Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2205.01371 · Physical review. B./Physical review. B

Microscopic model of spin flip-flop processes in crystals doped by rare-earth ions

Hafsa Syed, Adam Kinos, Chunyan Shi, Lars Rippe, Stefan Kröll

Published Nov 28, 2022• 4 citations
arXivHTMLPDF

Abstract

Flip-flop processes due to magnetic dipole-dipole interaction between neighboring ions in crystals doped by rare-earth ions are one of the mechanisms of relaxation between hyperfine levels. Modeling of this mechanism has so far been macroscopic, characterized by an average rate describing the relaxation of all ions. Here, however, we present a microscopic model of flip-flop interactions between individual nuclear spins of dopant ions. Every ion is situated in a unique local environment in the crystal, where each ion has different distances and a unique orientation relative to its nearest neighbors, as determined by the lattice structure. Thus each ion has a unique flip-flop rate and the collective relaxation dynamics of all ions in a bulk crystal is a sum of many exponential decays, giving rise to a distribution of rates rather than a single average decay rate. We employ this model to calculate flip-flop rates in ${\mathrm{Pr}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ and show experimental measurements of population decay of the ground state hyperfine levels at $\ensuremath{\sim}2$ K. We also present a method to measure rates of individual transitions from hole burning spectra that requires significantly fewer fitting parameters in theoretical rate equations compared to earlier work. Furthermore, we measure the effect of external magnetic field on the flip-flop rates and observe that the rates slow down by two orders of magnitude in a field of 5--10 mT.

DOI
10.1103/physrevb.106.184109

Related papers

Optical study of the anisotropic erbium spin flip-flop dynamics

B. Car, Lucile Veissier, Anne Louchet-Chauvet +2 more

We investigate the erbium flip-flop dynamics as a limiting factor of the electron-spin lifetime and more generally as an indirect source of decoherence in rare-earth-doped insulators. Despite the random isotropic arrangement of dopants in the host crystal, the dipolar interaction strongly depends on the magnetic field orientation following the strong anisotropy of the $g$ factor. In ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$, we observe in a 10-ppm doped sample a 3 orders-of-magnitude variation of the erbium flip-flop rate, as expected from the dipolar coupling term between identical spins with an anisotropic $g$ tensor. We can estimate the correct order of magnitude for a 50-ppm concentration, but we can only reproduce qualitatively the orientational variation of the flip-flop rate.

arXiv:1811.10285•Physical review. B./Physical review. B•Oct 4, 2019•22 citations

Probing the collective dynamics of nuclear spin bath in a rare-earth ion doped crystal

Zong‐Quan Zhou, Ma, Yu, Tu, Tao +13 more

Probing collective spin dynamics is a current challenge in the field of magnetic resonance spectroscopy and has important applications in material analysis and quantum information protocols. Recently, the rare-earth ion doped crystals are an attractive candidate for making long-lived quantum memory. Further enhancement of its performance would benefit from the direct knowledge on the dynamics of nuclear-spin bath in the crystal. Here we detect the collective dynamics of nuclear-spin bath located around the rare-earth ions in a crystal using dynamical decoupling spectroscopy method. From the measured spectrum, we analyze the configuration of the spin bath and characterize the flip-flop time between two correlated nuclear spins in a long time scale ($\sim $1s). Furthermore, we experimentally demonstrate that the rare-earth ions can serve as a magnetic quantum sensor for external magnetic field. These results suggest that the rare-earth ion is a useful probe for complex spin dynamics in solids and enable quantum sensing in the low-frequency regime, revealing promising possibilities for applications in diverse fields.

arXiv:1803.03075•Mar 8, 2018•0 citations

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.

Physical Review B•May 12, 2005•56 citations

Spectroscopic Theories and First-principles Calculations for Using Rare-Earth Ions Doped in Nanofabricated Materials to Build Quantum Computers: Showcases of RE3+ Doped Y2SiO5

Yau Yuen Yeung, Meng Ju

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 $4 f$ 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 $\mathrm{Er}^{3+}$ to 6 hours for $\mathrm{Eu}^{3+}$) 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 ${ }^{167} \mathbf{E r}$ and ${ }^{171} \mathbf{Y b}$ doped in yttrium orthosilicate ${Y}_{2} {SiO}_{5}$ (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.

