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:1811.10285 · Physical review. B./Physical review. B

Optical study of the anisotropic erbium spin flip-flop dynamics

B. Car, Lucile Veissier, Anne Louchet-Chauvet, J.-L. Le Gouët, T. Chanelière

Published Oct 4, 2019• 22 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.100.165107

Related papers

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

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

Hafsa Syed, Adam Kinos, Chunyan Shi +2 more

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.

arXiv:2205.01371•Physical review. B./Physical review. B•Nov 28, 2022•4 citations

Effects of magnetic field orientation on optical decoherence in Er 3 + : Y 2 SiO 5

Thomas Böttger, Charles W. Thiel, R. L. Cone +1 more

The influence of the anisotropic Zeeman effect on optical decoherence was studied for the 1.54 μm telecom transition in Er3+:Y2SiO5 using photon echo spectroscopy as a function of applied magnetic field orientation and strength. The decoherence strongly correlates with the Zeeman energy splittings described by the ground- and excited-state g factor variations for all inequivalent Er3+ sites, with the observed decoherence times arising from the combined effects of the magnetic dipole-dipole coupling strength and the ground- and excited-state spin-flip rates, along with the natural lifetime of the upper level. The decoherence time was maximized along a preferred magnetic field orientation that minimized the effects of spectral diffusion and that enabled the measurement of an exceptionally narrow optical resonance in a solid—demonstrating a homogeneous linewidth as narrow as 73 Hz.

Physical Review B•Mar 10, 2009•175 citations

29-21

Eloïse Lafitte-Houssat, Alban Ferrier, Mikael Afzelius +4 more

Rare earth ions are actively investigated as optically addressable spin systems for quantum technologies thanks to their long optical and spin coherence lifetimes. 171Yb3+, which has 1/2 electron and nuclear spins, recently raised interest for its simple hyperfine structure that moreover can result in long coherence lifetimes at zero magnetic field, an unusual property for paramagnetic rare earth ions. Here, we report on the optical inhomogeneous and homogeneous linewidths in 171Yb3+:Y2SiO5 (site 2) for different doping concentrations. While inhomogeneous linewidth is not correlated to 171Yb3+ concentration, the homogeneous one strongly decreases between 10 and 2 ppm doping level, reaching 255 Hz at 3 K. This is attributed to a slowing down of 171Yb3+ ground state spin flip-flops.

Оптика и спектроскопия•Jan 1, 2022•0 citations

Optical decoherence, spectroscopy, and magnetic g tensors for the 1.5-µm I 15 / 2 4 − I 13 / 2 4 transitions of E r 3 + dopants at the C 2 -symmetry site in Y 2 O 3

Thomas Böttger, Todd L. Harris, G. D. Reinemer +2 more

Erbium-doped solids are a promising platform for quantum technology due to the $\mathrm{E}{\mathrm{r}}^{3+}$ 1.5-\textmu{}m optical transition in the telecom C band that can offer long coherence times. To characterize the intrinsic ${\mathrm{C}}_{2}$ site of $\mathrm{E}{\mathrm{r}}^{3+}$ in ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ for quantum information and photonic signal-processing applications, absorption and site-selective fluorescence spectroscopy were used to assign the $\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}$$\ensuremath{\leftrightarrow}$$^{4}I_{13/2}$ transitions. The lowest-to-lowest transition occurs at 1535.608 nm and laser absorption determined an inhomogeneous linewidth of 780 MHz in a 0.005%-doped crystal at 3.4 K. Time-resolved fluorescence established an upper limit for the excited-state lifetime of 8.5 ms. Angular-dependent Zeeman absorption was used to determine ground- and excited-state $g$ tensors. The ${\mathrm{C}}_{2}$-site $g$ tensor components for the ground state are ${g}_{x}=1.60$, ${g}_{y}=4.71$, and ${g}_{z}=11.93$ with a tipping angle of \ensuremath{\alpha} = $2.{06}^{\ensuremath{\circ}}$, whereas for the excited state the components are ${g}_{x}=1.08$, ${g}_{y}=4.36$, and ${g}_{z}=10.07$ with a tipping angle of \ensuremath{\alpha} = $\ensuremath{-}11.{7}^{\ensuremath{\circ}}$. Optical decoherence can be suppressed by the application of a magnetic field parallel to $\ensuremath{\langle}111\ensuremath{\rangle}$ crystal axes where all ${\mathrm{C}}_{2}$ sites become nearly magnetically equivalent with large $g$ values so that spin flips of neighboring $\mathrm{E}{\mathrm{r}}^{3+}$ ions can be simultaneously suppressed. Using this magnetic field direction, two-pulse photon echoes gave a homogeneous linewidth of 5 kHz for an applied magnetic field of 0.5 T, narrowing and saturating at 2.5 kHz at 3.5 T. Decoherence over intermediate magnetic fields was described by spectral diffusion due to $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic dipole interactions driven by the direct phonon process. With $\mathrm{E}{\mathrm{r}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ absorption at a convenient telecom laser wavelength and the ability to fabricate waveguides, our study suggests that this is a promising material system for quantum information and spectral hole-burning signal-processing applications.

