High-precision broadband ESR spectroscopy of rare-earth ions in CaWO₄

Hybrid systems are a key building block of scalable quantum technologies as they combine platforms with additive strengths. Among spin systems, diluted solid-state ensembles of rare-earth ions are best suited for memory and transduction applications. The Hahn-echo coherence times of their spin states exceed milliseconds at low temperatures allowing to reach hours of coherent storage when applying dynamic decoupling techniques. We employ the broadband electron spin resonance (ESR) spectroscopy to probe spin transitions of Er³⁺:CaWO₄ with superconducting coplanar waveguides below 10 mK, enabling a detailed characterization of the Er energy level structure in the vicinity of zero magnetic fields. Due to the hyperfine coupling accompanied by the quadrupolar interaction arising from the nuclear spin 7/2 of the ¹⁶⁷Er isotope, these systems exhibit a rich microwave spectrum in the frequency range between 0-4 GHz, which we are able to locate at high precision with our technique. This in turn, allows us to identify the Zero First Order Zeeman shift (ZEFOZ) transitions, which allow for the longest coherence times due to their first-order insensitivity to fluctuations of external magnetic fields. Our approach in broadband microwave spectroscopy enables the reconstruction of the full Hamiltonian and is a crucial step toward achieving coherent control of the spin excitations in these systems.