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arXiv:2610.13664

Judd-Ofelt analysis and coherent spectroscopy of europium-based molecular complexes for quantum information applications

Nicholas Lester Jobbitt, Sascha Weis, Timo Schweizer, Vishnu Unni Chorakkunnath, Evgenij Vasilenko, Tobias Haas, Barbora Brachnakova, Senthil Kumar Kuppusamy, Hartmut Schubert, Mario Ruben, Michael Seitz, David Hunger

quant-phphysics.opticsSubmitted Oct 9, 2026• Announced Oct 12, 2026• 0 citations
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Abstract

Rare-earth-ion based molecular crystals are emerging as a promising platform for quantum information applications, combining long optical coherence times with the chemical tunability of coordination chemistry. Here we present a comprehensive optical characterisation of twelve Eu$^{3+}$-based molecular complexes, with a focus on the coherent $^{5}\text{D}_{0} \longrightarrow \ ^{7}\text{F}_{0}$ transition at $\sim$580 nm. Judd-Ofelt analyses are performed across all complexes, providing insights into ligand-field environments, local point-group symmetries, and the resulting branching ratios of the coherent transition. We find that lower point-group symmetry (C$_1$, C$_2$) yields higher branching ratios of the $^{5}\text{D}_{0} \longrightarrow \ ^{7}\text{F}_{0}$ transition, exceeding 1\% in several complexes. Optical inhomogeneous linewidths measured at 4.2 K reveal narrow linewidths for some complexes of below ten GHz, indicative of a highly ordered crystalline environment. Optical coherence measurements of one of the complexes, 5-Eu, yields an optical coherence time of $T_{\text{2}}^{\text{opt}} = 2.3~μ\mathrm{s}$ at 4.2 K, comparable to the best-performing molecular systems reported to date. Systematic characterisation and quantitative comparison will be key to find structure-property relations guiding rational design of optimised complexes for quantum information applications.

