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.
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.
Various spectroscopic properties of Yb 3+ -doped Y 2 SiO 5 crystal have been extensively investigated due to its promising application in quantum information processing. However, the local structure, electronic structure of Yb 3+:Y 2 SiO 5 crystal, and its optical and magnetic properties have not been comprehensively studied from a theoretical viewpoint. In this work, the geometric and electronic structures of Yb 3+ that replaces two crystallographic Y 3+ sites in the Y 2 SiO 5 crystal are first obtained by the method of density functional theory (DFT). Then, the optical, electron paramagnetic resonance (EPR), and optically detected magnetic resonance (ODMR) spectra for 171 Yb 3+ (nuclear spin I = 1/2) at such two sites are simultaneously calculated in the framework of the complete diagonalization (of energy) matrix (CDM) based on the optimized local structure around 171 Yb 3+ ion by DFT. The various calculated spectroscopic properties by such combined theoretical approach are consistent with the experimental ones, which demonstrates that CDM is effective and particularly suitable for calculating hyperfine A -tensors under zero, low, and intermediate magnetic field. More importantly, based on the obtained accurate hyperfine structure of 171 Yb 3+ in Y 2 SiO 5 crystal, the possible “clock transitions”, which can enhance the optical coherence time, can be assigned or predicted by the present approach. This study successfully explains the spectroscopic properties of 171 Yb 3+ -doped Y 2 SiO 5 and provides a feasible method to design and search for practical rare-earth-doped quantum information materials for the community.
The application of rare earth (RE) doped crystals in quantum information processing has attracted more and more attention in the past decade. How to change the clock transitions of RE ion in crystal and control their lifetime of maintaining coherent quantum state is a valuable question. In this work, the trigonal 171Yb3+ centers in lithium niobate (LN) crystal are investigated theoretically to obtain their accurate ground and excited hyperfine sublevels under external magnetic field B by a combined method of density functional theory-based geometric optimization and parametric effective Hamiltonian modeling. An optical clock transition at |B| = 45.73 mT along the c axis of the LN crystal is successfully found by calculation. To show the pressure-dependent behavior of optical clock transition, the variation of such transition under hydrostatic pressure up to 3 GPa is also obtained theoretically. The calculated results show that applying external pressure is an effective way to control these transitions of RE ion doped crystal. Moreover, the optical coherence time T2 at zero magnetic field for 171Yb3+ ion with C3 symmetry in the LN crystal is estimated by our calculations. The calculated results indicate that if the magnetic field noise is 33 μT in the LN crystal, it is possible to find an optical clock transition with long coherence time T2 (≈382 μs) at the zero magnetic field. The present methods of seeking optical clock transition and calculating its coherence time T2 caused by a fluctuating magnetic field noise in the host crystal can be applied to other Kramers RE ions doped materials.
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 crystal doped with 171Yb3+ ions. This isotope is particularly interesting since it is the only rare--earth ion having electronic spin S=21 and nuclear spin 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 crystal.
Without using any trapping lasers, rare-earth (RE) ions can be doped into some nanofabricated materials in form of nanocrystals in a solid state matrix, thus rendering a natural trap for potential application as a quantum computing device. In particular, passive nuclear spin states of RE ions can be utilized as (i) optical quantum memory (with huge density as yielded from nanocrystals), (ii) qubits by encoding in ground hyperfine states and operated as (iii) two-qubit gate when transferring them to active magnetized electronic states. A feasible implementation of qubits is realised by using those doped RE ions whose open-shell (for inner highly shielded 4f shell electrons) energy levels and statevectors are well described by the crystal field (CF) interaction and hyperfine coupling in which the Hamiltonian is composed of various freeion interactions, the CF potential, electronic and nuclear Zeeman effects as well as the hyperfine interaction. For those qubit encoded in the two ground hyperfine states of RE ions, they can have fairly long lifetimes of days and coherence times (from 1.3s for Er3+ to 6 hours for Eu3+) due to the unique spectroscopic properties of RE ions. Because of the recent progress in optical single-ion detection for addressing individual qubits with a specific frequency channel, RE ions could be packed in a solid state 3D matrix at nanometer spacing, hence rendering very high qubit densities for quantum memories. Meanwhile, this configure also leads to strong dipole-dipole interactions (or high connectivity) between qubits which are not nearest neighbors. In this study, Kramers ions like 167Er and 171Yb doped in yttrium orthosilicate Y2SiO5 (YSO) nanocrystals will be investigated as a promising system for quantum computing because of their weak spin bath and possibility for being directly milled in single nanocrystals as nano-resonators. By using the famous Wien2k package to carry out the first-principles calculations, we can obtain the CF parameters and hyperfine constants as well as various electronic properties like energy gap and band structure for those Kramers RE ions doped in YSO. We shall present some essential findings from first-principles calculations to obtain various properties of the ground and excited CF and hyperfine states for those RE ions with an aim to optimize RE ions doping in YSO nanocrystals for quantum memories and qubits, contributing to scalable quantum computing architectures.
