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Molecular Physics

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

Philippe Goldner, O. Guillot-Noël

Published Jun 10, 2004• 26 citations
Publisher

Abstract

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.

DOI
10.1080/00268970410001728744

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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.
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.
Near-UV excited-state absorption spectra obtained with a pulsed pump–probe technique were recorded in LiYF4:Pr3+ at 77 and at 8 K and revealed a detailed structure of the 4f2 1D2→4f5d and 4f2 (3P0+1I6)→4f5d optical transitions. These experimental results, together with those previously obtained at room temperature, are compared with the numerical predictions of a full calculation of the 4f5d sublevels and of the electric dipole transitions toward these sublevels from different states of the 4f2 configuration. The agreement is good, provided that the four adjustable parameters of the theory are taken as B20(5d)=7290 cm-1,B40(5d)=-14 900 cm-1,F0=60 557 cm-1, and 〈r〉fd=0.245 Å. The level structure of the 4f5d configuration of LiYF4:Pr3+ is shown to be dominated, as expected, by the crystal field coupling of the 5d electron but also, to a noticeable extent, by the spin–orbit coupling of the 4f electron and the Coulomb repulsion of both electrons. The former of these two interactions is somewhat more efficient than the latter in the low-energy part of the 4f5d configuration, i.e., in the spectral region where the largest amount of experimental data is currently available.
Rare-earth ions in dielectric crystals are interesting candidates for storing quantum states of photons. A limiting factor on the optical density and thus the conversion efficiency is the distortion introduced in the crystal by doping elements of one type into a crystal matrix of another type. Here we investigate the system Pr3+{}^{3+}3+:La2{}_{2}2​(WO4{}_{4}4​)3{}_{3}3​, where the similarity of the ionic radii of Pr and La minimizes distortions due to doping. We characterize the praseodymium hyperfine interaction of the ground-state (3{}^{3}3HHH4{}_{4}4​) and one excited state (1{}^{1}1DDD2{}_{2}2​) and determine the spin Hamiltonian parameters by numerical analysis of Raman-heterodyne spectra, which were collected for a range of static external magnetic-field strengths and orientations. On the basis of a crystal-field analysis, we discuss the physical origin of the experimentally determined quadrupole and Zeeman tensor characteristics. We show the potential for quantum memory applications by measuring the spin coherence lifetime in a magnetic field that is chosen such that additional magnetic fields do not shift the transition frequency in first order. Experimental results demonstrate a spin coherence lifetime of 158 ms --- almost 3 orders of magnitude longer than in zero field.
As part of a search for suitable materials for coherent quantum operations, relaxation times and hyperfine structure of the $^{1}D_{2}(1)\text{\ensuremath{-}}^{3}H_{4}(1)$ transition in Pr3+:KY(WO4)2{\mathrm{Pr}}^{3+}:\mathrm{KY}{({\mathrm{WO}}_{4})}_{2}Pr3+:KY(WO4​)2​ (0.29 at. %) at 4 K have been obtained using photon-echo and spectral hole burning techniques. The homogeneous linewidth and the effect of excitation-induced dephasing were measured using two-pulse photon-echo techniques. Linewidths of $23.4\ifmmode\pm\else\textpm\fi{}1.0$ and $17.6\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ were obtained in the absence and presence of an external magnetic field of about 9 mT. The radiative lifetime (T1)({T}_{1})(T1​) of the 1D2^{1}D_{2}1D2​ state was measured to be $43\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ using time-resolved laser-induced fluorescence and three-pulse photon-echo measurements. The transmission hole spectra were measured and directly yielded the quadrupole level splitting in the 1D2^{1}D_{2}1D2​ ($3.77\ifmmode\pm\else\textpm\fi{}0.03$ and $4.58\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) and 3H4^{3}H_{4}3H4​ ($17.1\ifmmode\pm\else\textpm\fi{}0.1$ and $33.2\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) states. The spectral hole lifetime due to population redistribution between the ground-state nuclear levels was also determined to be $70\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$. A strong dipole-dipole interaction observed in this crystal opens for potential applications in quantum computing schemes for performing quantum logic operations, but the short dephasing time makes it less useful in data storage applications.
Rare-earth ions in dielectric crystals play an important role in high-resolution laser spectroscopy and are interesting candidates for storing quantum states of photons. We characterize the praseodymium hyperfine interaction of the ground-state (3{}^{3}3H4{}_{4}4​) and one excited-state (1{}^{1}1D2{}_{2}2​) for two important compounds: praseodymium doped in yttrium aluminum perovskite and praseodymium doped in yttrium orthosilicate. The spin Hamiltonian parameters are determined by numerical analysis of Raman-heterodyne spectra, which were collected for a range of static external magnetic field strengths and orientations. For Pr3+{}^{3+}3+:YAlO3{}_{3}3​, we present a full analysis without restrictions for the Zeeman and quadrupole tensors, and our new characterization for Pr3+{}^{3+}3+:Y2{}_{2}2​SiO5{}_{5}5​ resolves a controversy in the literature.