Physical review. B./Physical review. B•Jul 17, 2024•8 citations

Coherent manipulation of dipolar coupled spins in an anisotropic environment

E. I. Baibekov, Marat Revgerovich Gafurov, Д. Г. Зверев +3 more

We study coherent dynamics in a system of dipolar coupled spin qubits diluted in a solid and subjected to a driving microwave field. In the case of rare earth ions, an anisotropic crystal background results in anisotropic $g$ tensor and thus modifies the dipolar coupling. We develop a microscopic theory of spin relaxation in a transient regime for the frequently encountered case of axially symmetric crystal field. The calculated decoherence rate is nonlinear in the Rabi frequency. We show that the direction of a static magnetic field that corresponds to the highest spin $g$ factor is preferable in order to obtain a higher number of coherent qubit operations. The results of calculations are in excellent agreement with our experimental data on Rabi oscillations recorded for a series of $\mathrm{CaW}{\mathrm{O}}_{4}$ crystals with different concentrations of $\mathrm{N}{\mathrm{d}}^{3+}$ ions.

arXiv:1406.5740•Physical Review B•Nov 4, 2014•10 citations
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.
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.
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 $\ensuremath{\sim}2$ 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.
The influence of the anisotropic Zeeman effect on optical decoherence was studied for the 1.54 μm telecom transition in Er3+:Y2SiO5 using photon echo spectroscopy as a function of applied magnetic field orientation and strength. The decoherence strongly correlates with the Zeeman energy splittings described by the ground- and excited-state g factor variations for all inequivalent Er3+ sites, with the observed decoherence times arising from the combined effects of the magnetic dipole-dipole coupling strength and the ground- and excited-state spin-flip rates, along with the natural lifetime of the upper level. The decoherence time was maximized along a preferred magnetic field orientation that minimized the effects of spectral diffusion and that enabled the measurement of an exceptionally narrow optical resonance in a solid—demonstrating a homogeneous linewidth as narrow as 73 Hz.
Rare earth ions are actively investigated as optically addressable spin systems for quantum technologies thanks to their long optical and spin coherence lifetimes. 171Yb3+, which has 1/2 electron and nuclear spins, recently raised interest for its simple hyperfine structure that moreover can result in long coherence lifetimes at zero magnetic field, an unusual property for paramagnetic rare earth ions. Here, we report on the optical inhomogeneous and homogeneous linewidths in 171Yb3+:Y2SiO5 (site 2) for different doping concentrations. While inhomogeneous linewidth is not correlated to 171Yb3+ concentration, the homogeneous one strongly decreases between 10 and 2 ppm doping level, reaching 255 Hz at 3 K. This is attributed to a slowing down of 171Yb3+ ground state spin flip-flops.
Erbium-doped solids are a promising platform for quantum technology due to the Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ 1.5-\textmu{}m optical transition in the telecom C band that can offer long coherence times. To characterize the intrinsic C2{\mathrm{C}}_{2}C2​ site of Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ in Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ for quantum information and photonic signal-processing applications, absorption and site-selective fluorescence spectroscopy were used to assign the Er3+4I15/2\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}Er3+4I15/2​$\ensuremath{\leftrightarrow}$4I13/2^{4}I_{13/2}4I13/2​ transitions. The lowest-to-lowest transition occurs at 1535.608 nm and laser absorption determined an inhomogeneous linewidth of 780 MHz in a 0.005%-doped crystal at 3.4 K. Time-resolved fluorescence established an upper limit for the excited-state lifetime of 8.5 ms. Angular-dependent Zeeman absorption was used to determine ground- and excited-state ggg tensors. The C2{\mathrm{C}}_{2}C2​-site ggg tensor components for the ground state are gx=1.60{g}_{x}=1.60gx​=1.60, gy=4.71{g}_{y}=4.71gy​=4.71, and gz=11.93{g}_{z}=11.93gz​=11.93 with a tipping angle of \ensuremath{\alpha} = $2.{06}^{\ensuremath{\circ}}$, whereas for the excited state the components are gx=1.08{g}_{x}=1.08gx​=1.08, gy=4.36{g}_{y}=4.36gy​=4.36, and gz=10.07{g}_{z}=10.07gz​=10.07 with a tipping angle of \ensuremath{\alpha} = $\ensuremath{-}11.{7}^{\ensuremath{\circ}}$. Optical decoherence can be suppressed by the application of a magnetic field parallel to $\ensuremath{\langle}111\ensuremath{\rangle}$ crystal axes where all C2{\mathrm{C}}_{2}C2​ sites become nearly magnetically equivalent with large ggg values so that spin flips of neighboring Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ ions can be simultaneously suppressed. Using this magnetic field direction, two-pulse photon echoes gave a homogeneous linewidth of 5 kHz for an applied magnetic field of 0.5 T, narrowing and saturating at 2.5 kHz at 3.5 T. Decoherence over intermediate magnetic fields was described by spectral diffusion due to $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic dipole interactions driven by the direct phonon process. With Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+:Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ absorption at a convenient telecom laser wavelength and the ability to fabricate waveguides, our study suggests that this is a promising material system for quantum information and spectral hole-burning signal-processing applications.
We study coherent dynamics in a system of dipolar coupled spin qubits diluted in a solid and subjected to a driving microwave field. In the case of rare earth ions, an anisotropic crystal background results in anisotropic ggg tensor and thus modifies the dipolar coupling. We develop a microscopic theory of spin relaxation in a transient regime for the frequently encountered case of axially symmetric crystal field. The calculated decoherence rate is nonlinear in the Rabi frequency. We show that the direction of a static magnetic field that corresponds to the highest spin ggg factor is preferable in order to obtain a higher number of coherent qubit operations. The results of calculations are in excellent agreement with our experimental data on Rabi oscillations recorded for a series of CaWO4\mathrm{CaW}{\mathrm{O}}_{4}CaWO4​ crystals with different concentrations of Nd3+\mathrm{N}{\mathrm{d}}^{3+}Nd3+ ions.