Impact of the ion-ion energy transfer on quantum computing schemes in rare-earth doped solids

We analyze the Ce3+-Pr3+:Y2SiO5 emission spectra obtained under selective excitation of the two Ce3+ sites in Y2SiO5 and we show clear evidence of direct energy transfer from Ce3+ to Pr3+. Energy transfer microparameters were calculated from the experimental spectral overlap between the Ce3+ emission and the Pr3+ and Eu3+ absorptions from which, the transfer mechanisms Ce3+→Pr3+ are concluded to be more efficient than the transfer mechanisms Ce3+→Eu3+. The energy transfer processes demonstrated here are potentially detrimental for an efficient qubit readout, using Ce3+ as readout ion, as they lead to a quenching of the Ce3+ luminescence and can give rise to the unwanted change of Pr3+ and Eu3+ qubit states. The quantum computing readout scheme is based on permanent electric dipole interactions scaling as R−3, where R is the distance between the Ce3+ and the qubit ion. The non-radiative energy transfer processes also depend on the ion-ion distances, however as R−6. A discussion about the microscopic dopant distributions leading to an efficient single-ion readout quantum computing scheme is here presented. The likely existence of energy transfer paths between the qubits or, as in this case, between the readout ion and the qubit ions, has not been taken into account so far by the rare-earth based quantum computing approaches. The results of this study suggest the need to consider them in order to design realistic and efficient quantum computing schemes for rare-earth doped solids.