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:2412.10126 · Physical review. B./Physical review. B

Exploration of optimal hyperfine transitions for spin-wave storage in Er 3 + 167 : Y 2 SiO 5

K. Matsuura, S. Yasui, Reina Kaji, H. Sasakura, Takehiko Tawara, S. Adachi

Published Jan 28, 2026• 0 citations
arXivHTMLPDF

Abstract

The dependence of the magnetic fluctuations and the spin coherence time $T_2^{\rm hyp}$ of the lowest Stark states $^4I_{15/2}\ (Z_1)$ in $^{167}$Er$^{3+}$:Y$_2$SiO$_5$ under zero magnetic field on Er concentration is numerically investigated in the range of 10 to 100 parts per million (ppm). We investigate two primary sources of magnetic fluctuation limiting spin coherence: a constant contribution from host Y nuclei and a concentration-dependent component from dipole-dipole interactions among Er ions. Due to these two components, the Er-concentration dependence of $T_2^{\rm hyp}$ at the zero first-order Zeeman (ZEFOZ) points saturates for crystals with Er concentration below 10 ppm and no extension of the $T_2^{\rm hyp}$ is expected without an external magnetic field. Under a magnetic field, the longest $T_2^{\rm hyp}$ at a particular ZEFOZ point is expected to be over 170 s (90 s) for site 1 (site 2), which is more than $10^4$ times longer than that at zero field for 10-ppm $^{167}$Er$^{3+}$:Y$_2$SiO$_5$. Remarkably, these optimal ZEFOZ points form striking geometric patterns: a line for site 1 and a plane for site 2. This trend, which is favorable for experiments, can be explained by the anisotropy of the effective spin Hamiltonian parameters. Finally, the tolerance of the ZEFOZ point at each site with the longest $T_2^{\rm hyp}$ against the errors in the applied magnetic field vector is evaluated.

DOI
10.1103/g23x-14ks

Related papers

Reducing decoherence in optical and spin transitions in rare-earth-metal-ion–doped materials

D. L. McAuslan, John G. Bartholomew, Matthew J. Sellars +1 more

In many important situations, the dominant dephasing mechanism in cryogenic rare-earth-metal-ion--doped systems is due to magnetic field fluctuations from spins in the host crystal. Operating at a magnetic field where a transition has a zero first-order Zeeman (ZEFOZ) shift can greatly reduce this dephasing. Here we identify the location of transitions with a zero first-order Zeeman shift for optical transitions in Pr${}^{3+}$:YAG and for spin transitions in Er${}^{3+}$:Y${}_{2}$SiO${}_{5}$. The long coherence times that ZEFOZ can enable would make Pr${}^{3+}$:YAG a strong candidate for achieving the strong-coupling regime of cavity QED, and would be an important step forward in creating long-lived telecommunications wavelength quantum memories in Er${}^{3+}$:Y${}_{2}$SiO${}_{5}$. This work relies mostly on published spin-Hamiltonian parameters, but Raman heterodyne spectroscopy was performed on Pr${}^{3+}$:YAG to measure the parameters for the excited state.

arXiv:1201.4610•Physical Review A•Mar 30, 2012•61 citations

Magnetic g tensors for the I 15 ∕ 2 4 and I 13 ∕ 2 4 states of Er 3 + : Y 2 Si O 5

Yongchen Sun, Thomas Böttger, Charles W. Thiel +1 more

We present the complete Zeeman $g$ tensors for the lowest-energy $^{4}\mathrm{I}_{15∕2}$ and $^{4}\mathrm{I}_{13∕2}$ states of ${\mathrm{Er}}^{3+}$ doped into ${\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ for both crystallographic sites deduced from orientation-dependent optical Zeeman spectroscopy over three orthogonal crystal planes. From these data, principal axes of the $g$ tensors were determined for each crystallographic site. Along axes with maximum values, the effective $g$ factors are 14.65 (site 1) and 15.46 (site 2) for the ground state, and 12.97 (site 1) and 13.77 (site 2) for the excited state. To minimize optical decoherence and spectral diffusion in device applications and high resolution spectroscopy, special directions for applying an external magnetic field have been found for each site, for which the ground- and excited-state $g$ factors are equal. Among those directions, choices are presented that also maximize the ground-state splittings for all four magnetically inequivalent sites, thus optimizing the prospects for freezing out electron spin fluctuations and reducing decoherence and spectral diffusion significantly.