Comments
12 pages, 8 Figures

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Rare-earth-ion based molecular crystals are emerging as a promising platform for quantum information applications, combining long optical coherence times with the chemical tunability of coordination chemistry. Here we present a comprehensive optical characterisation of twelve Eu3+^{3+}3+-based molecular complexes, with a focus on the coherent 5D0⟶ 7F0^{5}\text{D}_{0} \longrightarrow \ ^{7}\text{F}_{0}5D0​⟶ 7F0​ transition at ∼\sim∼580 nm. Judd-Ofelt analyses are performed across all complexes, providing insights into ligand-field environments, local point-group symmetries, and the resulting branching ratios of the coherent transition. We find that lower point-group symmetry (C1_11​, C2_22​) yields higher branching ratios of the 5D0⟶ 7F0^{5}\text{D}_{0} \longrightarrow \ ^{7}\text{F}_{0}5D0​⟶ 7F0​ transition, exceeding 1% in several complexes. Optical inhomogeneous linewidths measured at 4.2 K reveal narrow linewidths for some complexes of below ten GHz, indicative of a highly ordered crystalline environment. Optical coherence measurements of one of the complexes, 5-Eu, yields an optical coherence time of T2opt=2.3 μsT_{\text{2}}^{\text{opt}} = 2.3~μ\mathrm{s}T2opt​=2.3 μs at 4.2 K, comparable to the best-performing molecular systems reported to date. Systematic characterisation and quantitative comparison will be key to find structure-property relations guiding rational design of optimised complexes for quantum information applications.
Comparative Optical Spectroscopy of Er3+^{3+}3+, Tm3+^{3+}3+, and Eu3+^{3+}3+ Molecular Complexes at Cryogenic Temperature
Rare-earth molecular complexes are attracting increasing interest for quantum information applications because of their structural flexibility and chemical tunability. Here, we compare the cryogenic optical properties of Er3+^{3+}3+, Tm3+^{3+}3+, and Eu3+^{3+}3+ complexes in the same ligand environment. Optical spectroscopy shows differing behavior across the three systems: spectral hole burning is observed in the Eu3+^{3+}3+ complex, whereas no measurable hole is detected in the Er3+^{3+}3+ and Tm3+^{3+}3+ complexes. We measure laser-induced local heating and rethermalization in the Er3+^{3+}3+ and Tm3+^{3+}3+ powder-like samples, observing strong local heating and slow thermal relaxation in the cold-plate cryostat. The recovery occurs over several seconds and, for some Er3+^{3+}3+ excitation conditions, extends over tens of seconds. The comparison across the three ions nevertheless suggests that heating alone is unlikely to account for the full contrast. Rather, the different behaviors of Eu3+^{3+}3+, Tm3+^{3+}3+, and Er3+^{3+}3+ point to ion-dependent relaxation and decoherence processes associated with their electronic level structure and coupling to the molecular environment. Temperature-dependent linewidth and line-shift measurements are further consistent with phonon-mediated broadening through coupling to crystal-field levels.
The success of the emerging field of solid-state optical quantum information processing (QIP) critically depends on the access to resonant optical materials. Rare-earth ions (REIs) are suitable candidates for QIP protocols due to their extraordinary photo-physical and magnetic quantum properties such as long optical and spin coherence lifetimes (T2T_2T2​). However, molecules incorporating REIs, despite having advantageous properties such as atomically exact quantum tunability, inherent scalability, and large portability, have not yet been studied for QIP applications. As a first testimony of the usefulness of REI molecules for optical QIP applications, we demonstrate in this study that narrow spectral holes can be burned in the inhomogeneously broadened 5^55D0→7_0\to^70​→7F0_00​ optical transition of a binuclear Eu(III) complex, rendering a homogeneous linewidth (ΓhΓ_hΓh​) = 22 ±\pm± 1 MHz, which translates as T2=14.5T_2 = 14.5T2​=14.5 ±\pm± 0.7 ns at 1.4 K. Moreover, long-lived spectral holes are observed, demonstrating efficient polarization of Eu(III) ground state nuclear spins, a fundamental requirement for all-optical spin initialization and addressing. These results elucidate the usefulness of REI-based molecular complexes as versatile coherent light-spin interfaces for applications in quantum communications and processing.
Controlled ion-ion interactions and cavity-enhanced emission of a coherent dinuclear Eu3+^{3+}3+ complex
Molecular rare-earth-ion complexes offer unique opportunities for quantum technologies by combining the intrinsic coherence properties of rare-earth ions with chemically tunable molecular environments. A crucial capability is the realization of multi-qubit architectures with defined qubit couplings to enable two-qubit quantum gates. Here, we investigate the optical coherence properties and excitation-induced interactions of two Eu3+^{3+}3+-based molecular complexes, comparing a mononuclear reference system with a dinuclear analogue in which two Eu3+^{3+}3+ ions are positioned at a well-defined intramolecular distance of about 7 Angstrom. Using cryogenic ensemble spectroscopy, including spectral hole burning, free-induction decay, and photon echo measurements at temperatures down to 100 mK, we demonstrate long optical coherence times T2,oT_{2,\text{o}}T2,o​ of up to 9 μμμs. As a key step toward scalable multi-qubit architectures, a control-target sequence was implemented to probe conditional ion-ion interactions, revealing a stronger interaction-induced dephasing in the dinuclear complex. Finally, we show the integration of the dinuclear complex into a fiber-based optical microcavity, and observe an 380-fold emission enhancement of the 5D0→7F0\mathrm{}^5\mathrm{D}_0\rightarrow\mathrm{}^7\mathrm{F}_05D0​→7F0​ transition. Together, these results position molecular rare-earth complexes as versatile and chemically tunable building blocks for scalable quantum technologies.
