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arXiv:2005.13626 · Optical Materials X

Demonstration of site-selective angular-resolved absorption spectroscopy of the 4 I 15 ∕ 2 → 4 I 13 ∕ 2 erbium transition in the monoclinic crystal Y 2 SiO 5

Yannick G. Petit, Benoı̂t Boulanger, Jérôme Debray, T. Chanelière

Published Aug 8, 2020• 7 citations
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Abstract

We study the angular dependence in polarized light of the optical absorption for the Er 3 + transition 4 I 15 ∕ 2 → 4 I 13 ∕ 2 in Y 2 SiO 5 , revealing thus the associated anisotropy and the orientation of the related absorption principal directions in the dielectric plan perpendicular to the monoclinic axis b. The measurements are performed at low temperature. This allows us to isolate the lowest crystal field levels in the ground and excited states. We spectrally resolve and independently characterize the two yttrium substitution sites in the Y 2 SiO 5 matrix. The absorption tensor components cannot be unambiguously determined yet while only considering the investigated dielectric plane. Still, measurements remarkably demonstrate that this transition of interest well resolved at low temperature is not only a magnetic-dipole allowed transition but indeed a hybrid electric–magnetic transition.

DOI
10.1016/j.omx.2020.100062

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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.

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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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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.

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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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Erbium ions in crystals show considerable promise for the technologies that will form the backbone of future networked quantum information technology. Despite advances in leveraging erbium's fibre-compatible infrared transition for classical and quantum applications, the transitions are, in general, not well understood. We present detailed absorption and laser site-selective spectroscopy of the C$_{\rm 3v}$(O$^{2-}$) centre in CaF$_2$:Er$^{3+}$ as an interesting erbium site case study. The $^{4}$I$_{15/2}$Z$_1 \rightarrow {^{4}}$I$_{13/2}$Y$_1$ transition has a low-temperature inhomogeneous linewidth of 1 GHz with hyperfine structure observable from the $^{167}$Er isotope. A parametrized crystal-field Hamiltonian is fitted to 34 energy levels and the two ground state magnetic splitting factors. The wavefunctions are used to perform a transition intensity analysis and electric-dipole parameters are fitted to absorption oscillator strengths. Simulated spectra for the $^{4}$I$_{11/2}\rightarrow {^{4}}$I$_{15/2}$ and $^{4}$I$_{13/2} \rightarrow {^{4}}$I$_{15/2}$ inter-multiplet transitions are in excellent agreement with the experimentally measured spectra. The $^{4}$I$_{13/2}$ excited state lifetime is 25.0\,ms and the intensity calculation is in excellent agreement with this value.

arXiv:2409.15622•Sep 23, 2024•0 citations
We study the angular dependence in polarized light of the optical absorption for the Er 3 + transition 4 I 15 ∕ 2 → 4 I 13 ∕ 2 in Y 2 SiO 5 , revealing thus the associated anisotropy and the orientation of the related absorption principal directions in the dielectric plan perpendicular to the monoclinic axis b. The measurements are performed at low temperature. This allows us to isolate the lowest crystal field levels in the ground and excited states. We spectrally resolve and independently characterize the two yttrium substitution sites in the Y 2 SiO 5 matrix. The absorption tensor components cannot be unambiguously determined yet while only considering the investigated dielectric plane. Still, measurements remarkably demonstrate that this transition of interest well resolved at low temperature is not only a magnetic-dipole allowed transition but indeed a hybrid electric–magnetic transition.
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.
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.
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.
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.
Spectroscopy, Crystal-Field, and Transition Intensity Analyses of the C3v_{\rm 3v}3v​(O2−^{2-}2−) Centre in Er3+^{3+}3+ Doped CaF2_{2}2​ Crystals
Erbium ions in crystals show considerable promise for the technologies that will form the backbone of future networked quantum information technology. Despite advances in leveraging erbium's fibre-compatible infrared transition for classical and quantum applications, the transitions are, in general, not well understood. We present detailed absorption and laser site-selective spectroscopy of the C3v_{\rm 3v}3v​(O2−^{2-}2−) centre in CaF2_22​:Er3+^{3+}3+ as an interesting erbium site case study. The 4^{4}4I15/2_{15/2}15/2​Z1→4_1 \rightarrow {^{4}}1​→4I13/2_{13/2}13/2​Y1_11​ transition has a low-temperature inhomogeneous linewidth of 1 GHz with hyperfine structure observable from the 167^{167}167Er isotope. A parametrized crystal-field Hamiltonian is fitted to 34 energy levels and the two ground state magnetic splitting factors. The wavefunctions are used to perform a transition intensity analysis and electric-dipole parameters are fitted to absorption oscillator strengths. Simulated spectra for the 4^{4}4I11/2→4_{11/2}\rightarrow {^{4}}11/2​→4I15/2_{15/2}15/2​ and 4^{4}4I13/2→4_{13/2} \rightarrow {^{4}}13/2​→4I15/2_{15/2}15/2​ inter-multiplet transitions are in excellent agreement with the experimentally measured spectra. The 4^{4}4I13/2_{13/2}13/2​ excited state lifetime is 25.0\,ms and the intensity calculation is in excellent agreement with this value.