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Physical review. B./Physical review. B

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, Charles W. Thiel, R. L. Cone

Published Jul 17, 2024• 8 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.110.045132

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Optical spectroscopy, magnetic g tensors, and decoherence studies of magnetic dipole transitions of E r 3 + at C 3 i -symmetry lattice sites in Y 2 O 3 at 1.5 µm

Thomas Böttger, G. D. Reinemer, Charles W. Thiel +1 more

When introduced as dopants into ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$, $\mathrm{E}{\mathrm{r}}^{3+}$ ions replace ${\mathrm{Y}}^{3+}$ ions at two crystallographic sites of ${\mathrm{C}}_{2}$ and ${\mathrm{C}}_{3\mathrm{i}}$ point symmetries. The ${\mathrm{C}}_{3\mathrm{i}}$ site is particularly interesting, given that the inversion symmetry prohibits static electric-dipole moments and electric-dipole transitions, resulting in 1.5 \textmu{}m optical transitions characterized by purely magnetic-dipole properties. Employing $\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}\ensuremath{\leftrightarrow}^{4}I_{13/2}$ transitions, we examined the inherent ${\mathrm{C}}_{3\mathrm{i}}$ site of $\mathrm{E}{\mathrm{r}}^{3+}$ in ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ for its potential in quantum information science and spectral hole burning applications. Our approach involved absorption and site-selective fluorescence spectroscopy to discern $\mathrm{E}{\mathrm{r}}^{3+}$ energy levels and revealed an excited-state lifetime of 14.6 ms. High-resolution laser spectroscopy at 3.7 K indicated an inhomogeneous linewidth of 1.3 GHz in our sample. Orientation-dependent Zeeman laser absorption spectroscopy facilitated the determination of the full $g$ tensors for both the ground and excited states, confirming the ${\mathrm{C}}_{3\mathrm{i}}$ site assignment. Furthermore, it identified a suitable magnetic field direction for mitigating decoherence, a finding corroborated through two-pulse photon echo spectroscopy. Our study presents photon echo coherent transient measurements related to magnetic-dipole-allowed rare-earth ion transitions at the ${\mathrm{C}}_{3\mathrm{i}}$ site. The observed decoherence, attributed to spectral diffusion arising from $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic-dipole interactions, underscores the complex spin dynamics at play in systems with multiple inequivalent dopant sites. Coupled with the practicality of telecom laser wavelengths, our investigation highlights the promise of magnetic-dipole transitions in advancing quantum information science and spectral hole burning applications.

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Thomas Böttger, Charles W. Thiel, R. L. Cone +2 more

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Rare-earth doped crystals are promising systems for quantum information processing. In particular, paramagnetic rare earths could be used to build coherent interfaces with optical and microwave photons. In addition, isotopes with nonzero nuclear spins could provide long-lived states for quantum state storage and processing. ${\mathrm{Yb}}^{3+}$ is particularly interesting in this respect since it is the only paramagnetic rare earth with a spin-$\frac{1}{2}$ isotope, which corresponds to the simplest possible level structure. In this paper, we report on the optical and magnetic properties of ${\mathrm{Yb}}^{3+}$ in the two sites of ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$, a commonly used crystal for quantum applications. We measured optical inhomogeneous linewidths, peak absorption coefficients, oscillator strengths, and excited-state lifetimes. The Zeeman tensors were also determined in the ground and excited states, as well as the ground-state hyperfine tensor for the $^{171}\mathrm{Yb}^{3+}$ ($I=\frac{1}{2}$) isotope. These results suggest that ${\mathrm{Yb}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ is a promising material for applications like solid-state optical and microwave quantum memories.