Physical Review B•Feb 29, 2008•91 citations

Nuclear quadrupole interaction and zero first-order Zeeman transitions of Er 167 3 + in CaWO 4

Lewin Marsh, Yang Yikai, Cesare Mattiroli +5 more

We report microwave spectroscopy of $^{167}$Er$^{3+}$ doped in CaWO$_4$ which reveals the hyperfine splitting of the erbium electronic ground state ($Z_1$, $J_\mathrm{eff.}$=15/2) induced by the $I$=7/2 nuclear spin. From spectra measured below$\sim$50 mK in magnetic fields up to 200 mT, we extract spin Hamiltonian parameters including the electron $\textbf{g}$, hyperfine $\textbf{A}$, and nuclear electric quadrupolar $\textbf{Q}$ tensors. Crucially, our analysis demonstrate unambiguously, that the previously unobserved nuclear electric quadrupolar moment is essential to reproduce the experimental data. With these refined parameters, we identify zero first-order Zeeman (ZEFOZ) transitions at zero magnetic field. Extending the analysis to finite fields, we uncover that ZEFOZ points lie either along the $c$ axis or within the $a$-$b$ plane. These results establish CaWO$_4$ as a promising host for long lifetime quantum memories.

arXiv:2601.16362•Physical review. B./Physical review. B•Jan 6, 2026•0 citations

Elucidating magnetic structure with optical dopants: erbium-doped Gd$_2$SiO$_5$

Luke S. Trainor, Masaya Hiraishi, J. -R. Soh +1 more

The narrowness of the optical transitions of rare-earth-ion dopants makes them highly sensitive probes of their environment. We measured the optical transitions Er$^{3+}$ dopants to determine the previously unknown magnetic ordering of Gd$_{2}$SiO$_{5}$ -- 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 $a^*$ 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 $1.86\pm0.01_\mathrm{stat.}\pm0.07_\mathrm{syst.}$ 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.

cond-mat.str-elCross-listedarXiv:2603.12603•Mar 16, 2026•0 citations

Static Magnetic‑Field and ZEFOZ‑Point Performance Prediction for Eu:YSO Long‑Time Coherent Optical Storage Based on the Phenomenological Theory of Coherence Scale Evolution

Lingguang Xu

Nuclear‑spin‑induced magnetic noise is one dominant decoherence source limiting hour‑scale coherent optical storage in Eu3+:Y2SiO5 (Eu:YSO). Appropriately oriented static external magnetic fields can suppress spin‑flip fluctuations and extend coherent retention time, yet unified quantitative predictions for usable field window, crystal axis preference and ZEFOZ (Zero‑First‑Order‑Zeeman) working points remain scarce. Built upon the phenomenological theory of coherence‑scale evolution established in our preceding work, spin‑magnetic perturbation is incorporated as an additional macroscopic decoherence channel. System characteristic parameters are calibrated against published low‑temperature spectroscopic benchmarks for Eu:YSO at 1.7 K. All internal microscopic evolution routines are not disclosed; only measurable forward‑looking outputs are presented. Quantitative experimentally‑testable predictions are reported: the favorable static‑magnetic‑field amplitude window is 0.11 T - 0.36 T with maximum lifetime enhancement factor up to 2.61 relative to zero‑field baseline; high‑field degradation threshold locates near 0.42 T; among three principal crystallographic axes, the D1 axis delivers optimal performance, D2 axis gives intermediate improvement, and D3 axis is unfavorable for long‑time storage. Under the preferred D1 orientation, the primary ZEFOZ working point occurs at 0.227 T, bringing an extra 32.4% suppression of residual magnetic noise and further lifting theoretical storage‑time upper bound. Practical tuning suggestions for cryogenic rare‑earth quantum‑memory setups are provided, together with explicit validity limits for the present phenomenological framework.