IEEE International Conference Nanomaterials: Applications & Properties (NAP)•Sep 8, 2024•0 citations

Decoherence induced by dipole-dipole couplings between atomic species in rare earth ion doped Y 2 SiO 5

Charlotte Pignol, Antonio Ortu, L. Nicolas +5 more

Rare earth ion doped crystals are state-of-the-art platforms for processing quantum information, particularly thanks to their excellent optical and spin coherence properties at cryogenic temperatures. Experimental observations have shown that the application of a static magnetic bias field significantly improves the coherence times in the rare earth ions ensemble, but only a few studies have focused on its dependency as a function of both magnetic field direction and amplitude. This is especially true for magnetic field amplitudes under the mT, and for low magnetic dipole moment ions. In this paper, we investigate the relationship between the magnetic field parameters and the decoherence caused by magnetic dipole-dipole coupling with the nearest-neighbor nuclear spins in the crystal. The primary non-Kramers rare earth ions investigated here are europium and praseodymium, but we also extend our study to the ytterbium Kramers ion due to its low magnetic dipole in the mT range. We perform theoretical investigations and simulations of the energy structure and coherence time evolution and identify good correspondences between experimental and simulated spin echo data. This work allows us to pinpoint the most relevant decoherence mechanisms in the considered magnetic field regime, and to predict favorable magnetic configurations.

arXiv:2408.01958•Physical review. B./Physical review. B•Dec 24, 2024•6 citations

Transient hole-burning and free induction decay as a probe of multi-timescale host spin dynamics in low-temperature ion-doped crystals

Pavel A Apanasevich, S. Ya. Kilin, Alexander P. Nizovtsev +1 more

Transient hole-burning and free induction decay (FID) in low-temperature ion-doped crystals are studied consistently using the model of two jump processes Ut equals Ut1 + Ut2 characterized by essentially different jump rates v1 >> v2 and distribution widths (sigma) 1 << (sigma) 2 for the impurity ion optical transition frequency fluctuations Ut due to the bulk and the frozen core spin flipping. At short pump/probe pulsewidth T and short delay time (tau) d ((tau) d, T << v2-1) the calculated hole shape is narrow with the hole width determined by Ut1 process characteristics only. The hole width in this case coincides with the calculated FID rate. At long delay (tau) d >= v2-1 the hole becomes a wide lorentzian with the halfwidth 2(sigma) 2. The theory fits well the experimental data by A. Szabo et. al. on narrow hole burning and FID in ruby under low and high magnetic fields supposing the fluctuations Ut1 to be rather slow ((sigma) 21/v21 equals 0.5).

