Optical clock transition in a rare-earth-ion-doped crystal: coherence lifetime extension for quantum storage applications

Atomic clock transitions are desirable for quantum information storage and processing thanks to the protection from decoherence they provide. In the context of rare- earth-ion-doped crystals for quantum information storage, clock Zeeman or hyperfine transitions have been identified and exploited for long-lived storage in spin degrees of freedom. We present a theoretical and experimental analysis on the existence of an optical clock transition in Tm³⁺:YAG, in view of storage in optical coherences. The combination of a Zeeman-like term and a quadratic electronic Zeeman term in the Hamiltonian, lead to the existence of a magnetic field amplitude (12 mT) for which the derivative of the optical transition energy with respect to the field amplitude vanishes, regardless of the magnetic field orientation. We have verified this prediction through hole-burning spectroscopy experiments. In addition to that, a study of the behavior of the Hamiltonian as a function of the magnetic field orientation yields the direction for which both derivatives with respect to the magnetic field angular coordinates also vanish. The condition for an optical clock transition with three vanishing partial derivatives is met. (paper)