Electron Paramagnetic Resonance Spectroscopy of Er³⁺:Y₂SiO₅ Using Josephson Bifurcation Amplifier: Observation of Hyperfine and Quadrupole Structures

We performed magnetic field and frequency tunable electron paramagnetic resonance spectroscopy of an Er$^{3+}$ doped Y$_2$SiO$_5$ crystal by observing the change in flux induced on a direct current-superconducting quantum interference device (dc-SQUID) loop of a tunable Josephson bifurcation amplifer. The observed spectra show multiple transitions which agree well with the simulated energy levels, taking into account the hyperfine and quadrupole interactions of $^{167}$Er. The sensing volume is about 0.15 pl, and our inferred measurement sensitivity (limited by external flux noise) is approximately $1.5\times10^4$ electron spins for a 1 s measurement. The sensitivity value is two orders of magnitude better than similar schemes using dc-SQUID switching readout.