Magnetic interactions in Pr3+ and Tm3+ doped crystals for quantum manipulation

The possibility of obtaining three-level A systems from the hyperfine levels of Tm 3 + and Pr 3 + ions in crystals is discussed. To be efficient, these A systems require that the two optical transitions involved have equal transition strengths. This is not possible without a different mixing of the pure nuclear spin states in the ground and excited states. From a two-level analysis of the spin Hamiltonian, we show that this condition can be reached without an external magnetic field in Pr 3 + doped compounds with low symmetry. In this case, the ratios EID between the spin Hamiltonian parameters have to be different enough in the ground and excited states. With an external magnetic field, both Tm 3 + and Pr 3 + compounds can be used as efficient A systems. The more complex hyperfine structure of Pr 3 + ions allows one to find external magnetic field which give equal strengths for the optical transition. In Tm 3 + doped compounds, it is generally only possible to have optical transition strengths of the same order of magnitude. However. Tm 3 + ions can be excited by ultra-stable laser diodes whereas Pr 3 + ions require dye lasers.