Reducing decoherence in optical and spin transitions in rare-earth-metal-ion–doped materials

Abstract

In many important situations, the dominant dephasing mechanism in cryogenic rare-earth-metal-ion--doped systems is due to magnetic field fluctuations from spins in the host crystal. Operating at a magnetic field where a transition has a zero first-order Zeeman (ZEFOZ) shift can greatly reduce this dephasing. Here we identify the location of transitions with a zero first-order Zeeman shift for optical transitions in Pr${}^{3+}$:YAG and for spin transitions in Er${}^{3+}$:Y${}_{2}$SiO${}_{5}$. The long coherence times that ZEFOZ can enable would make Pr${}^{3+}$:YAG a strong candidate for achieving the strong-coupling regime of cavity QED, and would be an important step forward in creating long-lived telecommunications wavelength quantum memories in Er${}^{3+}$:Y${}_{2}$SiO${}_{5}$. This work relies mostly on published spin-Hamiltonian parameters, but Raman heterodyne spectroscopy was performed on Pr${}^{3+}$:YAG to measure the parameters for the excited state.