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Physical review. B./Physical review. B

Engineering closed optical transitions in rare-earth ion crystals

John G. Bartholomew, Rose L. Ahlefeldt, Matthew J. Sellars

Published Jan 4, 2016• 15 citations
Publisher

Abstract

Previously, closed optical transitions were only possible in crystals where the rare-earth ion site had perfect axial symmetry. The possibility of creating closed hyperfine transitions for all site symmetries by applying an appropriate oriented magnetic field is explored. The new technique should allow studies that are currently impossible for rare-earth-ion crystals both in the single ion and ensemble regimes.

DOI
10.1103/physrevb.93.014401

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•Jan 1, 2005•5 citations
Previously, closed optical transitions were only possible in crystals where the rare-earth ion site had perfect axial symmetry. The possibility of creating closed hyperfine transitions for all site symmetries by applying an appropriate oriented magnetic field is explored. The new technique should allow studies that are currently impossible for rare-earth-ion crystals both in the single ion and ensemble regimes.
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.
We show that crystal-field calculations for C_{1} point-group symmetry are possible, and that such calculations can be performed with sufficient accuracy to have substantial utility for rare-earth based quantum information applications. In particular, we perform crystal-field fitting for a C_{1}-symmetry site in ^{167}Er^{3+}:Y_{2}SiO_{5}. The calculation simultaneously includes site-selective spectroscopic data up to 20 000 cm^{-1}, rotational Zeeman data, and ground- and excited-state hyperfine structure determined from high-resolution Raman-heterodyne spectroscopy on the 1.5 μm telecom transition. We achieve an agreement of better than 50 MHz for assigned hyperfine transitions. The success of this analysis opens the possibility of systematically evaluating the coherence properties, as well as transition energies and intensities, of any rare-earth ion doped into Y_{2}SiO_{5}.
Elucidating magnetic structure with optical dopants: erbium-doped Gd2_22​SiO5_55​
The narrowness of the optical transitions of rare-earth-ion dopants makes them highly sensitive probes of their environment. We measured the optical transitions Er3+^{3+}3+ dopants to determine the previously unknown magnetic ordering of Gd2_{2}2​SiO5_{5}5​ -- a promising host for quantum applications of rare-earth dopants. By measuring the transitions' magnetic-field dependence we determined an antiferromagnetic ordering with spins oriented along or slightly canted from the crystal's a∗a^*a∗ axis. The optical transitions are narrower than the coupling to gadolinium spins revealing information about the coupling strengths. We further optically measured a Néel temperature of 1.86±0.01stat.±0.07syst.1.86\pm0.01_\mathrm{stat.}\pm0.07_\mathrm{syst.}1.86±0.01stat.​±0.07syst.​ K, and assembled a phase diagram in applied field and temperature showcasing a triple point where two gadolinium sites order semi-independently from each other. At high applied field the erbium dopants show long optical coherence times up to 0.4 ms at 3 T; at low fields these are probably limited by three low-frequency magnon modes below 10 GHz, observed directly. This study can be used to benchmark a method of magnetic structure determination.
This work has demonstrated that hyperfine decoherence times sufficiently long for QIP and quantum optics applications are achievable in rare earth ion centres. Prior to this work there were several QIP proposals using rare earth hyperfine states for long term coherent storage of optical interactions. The very long T_1 (~weeks ) observed for rare-earth hyperfine transitions appears promising but hyperfine T_2s were only a few ms, comparable to rare earth optical transitions and therefore the usefulness of such proposals was doubtful. ¶ This work demonstrated an increase in hyperfine T_2 by a factor of 7 × 10^4 compared to the previously reported hyperfine T_2 for Pr^[3+]:Y_2SiO_5 through the application of static and dynamic magnetic field techniques. This increase in T_2 makes previous QIP proposals useful and provides the first solid state optically active Lamda system with very long hyperfine T_2 for quantum optics applications. ¶ ...