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Spectroscopy and dynamics of Er 3 + : Y 2 Si O 5 at 1.5 μ m

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We present the results of detailed site-selective spectroscopy performed on the $^{4}I_{15∕2}\ensuremath{\leftrightarrow}^{4}I_{13∕2}$ transition of ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ at $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$. New determinations of the $^{4}I_{13∕2}$ and $^{4}I_{15∕2}$ crystal-field-level structure for the two crystallographically inequivalent ${\mathrm{Er}}^{3+}$ sites have been made. The fluorescence dynamics of the metastable $^{4}I_{13∕2}:{\mathrm{Y}}_{1}$ excited state was investigated, showing exponential decays for ${\mathrm{Er}}^{3+}$ at both crystallographic sites with fluorescence lifetimes of $11.4\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ for site 1 and $9.2\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ for site 2. Exceptionally sharp inhomogeneous absorption lines of 180, 390, and $510\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ were observed in 0.0015% ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$, 0.005% ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$, and 0.02% ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ crystals, respectively. The $g$-values for the lowest energy $^{4}I_{15∕2}$ $({\mathrm{Z}}_{1})$ and $^{4}I_{13∕2}$ $({\mathrm{Y}}_{1})$ doublets were measured to be 5.5 and 4.6 for site 1 and 15.0 and 12.9 for site 2 when the magnetic field was oriented along the crystal's ${\mathbit{D}}_{1}$ axis.

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Optical decoherence and spectral diffusion at 1.5 μ m in Er 3 + : Y 2 SiO 5 versus magnetic field, temperature, and Er 3 + concentration

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

The mechanisms and effects of spectral diffusion for optical transitions of paramagnetic ions have been explored using the inhomogeneously broadened 1536 nm $^{4}\mathrm{I}_{15∕2}\ensuremath{\rightarrow}^{4}\mathrm{I}_{13∕2}$ transition in ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$. Using photon echo spectroscopy, spectral diffusion was measured by observing the evolution of the effective coherence lifetimes over time scales from $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ to 20 ms for magnetic-field strengths from 0.3 to 6.0 T, temperatures from 1.6 to 6.5 K, and nominal ${\mathrm{Er}}^{3+}$ concentrations of 0.0015%, 0.005%, and 0.02%. To understand the effect of spectral diffusion on material decoherence for different environmental conditions and material compositions, data and models were compared to identify spectral diffusion mechanisms and microscopic spin dynamics. Observations were successfully modeled by ${\mathrm{Er}}^{3+}\ensuremath{-}{\mathrm{Er}}^{3+}$ magnetic dipole interactions and ${\mathrm{Er}}^{3+}$ electron spin flips driven by the one-phonon direct process. At temperatures of 4.2 K and higher, spectral diffusion due to $^{89}\mathrm{Y}$ nuclear spin flips was also observed. The success in describing our extensive experimental results using simple models provides an important capability for exploring larger parameter spaces, accelerating the design and optimization of materials for spatial-spectral holography, and spectral hole-burning devices. The broad insight into spectral diffusion mechanisms and dynamics is applicable to other paramagnetic materials, such as those containing ${\mathrm{Yb}}^{3+}$ or ${\mathrm{Nd}}^{3+}$.