•Aug 10, 2026•0 citations

Zeeman and hyperfine interactions of a single Er 3+ 167 ion in Si

Jiliang Yang, Wenda Fan, Yangbo Zhang +1 more

Er-doped Si is a promising candidate for quantum information applications due to its telecom wavelength optical transition and its compatibility with Si nanofabrication technologies. Recent spectroscopic studies based on photoluminescence excitation have shown multiple well-defined lattice sites that Er occupies in Si. Here we report a measurement of the Zeeman and hyperfine tensors of a single Er3+167 ion in Si. All the obtained tensors are highly anisotropic with the largest value principal axes aligning in nearly the same direction, and the trace of the lowest crystal field level g-tensor is 17.78±0.40. The results indicate that this specific Er site is likely to be a distorted cubic site that exhibits monoclinic (C1) symmetry. Finally, zero first-order-Zeeman fields are identified for this site and could be used to reduce decoherence of hyperfine spin states in future experiments.

•Nov 2, 2024•0 citations
The dependence of the magnetic fluctuations and the spin coherence time T2hypT_2^{\rm hyp}T2hyp​ of the lowest Stark states 4I15/2 (Z1)^4I_{15/2}\ (Z_1)4I15/2​ (Z1​) in 167^{167}167Er3+^{3+}3+:Y2_22​SiO5_55​ under zero magnetic field on Er concentration is numerically investigated in the range of 10 to 100 parts per million (ppm). We investigate two primary sources of magnetic fluctuation limiting spin coherence: a constant contribution from host Y nuclei and a concentration-dependent component from dipole-dipole interactions among Er ions. Due to these two components, the Er-concentration dependence of T2hypT_2^{\rm hyp}T2hyp​ at the zero first-order Zeeman (ZEFOZ) points saturates for crystals with Er concentration below 10 ppm and no extension of the T2hypT_2^{\rm hyp}T2hyp​ is expected without an external magnetic field. Under a magnetic field, the longest T2hypT_2^{\rm hyp}T2hyp​ at a particular ZEFOZ point is expected to be over 170 s (90 s) for site 1 (site 2), which is more than 10410^4104 times longer than that at zero field for 10-ppm 167^{167}167Er3+^{3+}3+:Y2_22​SiO5_55​. Remarkably, these optimal ZEFOZ points form striking geometric patterns: a line for site 1 and a plane for site 2. This trend, which is favorable for experiments, can be explained by the anisotropy of the effective spin Hamiltonian parameters. Finally, the tolerance of the ZEFOZ point at each site with the longest T2hypT_2^{\rm hyp}T2hyp​ against the errors in the applied magnetic field vector is evaluated.
In many important situations, the dominant dephasing mechanism in cryogenic rare-earth-metal-ion--doped systems is due to magnetic field fluctuations from spins in the host crystal. Operating at a magnetic field where a transition has a zero first-order Zeeman (ZEFOZ) shift can greatly reduce this dephasing. Here we identify the location of transitions with a zero first-order Zeeman shift for optical transitions in Pr3+{}^{3+}3+:YAG and for spin transitions in Er3+{}^{3+}3+:Y2{}_{2}2​SiO5{}_{5}5​. The long coherence times that ZEFOZ can enable would make Pr3+{}^{3+}3+:YAG a strong candidate for achieving the strong-coupling regime of cavity QED, and would be an important step forward in creating long-lived telecommunications wavelength quantum memories in Er3+{}^{3+}3+:Y2{}_{2}2​SiO5{}_{5}5​. This work relies mostly on published spin-Hamiltonian parameters, but Raman heterodyne spectroscopy was performed on Pr3+{}^{3+}3+:YAG to measure the parameters for the excited state.
We present the complete Zeeman ggg tensors for the lowest-energy 4I15∕2^{4}\mathrm{I}_{15∕2}4I15∕2​ and 4I13∕2^{4}\mathrm{I}_{13∕2}4I13∕2​ states of Er3+{\mathrm{Er}}^{3+}Er3+ doped into Y2SiO5{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}Y2​SiO5​ for both crystallographic sites deduced from orientation-dependent optical Zeeman spectroscopy over three orthogonal crystal planes. From these data, principal axes of the ggg tensors were determined for each crystallographic site. Along axes with maximum values, the effective ggg factors are 14.65 (site 1) and 15.46 (site 2) for the ground state, and 12.97 (site 1) and 13.77 (site 2) for the excited state. To minimize optical decoherence and spectral diffusion in device applications and high resolution spectroscopy, special directions for applying an external magnetic field have been found for each site, for which the ground- and excited-state ggg factors are equal. Among those directions, choices are presented that also maximize the ground-state splittings for all four magnetically inequivalent sites, thus optimizing the prospects for freezing out electron spin fluctuations and reducing decoherence and spectral diffusion significantly.
