We report measurements of discrete excitation-induced frequency shifts on the $^{7}F_{0}\ensuremath{\rightarrow}^{5}D_{0}$ transition of the ${\mathrm{Eu}}^{3+}$ center in $\mathrm{La}\mathrm{\text{:}}\mathrm{Lu}\mathrm{\text{:}}{\mathrm{EuCl}}_{3}\ifmmode\cdot\else\textperiodcentered\fi{}6{\mathrm{D}}_{2}\mathrm{O}$ resulting from the optical excitation of neighboring ${\mathrm{Eu}}^{3+}$ ions. Shifts of up to $46.081\ifmmode\pm\else\textpm\fi{}0.005\text{ }\text{ }\mathrm{MHz}$ were observed. The magnitude of the interaction between neighboring ions was found to be significantly larger than expected from the electric dipole-dipole mechanism often observed in rare earth systems. We show that a large network of interacting and individually addressable centers can be created by lightly doping crystals otherwise stoichiometric in the optically active rare earth ion, and that this network could be used to implement a quantum processor with more than ten qubits.
We report measurements of discrete excitation-induced frequency shifts on the 7F0\ensuremath→5D0 transition of the Eu3+ center in La:Lu:EuCl3\ifmmode⋅\else\textperiodcentered\fi6D2O resulting from the optical excitation of neighboring Eu3+ ions. Shifts of up to 46.081\ifmmode±\else\textpm\fi0.005MHz were observed. The magnitude of the interaction between neighboring ions was found to be significantly larger than expected from the electric dipole-dipole mechanism often observed in rare earth systems. We show that a large network of interacting and individually addressable centers can be created by lightly doping crystals otherwise stoichiometric in the optically active rare earth ion, and that this network could be used to implement a quantum processor with more than ten qubits.
Abstract Doping erbium ions into europium-based hosts offers a promising platform for quantum repeater nodes, combining europium’s exceptional coherence properties for long-term quantum storage with erbium’s microwave compatibility and direct telecom-band emission for efficient optical interfacing. In this work, we investigated erbium-doped EuCl3 · 6H2O stoichiometric crystals as a candidate for such nodes. We demonstrate that erbium doping shifts the optical transition frequencies of nearby Eu3+ ions, producing well resolved satellite lines in the inhomogeneous absorption profile. We experimentally probe the coupling between Er3+ and Eu3+ ions under varying temperature and magnetic field conditions, quantifying the interaction strength, which ranges from tens to hundreds of kilohertz, depending on field orientation, magnitude, and the lattice position of the Eu3+ ions. At 60 mK and a moderate magnetic field of 0.1 T, we observed a strong frozen core effect from Er3+ spins, substantially extending the Eu3+ optical coherence time from 62 us to 162 us, approaching the lifetime limit, and enabling hour-long hyperfine state lifetimes. These results underscore the potential of dual-species rare-earth systems for photonic quantum technologies and highlight their promise for precise quantum control.