Physical Review B•Feb 1, 2006•209 citations
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 \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 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∘2.{06}^{\ensuremath{\circ}}2.06\ensuremath∘, 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∘\ensuremath{-}11.{7}^{\ensuremath{\circ}}\ensuremath−11.7\ensuremath∘. Optical decoherence can be suppressed by the application of a magnetic field parallel to \ensuremath⟨111\ensuremath⟩\ensuremath{\langle}111\ensuremath{\rangle}\ensuremath⟨111\ensuremath⟩ 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 Er3+\ensuremath-Er3+\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}Er3+\ensuremath-Er3+ 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.
When introduced as dopants into Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​, Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ ions replace Y3+{\mathrm{Y}}^{3+}Y3+ ions at two crystallographic sites of C2{\mathrm{C}}_{2}C2​ and C3i{\mathrm{C}}_{3\mathrm{i}}C3i​ point symmetries. The C3i{\mathrm{C}}_{3\mathrm{i}}C3i​ site is particularly interesting, given that the inversion symmetry prohibits static electric-dipole moments and electric-dipole transitions, resulting in 1.5 \textmu{}m optical transitions characterized by purely magnetic-dipole properties. Employing $\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}\ensuremath{\leftrightarrow}^{4}I_{13/2}$ transitions, we examined the inherent C3i{\mathrm{C}}_{3\mathrm{i}}C3i​ site of Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ in Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ for its potential in quantum information science and spectral hole burning applications. Our approach involved absorption and site-selective fluorescence spectroscopy to discern Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ energy levels and revealed an excited-state lifetime of 14.6 ms. High-resolution laser spectroscopy at 3.7 K indicated an inhomogeneous linewidth of 1.3 GHz in our sample. Orientation-dependent Zeeman laser absorption spectroscopy facilitated the determination of the full ggg tensors for both the ground and excited states, confirming the C3i{\mathrm{C}}_{3\mathrm{i}}C3i​ site assignment. Furthermore, it identified a suitable magnetic field direction for mitigating decoherence, a finding corroborated through two-pulse photon echo spectroscopy. Our study presents photon echo coherent transient measurements related to magnetic-dipole-allowed rare-earth ion transitions at the C3i{\mathrm{C}}_{3\mathrm{i}}C3i​ site. The observed decoherence, attributed to spectral diffusion arising from $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic-dipole interactions, underscores the complex spin dynamics at play in systems with multiple inequivalent dopant sites. Coupled with the practicality of telecom laser wavelengths, our investigation highlights the promise of magnetic-dipole transitions in advancing quantum information science and spectral hole burning applications.
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.
The $^{2}F_{7/2}\ensuremath{\leftrightarrow}^{2}F_{5/2}$ optical transitions of Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+ doped into Y3Al5O12{\mathrm{Y}}_{3}\mathrm{A}{\mathrm{l}}_{5}{\mathrm{O}}_{12}Y3​Al5​O12​ (YAG) were studied for potential quantum information and photonic signal processing applications. Absorption and fluorescence spectroscopy located the energy levels of the ground 2F7/2^{2}F_{7/2}2F7/2​ and excited 2F5/2^{2}F_{5/2}2F5/2​ manifolds, allowing inconsistencies between previous assignments of crystal field splittings in the literature to be resolved. These measurements reveal an unusually large splitting between the first and second levels in both the ground and excited multiplets, potentially providing for reduced sensitivity to thermally induced decoherence and spin-lattice relaxation. Spectral hole burning through two-level saturation was observed, determining the excited state lifetime to be 860 \ensuremath{\mu}s and resolving ambiguities in previous fluorescence measurements that were caused by the large radiation trapping effects in this material. Optical decoherence measurements using two-pulse photon echoes gave a homogeneous linewidth of 18 kHz for an applied magnetic field of 1 T, narrowing to 5 kHz at 2.5 T. The observed decoherence was described by spectral diffusion attributed to $\mathrm{Y}{\mathrm{b}}^{3+}\mathrm{\ensuremath{-}}\mathrm{Y}{\mathrm{b}}^{3+}$ magnetic dipole interactions. Laser absorption determined an inhomogeneous linewidth of 3.6 GHz for this transition in this 0.05%-doped crystal, which is narrower than for any other rare-earth-ion transition previously studied in the YAG host. The temperature dependence of the transition energy and linewidth of the lowest 2F7/2^{2}F_{7/2}2F7/2​ to lowest 2F5/2^{2}F_{5/2}2F5/2​ transition centered at 968.571 nm measured from 4 K to 300 K was well described by phonon scattering at higher temperatures, with an additional anomalous linear temperature-dependent broadening at temperatures below 80 K. Two magnetically inequivalent subgroups of Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+ ions were identified when a magnetic field was applied along the $\ensuremath{\langle}111\ensuremath{\rangle}$ axis, as expected for the D2{D}_{2}D2​ sites in the cubic symmetry crystal, with ground and excited state effective ggg-values of gg=3.40{g}_{\mathrm{g}}=3.40gg​=3.40 (3.34) and ge=1.04{g}_{\mathrm{e}}=1.04ge​=1.04 (2.01), respectively. Together with the convenient diode laser wavelength of this transition, our study suggests that Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+:YAG is a promising material system for spectral hole burning and quantum information applications.
