission rates, we observe a noticeable increase in relaxation times with increasing spin-excitations, which exhibit a unique $[\tanh (\hbar \omega_0/k_\text{B} T)]^2$ temperature dependence. These observations are typical of a phonon-bottlenecked spin relaxation, and have implications for quantum technologies that exploit rare-earth spin ensembles as coherent resources.