We report the optical study of europium nitrate hexahydrate crystals Eu(NO 3 ) ⋅ 3 6H 2 O and their deuterated version Eu(NO 3 ) ⋅ 3 6D 2 O conducted at 50 mK. The crystals show sub-GHz inhomogeneous linewidths for the F 0 7 ↔ 5 D 0 transition and optical coherence times up to 136 μs for the non-deuterated crystal and 750 μs for the deuterated one. In addition, using the spectral hole burning technique, the hyperfine splittings in the absence of an external field have been estimated for the ground and optical levels. These results suggest that rare-earth nitrate crystals could represent a promising class of materials for quantum information applications as well as for fundamental physics experiments requiring narrow optical transitions and good coherence properties. • Deuterated and non-deuterated europium nitrate crystals were grown using the slow-cooling method. • Optical coherence times up to 0.75 ms were measured at 50 mK using the photon echo technique. • Sub-GHz optical inhomogeneous linewidths were observed. • The hyperfine splittings of the ground and optical states were assessed via spectral hole burning.
Chemical substitution o!ers a powerful route to tune molecular quantum materials, but its e!ects on optical decoherence extend beyond the simple dilution of interacting emitters; here, we investigate these e!ects in the molecular crystal [Eu(III)(TMHD)3(phen)], its dilution series in the isostructural host [Y(TMHD)3(phen)], and a partially deuterated analogue. The optical inhomogeneous linewidth of the 7F0 ↔ 5D0 transition near 580.4 nm exhibits a pronounced concentration dependence, ranging from 6 to 20 GHz, while the transition frequency shifts by up to ↗25 GHz across the dilution series. In contrast, the homogeneous linewidth measured by two-pulse photon echoes remains in the 50–130 kHz regime at 1.4 K, and shows a non-monotonic dependence on Eu(III) content. Partial phenanthroline deuteration also leaves the homogeneous linewidth essentially unchanged. Spectral-di!usion and temperature-dependent photon-echo measurements identify non-magnetic fluctuations of the molecular environment as the dominant residual dephasing channel. In contrast to rigid inorganic rare-earth hosts, the molecular crystal lattice supports low-frequency lattice modes that can dynamically modulate the anisotropic Eu(III) crystal field, while the extrapolated zero-temperature linewidth is most likely limited by electric-field perturbations. These results establish Eu(III) molecular crystals as chemically tunable materials with robust optical coherence and show that chemical dilution simultaneously reshapes static disorder, lattice dynamics, and decoherence, identifying molecular-lattice rigidity and electrostatic stability as central design parame-
Rare-Earth (RE) atoms possess a unique atomic energy level structure, leading to excellent electronic and spin coherence properties [1]. Consequently, RE-ion-doped materials are promising candidates for implementing light-matter interfaces for photonic quantum technologies, such as quantum memories. To exploit these properties in quantum technologies, the REs must be hosted in a solid-state material [1]. RE organic molecular crystals offer advantages over the well-known RE-doped inorganic crystals. In organic molecular crystals, RE ions are integral parts of the molecular structure, unlike in inorganic crystals, in which the RE ions are distributed randomly into the crystal lattice structure. This can potentially lead to narrower inhomogeneous broadening. These crystals provide unmatched flexibility in combining with photonic structures and in material composition, allowing the choice of different ligands and point group symmetries around the RE ion [2], [10], [4]. Our research focuses on crystals formed from a molecular complex hosting erbium ions⌈Er(C5H7O2)3(C12H8N2)⌉\lceil{E}r(C_{5}H_{7}O_{2})_{3}(C_{12}H_{8}N_{2})\rceil⌈Er(C5​H7​O2​)3​(C12​H8​N2​)⌉. As these crystals have not yet been studied for quantum information purposes, we conducted a series of optical spectroscopy measurements to characterize the platform. We performed absorption measurements and obtained the absorption profiles at room and cryogenic temperatures. The results show a narrow inhomogeneous broadening in samples with different relative concentrations, even at 100%, for which all molecules contain an erbium ion. We measured the lifetime of the second lowest crystal field level of the ground state manifold(30 cm−1(\boldsymbol{30}\ cm^{-1}(30 cm−1above ground state) to be 1.759 seconds. Additionally, we measured the inhomogeneous broadening of the lowest crystal field level versus temperature to investigate the effects of phonon processes. Finally, under an external magnetic field, we observed Zeeman splitting and determined the g-factor to be 3.23 for erbium ions in this molecular complex.