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arXiv:quant-ph/0606048 · Physical Review B

Branching ratio measurement of a Λ system in Tm3+:YAG under a magnetic field

Anne Louchet-Chauvet, J. Habib, Vincent Crozatier, I. Lorgeré, Fabienne Goldfarb, Fabien Bretenaker, J.-L. Le Gouët, O. Guillot-Noël, Philippe Goldner

Published Jan 31, 2007• 50 citations
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Abstract

A three-level $\ensuremath{\Lambda}$ system in ${\mathrm{Tm}}^{3+}$ 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, 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.

DOI
10.1103/physrevb.75.035131

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

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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 ${\mathrm{Tm}}^{3+}$ 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.

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Experimental Tailoring of a Three-Level Lambda System in Tm3+:YAG

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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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Analysis of magnetic interactions in rare-earth-doped crystals for quantum manipulation

O. Guillot-Noël, Philippe Goldner, E. Antic-Fidancev +1 more

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 $\ensuremath{\mid}{M}_{I}⟩=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}\ensuremath{\rightarrow}\ensuremath{\mid}{M}_{I}⟩=\ensuremath{\mp}\frac{1}{2}$ (${M}_{I}$ 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 ${\mathrm{Tm}}^{3+}$ ion in the ${\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ host (YAG) is discussed. ${\mathrm{Tm}}^{3+}$ 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.

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Magnetic interactions in Pr3+ : LiYF4for quantum manipulation : search for an efficient three-level Λ system

Philippe Goldner, O. Guillot-Noël

The influence of an external magnetic field on the hyperfine structure of the 3 H4(0) and 1D2(0) crystal field states of Pr3+ in LiYF4 is studied in order to find an efficient three-level Λ system. Using an experimentally determined spin Hamiltonian, we show that three-level Λ systems can be obtained with equal strengths for the optically excited transitions under various magnetic field magnitudes and orientations. An analytical analysis based on two levels is proposed to find useful magnetic fields without extensive numerical calculations and to understand the general behaviour of the system. Pr3+ hyperfine structure has also been directly calculated using a complete Hamiltonian including free ion, crystal field and magnetic interactions. A good agreement with the spin Hamiltonian approach is found for the ground state whereas the excited state results poorly reproduce the experiment. This is attributed to the low accuracy of 1D2 crystal field wavefunctions. This suggests that transition strengths ratios could be calculated directly from the crystal field Hamiltonian with improved crystal field parameters.

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Thulium ions in a yttrium aluminum garnet host for quantum computing applications : material analysis and single qubit operations

Ijaz Zafarullah

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.

•Jan 1, 2008•3 citations
A three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ 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 \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ systems. Here we report on the direct measurement of the transition probability ratio along the two legs of the \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ. Measurement techniques combine frequency selective optical pumping with optical nutation or photon echo processes.
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 $\ensuremath{\Lambda}$ 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 $\ensuremath{\Lambda}$. The resulting three-level $\ensuremath{\Lambda}$ 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.
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.
The $^{2}F_{7/2}\ensuremath{\leftrightarrow}^{2}F_{5/2}$ optical transitions of Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+ doped into Y3Al5O12{\mathrm{Y}}_{3}\mathrm{A}{\mathrm{l}}_{5}{\mathrm{O}}_{12}Y3​Al5​O12​ (YAG) were studied for potential quantum information and photonic signal processing applications. Absorption and fluorescence spectroscopy located the energy levels of the ground 2F7/2^{2}F_{7/2}2F7/2​ and excited 2F5/2^{2}F_{5/2}2F5/2​ manifolds, allowing inconsistencies between previous assignments of crystal field splittings in the literature to be resolved. These measurements reveal an unusually large splitting between the first and second levels in both the ground and excited multiplets, potentially providing for reduced sensitivity to thermally induced decoherence and spin-lattice relaxation. Spectral hole burning through two-level saturation was observed, determining the excited state lifetime to be 860 \ensuremath{\mu}s and resolving ambiguities in previous fluorescence measurements that were caused by the large radiation trapping effects in this material. Optical decoherence measurements using two-pulse photon echoes gave a homogeneous linewidth of 18 kHz for an applied magnetic field of 1 T, narrowing to 5 kHz at 2.5 T. The observed decoherence was described by spectral diffusion attributed to $\mathrm{Y}{\mathrm{b}}^{3+}\mathrm{\ensuremath{-}}\mathrm{Y}{\mathrm{b}}^{3+}$ magnetic dipole interactions. Laser absorption determined an inhomogeneous linewidth of 3.6 GHz for this transition in this 0.05%-doped crystal, which is narrower than for any other rare-earth-ion transition previously studied in the YAG host. The temperature dependence of the transition energy and linewidth of the lowest 2F7/2^{2}F_{7/2}2F7/2​ to lowest 2F5/2^{2}F_{5/2}2F5/2​ transition centered at 968.571 nm measured from 4 K to 300 K was well described by phonon scattering at higher temperatures, with an additional anomalous linear temperature-dependent broadening at temperatures below 80 K. Two magnetically inequivalent subgroups of Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+ ions were identified when a magnetic field was applied along the $\ensuremath{\langle}111\ensuremath{\rangle}$ axis, as expected for the D2{D}_{2}D2​ sites in the cubic symmetry crystal, with ground and excited state effective ggg-values of gg=3.40{g}_{\mathrm{g}}=3.40gg​=3.40 (3.34) and ge=1.04{g}_{\mathrm{e}}=1.04ge​=1.04 (2.01), respectively. Together with the convenient diode laser wavelength of this transition, our study suggests that Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+:YAG is a promising material system for spectral hole burning and quantum information applications.
The influence of an external magnetic field on the hyperfine structure of the 3 H4(0) and 1D2(0) crystal field states of Pr3+ in LiYF4 is studied in order to find an efficient three-level Λ system. Using an experimentally determined spin Hamiltonian, we show that three-level Λ systems can be obtained with equal strengths for the optically excited transitions under various magnetic field magnitudes and orientations. An analytical analysis based on two levels is proposed to find useful magnetic fields without extensive numerical calculations and to understand the general behaviour of the system. Pr3+ hyperfine structure has also been directly calculated using a complete Hamiltonian including free ion, crystal field and magnetic interactions. A good agreement with the spin Hamiltonian approach is found for the ground state whereas the excited state results poorly reproduce the experiment. This is attributed to the low accuracy of 1D2 crystal field wavefunctions. This suggests that transition strengths ratios could be calculated directly from the crystal field Hamiltonian with improved crystal field parameters.
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.