Title: Electron Paramagnetic Resonance Spectroscopy of Er$^{3+}$:Y$_2$SiO$_5$ Using Josephson Bifurcation Amplifier: Observation of Hyperfine and Quadrupole Structures,
Abstract: 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.