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

The possibility of obtaining three-level Λ systems from the hyperfine levels of Tm3+ and Pr3+ ions in crystals is discussed. To be efficient, these Λ 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 Pr3+ doped compounds with low symmetry. In this case, the ratios E/D between the spin Hamiltonian parameters have to be different enough in the ground and excited states. With an external magnetic field, both Tm3+ and Pr3+ compounds can be used as efficient Λ systems. The more complex hyperfine structure of Pr3+ ions allows one to find external magnetic field which give equal strengths for the optical transition. In Tm3+ doped compounds, it is generally only possible to have optical transition strengths of the same order of magnitude. However, Tm3+ ions can be excited by ultra-stable laser diodes whereas Pr3+ ions require dye lasers.