Evaluation of a stoichiometric rare earth crystal for quantum computing

Abstract

This thesis presents a spectroscopic study of the 7F0 ---t5D0 transition of Eu3+ in EuC13 ·6H2 0, which is used to evaluate the potential performance of a quantum com­ puting system implemented in EuCla·6H2 0 and, more generally, in stoichiometric rare earth crystals. EuC13 ·6H2 0 has one of the narrowest optical inhomogeneous linewidths of any solid but this linewidth is shown to be still much larger than that required for practical quantum computing in a rare earth crystal. To assess the possibility of reducing the linwidth, the contributions of isotopic impurities to both the optical linewidth and line structure were investigated, and ligand isotopes were identified as a major source of both inhomogeneous broadening and structure on the optical transition, suggesting that the linewidth could be substantially reduced by isotopi­ cally purifying EuC13 ·6H20. The effect of ligand isotopes on the optical lifetime and coherence time was also investigated. It was found that fully deuterating the crystal to EuC13·6D20 substantially improves both the lifetime and coherence time. The satellite lines formed in the optical spectrum of a rare earth crystal when it is doped with another rare earth are proposed as qubits. A crucial step in char­ acterising EuCla ·6H20 for quantum computing is associating these satellite lines in EuC13 ·6H2 0 with crystallographic sites. A new method for associating sites with lines, which works for low symmetry crystals such as EuC13·6H20, is presented. This method involves modelling the splitting of the ground state hyperfine levels caused by the magnetic dipole-dipole interaction between a Kramers dopant and the Eu3+ ion. Using this method, most of the outer satellite lines in rare earth doped EuCla·6H2 0 were assigned to crystallographic sites. It has been proposed that the electronic interactions between these satellite lines be used to enact two-qubit gates in a rare earth quantum computer. These interac­ tions were measured between a number of different satellite lines using a new two­ laser spectral holeburning technique. Interactions of up to 46.081±0.005 MHz were observed, and this was the first time that electronic interactions between weakly coupled rare earth ions had been measured. The two most common interactions identified between rare earth ions in solids are electric dipole-dipole and exchange, but the observed interactions are stronger than expected from a electric dipole-dipole model and occur at too large a distance to be superexchange. It is shown that the development of a moderate-sized quantum processor, one with more than 10 qubits, in a stoichiometric rare earth crystal is feasible provided that the optical inhomogeneous linewidth is reduced below 1MHz. Demonstrations of three or four qubit devices should be possible using existing materials.