Electron paramagnetic resonance (EPR) spectroscopy of rare earth ions in crystals is a powerful tool to analyze the hyperfine structure of the rare earth ground state. This can be useful for coherent spectroscopy and quantum information applications where the hyperfine structure of the electronic levels is used. In this work, we give a detailed analysis of the hyperfine structure of the ground state [4I15∕2(0)] of Er3+ ions in Y2SiO5. The electronic Zeeman, hyperfine, and quadrupole matrices are obtained from angular variations of the magnetic field in three orthogonal crystal planes. An excellent agreement is obtained between experimental and simulated magnetic field positions and relative intensities of EPR lines.
Erbium-167-doped yttrium orthosilicate (167Er3+:Y2SiO5) is a rare-earth-ion-doped crystal which possesses unique properties that would make it an ideal microwave-addressed quantum memory. It has an optical transition at 1.5 µm, which lies in the telecom C-band where much of the optical telecommunications infrastructure is already operating. It also possesses both nuclear and electron spin states, and hyperfine structure with transitions at microwave frequencies. The hyperfine structure exhibits microwave frequency transitions with or without an applied magnetic field, which would allow for a memory compatible with superconducting systems. However, the complicated hyperfine structure has prevented the transitions of 167Er3+:Y2SiO5 from being fully utilised.\nWith the recent publication of new spin Hamiltonian parameters for the ground state of 167Er3+:Y2SiO5, we can predict which transitions should have the longest coherence time at zero field. Based on calculations using these spin Hamiltonian parameters, we used Raman heterodyne spectroscopy to investigate the hyperfine structure of 167Er3+:Y2SiO5 for small magnetic fields and for energy level differences from 600 to 1200 MHz. We observed many transitions from the 4I15/2 ground state, as well as the 4I13/2 excited state that until now has had little investigation regarding its hyperfine structure.\nBy comparing our spectra to the existing ground state spin Hamiltonian parameters, and unpublished excited state parameters, we identified the origin of many of the transitions. We observed differences between the predicted transition frequencies from both sets of parameters and the experimental data. The data obtained using Raman heterodyne was used to improve both ground and excited state parameters to give a better description of the zero-field hyperfine splittings.\nIn addition, we identified transitions from both the 4I15/2 ground and 4I13/2 excited state that have a small dependence on magnetic field. These transitions, with zero field frequencies of 879.4 MHz and 896.7 MHz respectively, yielded coherence times of 67 µs and 300 µs at 3.2 K, when measured with a two-pulse spin echo sequence. By using a dynamic decoupling sequence, we extending the coherence times of the transitions at 879.4 MHz to 380 µs and for the transitions at 896.7 MHz, to 1.4 ms.\nThese coherence time measurements demonstrate an improvement of a previous zero field coherence measurement in 167Er3+:Y2SiO5. By operating at lower temperatures, reducing the 167Er3+ ion concentration or using a different transition, it should be possible to extend the coherence time of 167Er3+:Y2SiO5 even further.