Rare-earth doped crystals are promising systems for quantum information processing. In particular, paramagnetic rare earths could be used to build coherent interfaces with optical and microwave photons. In addition, isotopes with nonzero nuclear spins could provide long-lived states for quantum state storage and processing. Yb3+{\mathrm{Yb}}^{3+}Yb3+ is particularly interesting in this respect since it is the only paramagnetic rare earth with a spin-12\frac{1}{2}21​ isotope, which corresponds to the simplest possible level structure. In this paper, we report on the optical and magnetic properties of Yb3+{\mathrm{Yb}}^{3+}Yb3+ in the two sites of Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​, a commonly used crystal for quantum applications. We measured optical inhomogeneous linewidths, peak absorption coefficients, oscillator strengths, and excited-state lifetimes. The Zeeman tensors were also determined in the ground and excited states, as well as the ground-state hyperfine tensor for the 171Yb3+^{171}\mathrm{Yb}^{3+}171Yb3+ (I=12I=\frac{1}{2}I=21​) isotope. These results suggest that Yb3+{\mathrm{Yb}}^{3+}Yb3+:Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ is a promising material for applications like solid-state optical and microwave quantum memories.
We present the results of detailed site-selective spectroscopy performed on the $^{4}I_{15∕2}\ensuremath{\leftrightarrow}^{4}I_{13∕2}$ transition of Er3+:Y2SiO5{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}Er3+:Y2​SiO5​ at $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$. New determinations of the 4I13∕2^{4}I_{13∕2}4I13∕2​ and 4I15∕2^{4}I_{15∕2}4I15∕2​ crystal-field-level structure for the two crystallographically inequivalent Er3+{\mathrm{Er}}^{3+}Er3+ sites have been made. The fluorescence dynamics of the metastable 4I13∕2:Y1^{4}I_{13∕2}:{\mathrm{Y}}_{1}4I13∕2​:Y1​ excited state was investigated, showing exponential decays for Er3+{\mathrm{Er}}^{3+}Er3+ at both crystallographic sites with fluorescence lifetimes of 11.4ms11.4\phantom{\rule{0.3em}{0ex}}\mathrm{ms}11.4ms for site 1 and 9.2ms9.2\phantom{\rule{0.3em}{0ex}}\mathrm{ms}9.2ms for site 2. Exceptionally sharp inhomogeneous absorption lines of 180, 390, and 510MHz510\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}510MHz were observed in 0.0015% Er3+:Y2SiO5{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}Er3+:Y2​SiO5​, 0.005% Er3+:Y2SiO5{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}Er3+:Y2​SiO5​, and 0.02% Er3+:Y2SiO5{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}Er3+:Y2​SiO5​ crystals, respectively. The ggg-values for the lowest energy 4I15∕2^{4}I_{15∕2}4I15∕2​ (Z1)({\mathrm{Z}}_{1})(Z1​) and 4I13∕2^{4}I_{13∕2}4I13∕2​ (Y1)({\mathrm{Y}}_{1})(Y1​) doublets were measured to be 5.5 and 4.6 for site 1 and 15.0 and 12.9 for site 2 when the magnetic field was oriented along the crystal's ${\mathbit{D}}_{1}$ axis.
The mechanisms and effects of spectral diffusion for optical transitions of paramagnetic ions have been explored using the inhomogeneously broadened 1536 nm $^{4}\mathrm{I}_{15∕2}\ensuremath{\rightarrow}^{4}\mathrm{I}_{13∕2}$ transition in Er3+:Y2SiO5{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Er3+:Y2​SiO5​. Using photon echo spectroscopy, spectral diffusion was measured by observing the evolution of the effective coherence lifetimes over time scales from $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ to 20 ms for magnetic-field strengths from 0.3 to 6.0 T, temperatures from 1.6 to 6.5 K, and nominal Er3+{\mathrm{Er}}^{3+}Er3+ concentrations of 0.0015%, 0.005%, and 0.02%. To understand the effect of spectral diffusion on material decoherence for different environmental conditions and material compositions, data and models were compared to identify spectral diffusion mechanisms and microscopic spin dynamics. Observations were successfully modeled by ${\mathrm{Er}}^{3+}\ensuremath{-}{\mathrm{Er}}^{3+}$ magnetic dipole interactions and Er3+{\mathrm{Er}}^{3+}Er3+ electron spin flips driven by the one-phonon direct process. At temperatures of 4.2 K and higher, spectral diffusion due to 89Y^{89}\mathrm{Y}89Y nuclear spin flips was also observed. The success in describing our extensive experimental results using simple models provides an important capability for exploring larger parameter spaces, accelerating the design and optimization of materials for spatial-spectral holography, and spectral hole-burning devices. The broad insight into spectral diffusion mechanisms and dynamics is applicable to other paramagnetic materials, such as those containing Yb3+{\mathrm{Yb}}^{3+}Yb3+ or Nd3+{\mathrm{Nd}}^{3+}Nd3+.