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 10, 1996•0 citations
Flip-flop processes due to magnetic dipole-dipole interaction between neighboring ions in crystals doped by rare-earth ions are one of the mechanisms of relaxation between hyperfine levels. Modeling of this mechanism has so far been macroscopic, characterized by an average rate describing the relaxation of all ions. Here, however, we present a microscopic model of flip-flop interactions between individual nuclear spins of dopant ions. Every ion is situated in a unique local environment in the crystal, where each ion has different distances and a unique orientation relative to its nearest neighbors, as determined by the lattice structure. Thus each ion has a unique flip-flop rate and the collective relaxation dynamics of all ions in a bulk crystal is a sum of many exponential decays, giving rise to a distribution of rates rather than a single average decay rate. We employ this model to calculate flip-flop rates in Pr3+{\mathrm{Pr}}^{3+}Pr3+:Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ and show experimental measurements of population decay of the ground state hyperfine levels at \ensuremath∼2\ensuremath{\sim}2\ensuremath∼2 K. We also present a method to measure rates of individual transitions from hole burning spectra that requires significantly fewer fitting parameters in theoretical rate equations compared to earlier work. Furthermore, we measure the effect of external magnetic field on the flip-flop rates and observe that the rates slow down by two orders of magnitude in a field of 5--10 mT.
We investigate the erbium flip-flop dynamics as a limiting factor of the electron-spin lifetime and more generally as an indirect source of decoherence in rare-earth-doped insulators. Despite the random isotropic arrangement of dopants in the host crystal, the dipolar interaction strongly depends on the magnetic field orientation following the strong anisotropy of the ggg factor. In Er3+:Y2SiO5{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Er3+:Y2​SiO5​, we observe in a 10-ppm doped sample a 3 orders-of-magnitude variation of the erbium flip-flop rate, as expected from the dipolar coupling term between identical spins with an anisotropic ggg tensor. We can estimate the correct order of magnitude for a 50-ppm concentration, but we can only reproduce qualitatively the orientational variation of the flip-flop rate.
Probing collective spin dynamics is a current challenge in the field of magnetic resonance spectroscopy and has important applications in material analysis and quantum information protocols. Recently, the rare-earth ion doped crystals are an attractive candidate for making long-lived quantum memory. Further enhancement of its performance would benefit from the direct knowledge on the dynamics of nuclear-spin bath in the crystal. Here we detect the collective dynamics of nuclear-spin bath located around the rare-earth ions in a crystal using dynamical decoupling spectroscopy method. From the measured spectrum, we analyze the configuration of the spin bath and characterize the flip-flop time between two correlated nuclear spins in a long time scale ($\sim $1s). Furthermore, we experimentally demonstrate that the rare-earth ions can serve as a magnetic quantum sensor for external magnetic field. These results suggest that the rare-earth ion is a useful probe for complex spin dynamics in solids and enable quantum sensing in the low-frequency regime, revealing promising possibilities for applications in diverse fields.
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.
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 4f4 f4f 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+\mathrm{Er}^{3+}Er3+ to 6 hours for Eu3+\mathrm{Eu}^{3+}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{ }^{167} \mathbf{E r}167Er and 171Yb{ }^{171} \mathbf{Y b}171Yb doped in yttrium orthosilicate Y2SiO5{Y}_{2} {SiO}_{5}Y2​SiO5​ (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.
Rare earth ion doped crystals are state-of-the-art platforms for processing quantum information, particularly thanks to their excellent optical and spin coherence properties at cryogenic temperatures. Experimental observations have shown that the application of a static magnetic bias field significantly improves the coherence times in the rare earth ions ensemble, but only a few studies have focused on its dependency as a function of both magnetic field direction and amplitude. This is especially true for magnetic field amplitudes under the mT, and for low magnetic dipole moment ions. In this paper, we investigate the relationship between the magnetic field parameters and the decoherence caused by magnetic dipole-dipole coupling with the nearest-neighbor nuclear spins in the crystal. The primary non-Kramers rare earth ions investigated here are europium and praseodymium, but we also extend our study to the ytterbium Kramers ion due to its low magnetic dipole in the mT range. We perform theoretical investigations and simulations of the energy structure and coherence time evolution and identify good correspondences between experimental and simulated spin echo data. This work allows us to pinpoint the most relevant decoherence mechanisms in the considered magnetic field regime, and to predict favorable magnetic configurations.
Transient hole-burning and free induction decay (FID) in low-temperature ion-doped crystals are studied consistently using the model of two jump processes Ut equals Ut1 + Ut2 characterized by essentially different jump rates v1 >> v2 and distribution widths (sigma) 1 << (sigma) 2 for the impurity ion optical transition frequency fluctuations Ut due to the bulk and the frozen core spin flipping. At short pump/probe pulsewidth T and short delay time (tau) d ((tau) d, T << v2-1) the calculated hole shape is narrow with the hole width determined by Ut1 process characteristics only. The hole width in this case coincides with the calculated FID rate. At long delay (tau) d >= v2-1 the hole becomes a wide lorentzian with the halfwidth 2(sigma) 2. The theory fits well the experimental data by A. Szabo et. al. on narrow hole burning and FID in ruby under low and high magnetic fields supposing the fluctuations Ut1 to be rather slow ((sigma) 21/v21 equals 0.5).