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arXiv:quant-ph/0509099 · Physical Review B

Experimental tailoring of a three-level Λ system in Tm3+:YAG

F. de Sèze, Anne Louchet-Chauvet, Vincent Crozatier, I. Lorgeré, Fabien Bretenaker, J.-L. Le Gouët, O. Guillot-Noël, Philippe Goldner

Published Feb 16, 2006• 59 citations
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Abstract

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 ${\mathrm{Tm}}^{3+}$ ions capability to behave as three-level $\ensuremath{\Lambda}$ systems, a key ingredient to convert optical excitation into a spontaneous-emission-free spin wave. Indeed ${\mathrm{Tm}}^{3+}$ 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 ${\mathrm{Tm}}^{3+}:\mathrm{YAG}$. 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 $\ensuremath{\Lambda}$. The resulting three-level $\ensuremath{\Lambda}$ system should suit quantum information processing requirements.

DOI
10.1103/physrevb.73.085112

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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 Tm3+ ions capability to behave as three-level lambda systems, a key ingredient to convert optical excitation into a spontaneous- emission-free spin wave. Indeed Tm3+ 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 Tm3+: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 lambda. The resulting three-level lambda system should suit quantum information processing requirements.

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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 Tm3+{\mathrm{Tm}}^{3+}Tm3+ ions capability to behave as three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ systems, a key ingredient to convert optical excitation into a spontaneous-emission-free spin wave. Indeed Tm3+{\mathrm{Tm}}^{3+}Tm3+ 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 Tm3+:YAG{\mathrm{Tm}}^{3+}:\mathrm{YAG}Tm3+: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 \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ. The resulting three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system should suit quantum information processing requirements.
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 Tm3+ ions capability to behave as three-level lambda systems, a key ingredient to convert optical excitation into a spontaneous- emission-free spin wave. Indeed Tm3+ 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 Tm3+: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 lambda. The resulting three-level lambda system should suit quantum information processing requirements.
A three-level $\ensuremath{\Lambda}$ system in Tm3+{\mathrm{Tm}}^{3+}Tm3+ 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, 085112 (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 $\ensuremath{\Lambda}$ systems. Here we report on the direct measurement of the transition probability ratio along the two legs of the $\ensuremath{\Lambda}$. Measurement techniques combine frequency selective optical pumping with optical nutation or photon echo processes.
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 $\ensuremath{\Lambda}$ 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 $\ensuremath{\Lambda}$ system because nuclear-spin flipping such as $\ensuremath{\mid}{M}_{I}⟩=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}\ensuremath{\rightarrow}\ensuremath{\mid}{M}_{I}⟩=\ensuremath{\mp}\frac{1}{2}$ (MI{M}_{I}MI​ is the nuclear-spin projection) 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 $\ensuremath{\Delta}{M}_{I}=0$. 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 Tm3+{\mathrm{Tm}}^{3+}Tm3+ ion in the Y3Al5O12{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}Y3​Al5​O12​ host (YAG) is discussed. Tm3+{\mathrm{Tm}}^{3+}Tm3+ hyperfine structure is determined using a complete Hamiltonian including free-ion, crystal-field, and magnetic interactions. A good three-level $\ensuremath{\Lambda}$ system is obtained in Tm:YAG with a transition strength ratio of 0.24 $(\ensuremath{\sim}1:4)$ 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.
Rare-earth-doped crystals have been used for optical signal processing and storage applications. In this dissertation, their potential for quantum computing applications is explored. In one quantum computing scheme, information is stored in nuclear spin states and this information is then processed by using optical pulses through the coupling of these nuclear spin states to a common electronic level. To implement this scheme, nuclear spin states and coupling of these nuclear spin states to a common electronic level is required. Preliminary work in rare-earth materials like Pr3+ and Eu3+ has shown promising results regarding their suitability for quantum computing applications. One particular problem with these materials is that their transition wavelengths are only accessible with dye lasers. These lasers are inherently unstable, and currently few available systems exhibit the stability required for quantum computing applications. An alternative choice was to investigate other rare-earth ions like thulium. Thulium has a transition wavelength that can be accessed with diode lasers, which are commercially available, easy to stabilize, and compact. This dissertation is based on our investigations of Tm3+:YAG for quantum computing applications. Investigations involved a detailed characterization of the material. Nuclear spin states, in Tm3+:YAG, were obtained by applying an external magnetic field to the sample. First, interaction of an external magnetic field with the thulium ions at various sites in the crystal was analyzed. This analysis was used to measure the magnetic anisotropy in the material. These results show that it is possible, with the suitable choice of the magnetic orientation and the site in the crystal, to build a working 3-level quantum system. In the demonstration of single qubit operations in Tm3+:YAG, we first theoretically studied the effect of Gaussian spatial beam on the single qubit operations. Later on, we experimentally prepared a single isolated ensemble of ions in the inhomogeneously broadened absorption profile of the medium. This single isolated ensemble of ions was used as a test-bed to implement the single qubit operations. We also isolated two ensembles of ions in the inhomogeneous absorption profile of the medium. The interaction between these two isolated ensembles of ions was also studied.
Rare-earth ion-doped crystals are promising systems for quantum communication and quantum information processing. In particular, paramagnetic rare-earth centers can be utilized to realize quantum coherent interfaces simultaneously for optical and microwave photons. In this paper, we study hyperfine and magnetic properties of a Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ crystal doped with 171Yb3+^{171}\mathrm{Yb}^{3+}171Yb3+ ions. This isotope is particularly interesting since it is the only rare--earth ion having electronic spin S=12S=\frac{1}{2}S=21​ and nuclear spin I=12I=\frac{1}{2}I=21​, which results in the simplest possible hyperfine level structure. In this work, we determine the hyperfine tensors for the ground and excited states on the optical $^{2}\mathrm{F}_{7/2}(0)\ensuremath{\longleftrightarrow}^{2}\mathrm{F}_{5/2}(0)$ transition by combining spectral hole burning and optically detected magnetic resonance techniques. The resulting spin Hamiltonians correctly predict the magnetic-field dependence of all observed optical-hyperfine transitions, from zero applied field up to fields where the Zeeman interaction is dominating the hyperfine interaction. Using the optical absorption spectrum, we can also determine the order of the hyperfine levels in both states. These results pave the way for realizing solid-state optical and microwave quantum memories based on a 171Yb3+:Y2SiO5^{171}\mathrm{Yb}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}171Yb3+:Y2​SiO5​ crystal.
Rare-earth-ion-doped solids are promising materials as light-matter interfaces for quantum applications. Europium doped into an yttrium orthosilicate crystal in particular has interesting coherence properties and a suitable ground-state energy-level structure for a quantum memory for light. In this paper we report on spectroscopic investigations of this material from the perspective of implementing an atomic frequency comb (AFC)-type quantum memory with spin-wave storage. For this goal we determine the order of the hyperfine levels in the 7F0{}^{7}\phantom{\rule{-0.16em}{0ex}}{F}_{0}7F0​ ground state and 5D0{}^{5}\phantom{\rule{-0.16em}{0ex}}{D}_{0}5D0​ excited state, and we measure the relative strengths of the optical transitions between these levels. We also apply spectral hole burning techniques in order to prepare the system as a well-defined $\ensuremath{\Lambda}$ system, as required for further quantum memory experiments. Furthermore, we measure the optical Rabi frequency on one of the strongest hyperfine transitions, a crucial experimental parameter for the AFC protocol. From this we also obtain a value for the transition dipole moment which is consistent with that obtained from absorption measurements.