Hyperfine states of erbium doped yttrium orthosilicate for long-coherence-time quantum memories

Due to their unique optical transition at 1.5 μm, erbium-doped crystals are one of the best candidates for the realization of quantum memories at telecommunication wavelengths. While the hyperfine states of erbium doped yttrium orthosilicate hold the possibility of achieving ultra-long coherence times for a quantum memory, the complexity of their hyperfine structures leads to inaccurate theoretical prediction, thus hindering the extending of the coherence times. Here, we report a set of spin-Hamiltonian parameters with sufficient predictive power on the coherence times of the erbium hyperfine states. Our calculation simultaneously takes into account both the data measured in Electron-Paramagnetic-Resonance and Raman-heterodyne experiments. Based on the new parameters, the coherence properties of the hyperfine ground states are discussed. At zero applied magnetic field, all hyperfine transitions between the ground states are transitions with zero-first-order-Zeeman (ZEFOZ) effect, manifesting both long coherence times and strong transition strengths. By turning up the magnetic field, it is possible to further extend the coherence times to the scale of hours. The long coherence times at ZEFOZ transitions can be an important step forward in creating long-lived telecommunication quantum memories.