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Quantum information transfer from light to atom ensembles and vice versa has both basic and practical importance. Among the relevant topics let us mention entanglement and decoherence of macroscopic systems, together with applications to quantum memory for long distance quantum cryptography. Although the first experimental demonstrations have been performed in atomic vapors and clouds, rare earth ion doped crystals are also interesting media for such processes. In this paper we address Tm 3+ ions capability to behave as threelevel Λ systems, a key ingredient to convert optical excitation into a spontaneous-emissionfree spin wave. Indeed Tm 3+ falls within reach of light sources that can be stabilized easily to the required degree. In the absence of zero-field hyperfine structure we apply an external magnetic field to lift the nuclear spin degeneracy in Tm 3+ :YAG. We experimentally determine the gyromagnetic tensor components with the help of spectral hole-burning techniques. Then appropriate orientation of the applied field enables us to optimize the transition probability ratio along the two legs of the Λ . The resulting three-level Λ system should suit quantum information processing requirements.

The influence of magnetic interactions in rare-earth-doped crystals under an external magnetic field has been studied in order to obtain an efficient three-level ⌳ system with the hyperfine levels of the rare earth. Nuclear Zeeman effect under the action of an external magnetic field removes the nuclear degeneracy. This interaction does not provide an efficient ⌳ system because nuclear-spin flipping such as ͉M I ͘ = ± 1 2 → ͉M I ͘ = ϯ 1 2 ͑M I is the nuclear-spin projection͒ cannot be induced by an optical transition. However, this selection rule only applies to pure nuclear Zeeman effect. Indeed, it is shown that the coupling of the electronic Zeeman and of the hyperfine interactions releases the nuclear-spin selection rules ⌬M I = 0. This can be described in terms of a pseudonuclear Zeeman effect induced by an effective magnetic field. The relative strengths of the two optical transitions involved in the three-level system can be controlled by the orientation of the external magnetic field. The particular case of the Tm 3+ ion in the Y 3 Al 5 O 12 host ͑YAG͒ is discussed. Tm 3+ hyperfine structure is determined using a complete Hamiltonian including free-ion, crystal-field, and magnetic interactions. A good threelevel ⌳ system is obtained in Tm:YAG with a transition strength ratio of 0.24 ͑ϳ1:4͒ between the two optical transitions. An analytical analysis based on a spin-Hamiltonian approach is proposed to explain the results of the complete crystal-field calculations. Finally, an experimental protocol that makes a crystal similar to the atomic samples used in previous quantum information investigations, with the additional benefits of absence of motion and long coherence time, is described.where ij is the electric dipole moment matrix element between states ͉i͘ and ͉j͘ and k is the field amplitude of laser k.

A three-level Λ system in Tm 3+ doped YAG crystal is experimentally investigated in the prospect of quantum information processing. Zeeman effect is used to lift the nuclear spin degeneracy of this ion. In a previous paper [de Seze et al. Phys. Rev. B, 73, 85112 (2006)] we measured the gyromagnetic tensor components and concluded that adequate magnetic field orientation could optimize the optical connection of both ground state sublevels to each one of the excited state sublevels, thus generating Λ systems. Here we report on the direct measurement of the transition probability ratio along the two legs of the Lambda. Measurement techniques combine frequency selective optical pumping with optical nutation or photon echo processes.

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We demonstrate that Zeeman ground-state spin levels in Nd3+:YVO4Nd3+:YVO4 provides the possibility to create an efficient ΛΛ- system for optical pumping experiments. The branching ratio R in the ΛΛ-system is measured experimentally via absorption spectroscopy and is compared to a theoretical model. We show that R can be tuned by changing the orientation of the magnetic field. These results are applied to optical pumping experiments, where significant improvement is obtained compared to previous experiments in this system. The tunability of the branching ratio in combination with its good coherence properties and the high oscillator strength makes Nd3+:YVO4Nd3+:YVO4 an interesting candidate for various quantum information protocols