We report microwave spectroscopy of 167^{167}167Er3+^{3+}3+ doped in CaWO4_44​ which reveals the hyperfine splitting of the erbium electronic ground state (Z1Z_1Z1​, Jeff.J_\mathrm{eff.}Jeff.​=15/2) induced by the III=7/2 nuclear spin. From spectra measured below$\sim$50 mK in magnetic fields up to 200 mT, we extract spin Hamiltonian parameters including the electron g\textbf{g}g, hyperfine A\textbf{A}A, and nuclear electric quadrupolar Q\textbf{Q}Q tensors. Crucially, our analysis demonstrate unambiguously, that the previously unobserved nuclear electric quadrupolar moment is essential to reproduce the experimental data. With these refined parameters, we identify zero first-order Zeeman (ZEFOZ) transitions at zero magnetic field. Extending the analysis to finite fields, we uncover that ZEFOZ points lie either along the ccc axis or within the aaa-bbb plane. These results establish CaWO4_44​ as a promising host for long lifetime quantum memories.
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.
Nuclear‑spin‑induced magnetic noise is one dominant decoherence source limiting hour‑scale coherent optical storage in Eu3+:Y2SiO5 (Eu:YSO). Appropriately oriented static external magnetic fields can suppress spin‑flip fluctuations and extend coherent retention time, yet unified quantitative predictions for usable field window, crystal axis preference and ZEFOZ (Zero‑First‑Order‑Zeeman) working points remain scarce. Built upon the phenomenological theory of coherence‑scale evolution established in our preceding work, spin‑magnetic perturbation is incorporated as an additional macroscopic decoherence channel. System characteristic parameters are calibrated against published low‑temperature spectroscopic benchmarks for Eu:YSO at 1.7 K. All internal microscopic evolution routines are not disclosed; only measurable forward‑looking outputs are presented. Quantitative experimentally‑testable predictions are reported: the favorable static‑magnetic‑field amplitude window is 0.11 T - 0.36 T with maximum lifetime enhancement factor up to 2.61 relative to zero‑field baseline; high‑field degradation threshold locates near 0.42 T; among three principal crystallographic axes, the D1 axis delivers optimal performance, D2 axis gives intermediate improvement, and D3 axis is unfavorable for long‑time storage. Under the preferred D1 orientation, the primary ZEFOZ working point occurs at 0.227 T, bringing an extra 32.4% suppression of residual magnetic noise and further lifting theoretical storage‑time upper bound. Practical tuning suggestions for cryogenic rare‑earth quantum‑memory setups are provided, together with explicit validity limits for the present phenomenological framework.
Er-doped Si is a promising candidate for quantum information applications due to its telecom wavelength optical transition and its compatibility with Si nanofabrication technologies. Recent spectroscopic studies based on photoluminescence excitation have shown multiple well-defined lattice sites that Er occupies in Si. Here we report a measurement of the Zeeman and hyperfine tensors of a single Er3+167 ion in Si. All the obtained tensors are highly anisotropic with the largest value principal axes aligning in nearly the same direction, and the trace of the lowest crystal field level g-tensor is 17.78±0.40. The results indicate that this specific Er site is likely to be a distorted cubic site that exhibits monoclinic (C1) symmetry. Finally, zero first-order-Zeeman fields are identified for this site and could be used to reduce decoherence of hyperfine spin states in future experiments.