Robust millisecond coherence times of erbium electron spins

Abstract: Erbium-doped solids are prime candidates for optical quantum communication networks due to erbium's telecom C-band emission. A long-lived electron spin of erbium with millisecond coherence time is highly desirable for establishing entanglement between adjacent quantum repeater nodes while long-term storage of the entanglement could rely on transferring to erbium's second-long coherence nuclear spins. Here we report GHz-range electron spin transitions of $^{167}\mathrm{Er}^{3+}$ in yttrium oxide ($\mathrm{Y_2O_3}$) matrix with coherence times that are consistently longer than a millisecond. Instead of addressing field-specific Zero First-Order Zeeman transitions, we probe weakly mixed electron spins with the field orientation along the lower g-factors. Using pulsed electron spin resonance spectroscopy, we find paramagnetic impurities are the dominant source of decoherence, and by polarizing them we achieve a Hahn echo spin $\mathrm{T_2}$ up to 1.46 ms, and a coherence time up to 7.1 ms after dynamical decoupling. These coherence lifetimes are among the longest found in crystalline hosts especially those with nuclear spins. We further enhance the coherence time beyond conventional dynamical decoupling, using customized sequences to simultaneously mitigate spectral diffusion and Er-Er dipolar interactions. Despite nuclear and impurity spins in the host, this work shows that long-lived erbium spins comparable to non-nuclear spin hosts can be achieved. Our study not only establishes $^{167}\mathrm{Er}^{3+}$: $\mathrm{Y_2 O_3}$ as a significantly promising quantum memory platform but also provides a general guideline for engineering long-lived erbium spins in a variety of host materials for quantum technologies.