Electron Paramagnetic Resonance Spectroscopy of Er${}^{3+}$:Y${}_2$SiO${}_5$ 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 $1.5\times {10}^4$ electron spins for a 1 s measurement. The sensitivity value is two orders of magnitude better than similar schemes using dc-SQUID switching readout.