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arXiv:2107.08920 · Physical review. B./Physical review. B

Measurement of the thulium ion spin Hamiltonian in an yttrium gallium garnet host crystal

Jacob H. Davidson, Philip J. T. Woodburn, Aaron D. Marsh, Kyle Olson, Adam Olivera, Antariksha Das, Mohsen Falamarzi Askarani, Wolfgang Tittel, R. L. Cone, Charles W. Thiel

Published Oct 11, 2021• 8 citations
arXivHTMLPDF

Abstract

The magnetic properties of crystals doped with rare-earth ions have long been studied for their long coherence times and applications in signal processing. Here, the authors measure a complete tensor description of the hyperfine structure for a pair of optically addressable levels belonging to the Tm${}^{3+}$-ion defects within the host material. Certain orientations of interest stand out, such as some that realize optical clock transitions; they are shown to have an invariant response to fluctuations in the local magnetic environment.

DOI
10.1103/physrevb.104.134103

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Abstract Rare-earth ion-doped crystals are of great interest for quantum memories, a central component in future quantum repeaters. To assess the promise of 1 % Tm3+-doped yttrium gallium garnet (Tm:YGG), we report measurements of optical coherence and energy-level lifetimes of its 3H 6 ↔ 3 H4 transition at a temperature of around 500 mK and various magnetic fields. Using spectral hole burning (SHB), we find hyperfine ground-level (Zeeman level) lifetimes of several minutes at magnetic fields of less than 1000 G. We also measure coherence time exceeding one millisecond using two-pulse photon echoes. Three-pulse photon echo and SHB measurements reveal that due to spectral diffusion, the effective coherence time reduces to a few µs over a timescale of around two hundred seconds. Finally, temporal and frequency-multiplexed storage of optical pulses using the atomic frequency comb protocol is demonstrated. Our results suggest Tm:YGG to be promising for multiplexed photonic quantum memory for quantum repeaters.

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Clock transitions play an important role in extending the coherence time of rare-earth (RE) ion-doped crystals. It is still a challenge to accurately obtain the hyperfine structure of these crystals to determine their clock transitions and establish a proper solid-state quantum memory system. In this work, a nonspin-Hamiltonian method combining density functional theory (DFT)-based geometric optimization and effective Hamiltonian is utilized to obtain the hyperfine sublevels and clock transitions under an external magnetic field for the Kramers RE ion in crystals. To show clearly, the 173 Yb 3+:Y 2 SiO 5 crystal is first investigated to demonstrate that the complicated hyperfine structure of the Kramers RE ion can be correctly calculated by the complete diagonalization (of energy) matrix (CDM) formalism. Second, optical and angular-dependent electron paramagnetic resonance (EPR) spectra of the 171 Yb 3+:Lu 2 Si 2 O 7 crystal are studied by fitting calculations based on the DFT-optimized geometric structure. By reliable fitting parameters, the external magnetic field at clock transitions is determined successfully. Such two case studies indicate that the hyperfine structure and clock transitions of the Kramers RE ion in the crystal can be accurately predicted by the present approach. This is very useful for designing and searching practical RE-based quantum memory materials with longer optical or spin coherence time.

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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.

Physical Review B•May 12, 2005•56 citations
The magnetic properties of crystals doped with rare-earth ions have long been studied for their long coherence times and applications in signal processing. Here, the authors measure a complete tensor description of the hyperfine structure for a pair of optically addressable levels belonging to the Tm3+{}^{3+}3+-ion defects within the host material. Certain orientations of interest stand out, such as some that realize optical clock transitions; they are shown to have an invariant response to fluctuations in the local magnetic environment.
Abstract Rare-earth ion-doped crystals are of great interest for quantum memories, a central component in future quantum repeaters. To assess the promise of 1 % Tm3+-doped yttrium gallium garnet (Tm:YGG), we report measurements of optical coherence and energy-level lifetimes of its 3H 6 ↔ 3 H4 transition at a temperature of around 500 mK and various magnetic fields. Using spectral hole burning (SHB), we find hyperfine ground-level (Zeeman level) lifetimes of several minutes at magnetic fields of less than 1000 G. We also measure coherence time exceeding one millisecond using two-pulse photon echoes. Three-pulse photon echo and SHB measurements reveal that due to spectral diffusion, the effective coherence time reduces to a few µs over a timescale of around two hundred seconds. Finally, temporal and frequency-multiplexed storage of optical pulses using the atomic frequency comb protocol is demonstrated. Our results suggest Tm:YGG to be promising for multiplexed photonic quantum memory for quantum repeaters.
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.
We report measurements of the reflection and transmission spectra of 2% doped Thulium Yttrium Gallium Garnet (Tm:YGG) using variable-angle spectroscopic ellipsometry(VASE) over a wavelength range from 210 to 1680 nm (0.73-5.9 eV). The well-known Tm resonances are identified and separated from the aggregate data, allowing us to calculate the previously unknown frequency dependence of the complex refractive index of the host material. This information is important for many applications of YGG in classical and quantum photonics, including constructing optical cavities, laser-based applications, and quantum information devices. A complete database of the obtained parameters is included in the supplementary information.
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.
Clock transitions play an important role in extending the coherence time of rare-earth (RE) ion-doped crystals. It is still a challenge to accurately obtain the hyperfine structure of these crystals to determine their clock transitions and establish a proper solid-state quantum memory system. In this work, a nonspin-Hamiltonian method combining density functional theory (DFT)-based geometric optimization and effective Hamiltonian is utilized to obtain the hyperfine sublevels and clock transitions under an external magnetic field for the Kramers RE ion in crystals. To show clearly, the 173 Yb 3+:Y 2 SiO 5 crystal is first investigated to demonstrate that the complicated hyperfine structure of the Kramers RE ion can be correctly calculated by the complete diagonalization (of energy) matrix (CDM) formalism. Second, optical and angular-dependent electron paramagnetic resonance (EPR) spectra of the 171 Yb 3+:Lu 2 Si 2 O 7 crystal are studied by fitting calculations based on the DFT-optimized geometric structure. By reliable fitting parameters, the external magnetic field at clock transitions is determined successfully. Such two case studies indicate that the hyperfine structure and clock transitions of the Kramers RE ion in the crystal can be accurately predicted by the present approach. This is very useful for designing and searching practical RE-based quantum memory materials with longer optical or spin coherence time.
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.