This thesis presents a spectroscopic study of the 7F0 ---t5D0 transition of Eu3+ in EuC13 ·6H2 0, which is used to evaluate the potential performance of a quantum com puting system implemented in EuCla·6H2 0 and, more generally, in stoichiometric rare earth crystals. EuC13 ·6H2 0 has one of the narrowest optical inhomogeneous linewidths of any solid but this linewidth is shown to be still much larger than that required for practical quantum computing in a rare earth crystal. To assess the possibility of reducing the linwidth, the contributions of isotopic impurities to both the optical linewidth and line structure were investigated, and ligand isotopes were identified as a major source of both inhomogeneous broadening and structure on the optical transition, suggesting that the linewidth could be substantially reduced by isotopi cally purifying EuC13 ·6H20. The effect of ligand isotopes on the optical lifetime and coherence time was also investigated. It was found that fully deuterating the crystal to EuC13·6D20 substantially improves both the lifetime and coherence time. The satellite lines formed in the optical spectrum of a rare earth crystal when it is doped with another rare earth are proposed as qubits. A crucial step in char acterising EuCla ·6H20 for quantum computing is associating these satellite lines in EuC13 ·6H2 0 with crystallographic sites. A new method for associating sites with lines, which works for low symmetry crystals such as EuC13·6H20, is presented. This method involves modelling the splitting of the ground state hyperfine levels caused by the magnetic dipole-dipole interaction between a Kramers dopant and the Eu3+ ion. Using this method, most of the outer satellite lines in rare earth doped EuCla·6H2 0 were assigned to crystallographic sites. It has been proposed that the electronic interactions between these satellite lines be used to enact two-qubit gates in a rare earth quantum computer. These interac tions were measured between a number of different satellite lines using a new two laser spectral holeburning technique. Interactions of up to 46.081±0.005 MHz were observed, and this was the first time that electronic interactions between weakly coupled rare earth ions had been measured. The two most common interactions identified between rare earth ions in solids are electric dipole-dipole and exchange, but the observed interactions are stronger than expected from a electric dipole-dipole model and occur at too large a distance to be superexchange. It is shown that the development of a moderate-sized quantum processor, one with more than 10 qubits, in a stoichiometric rare earth crystal is feasible provided that the optical inhomogeneous linewidth is reduced below 1MHz. Demonstrations of three or four qubit devices should be possible using existing materials.
We report a series of measurements of the effect of an electric field on the frequency of the ultranarrow linewidth F70→ D50 optical transition of Eu3+ ions in an Y2SiO5 matrix at cryogenic temperatures. We provide linear Stark coefficients along two dielectric axes and for the two different substitution sites of the Eu3+ ions, with an unprecedented accuracy and an upper limit for the quadratic Stark shift. The measurements, which indicate that the electric field sensitivity is a factor of seven larger for site 1 relative to site 2 for a particular direction of the electric field, are of direct interest in the context of both quantum information processing and laser frequency stabilization with rare-earth doped crystals, in which electric fields can be used to engineer experimental protocols by tuning transition frequencies.
We describe a method for creating small quantum processors in a crystal stoichiometric in an optically active rare-earth ion. The crystal is doped with another rare earth, creating an ensemble of identical clusters of surrounding ions, whose optical and hyperfine frequencies are uniquely determined by their spatial position in the cluster. Ensembles of ions in each unique position around the dopant serve as qubits, with strong local interactions between ions in different qubits. These ensemble qubits can each be used as a quantum memory for light, and we show how the interactions between qubits can be used to perform linear operations on the stored photonic state. We also describe how these ensemble qubits can be used to enact, and study, error correction.
Controlled ion-ion interactions and cavity-enhanced emission of a coherent dinuclear Eu3+ 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+-based molecular complexes, comparing a mononuclear reference system with a dinuclear analogue in which two Eu3+ 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,o of up to 9 μs. 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 transition. Together, these results position molecular rare-earth complexes as versatile and chemically tunable building blocks for scalable quantum technologies.
We identify and analyze dephasing mechanisms that broaden the optical transitions of rare-earth ions in randomly oriented transparent ceramics. The study examines the narrow $^{7}F_{0}\phantom{\rule{4pt}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{4pt}{0ex}}^{5}D_{0}$ transition of Eu3+ dopants in a series of Y2O3 ceramic samples prepared under varying conditions. We characterize the temperature and magnetic field dependence of the homogeneous linewidth, as well as long-term spectral diffusion on time scales up to 1 s. The results highlight significant differences between samples with differing thermal treatments and Zr4+ additive concentrations. In particular, several distinct magnetic interactions from defect centers are observed, which are clearly distinguished from the broadening due to interactions with two-level systems and phonons. By minimizing the broadening due to the different defect centers, linewidths of the order of 4 kHz are achieved for all samples. The linewidths are limited by temperature-dependent interactions and by an interaction that is yet to be identified. Although the homogeneous linewidth can be narrowed further in these ceramic samples, the broadening is now comparable to the linewidths achieved in rare-earth-ion--doped single crystals. Thus, this work emphasizes the usefulness of studying ceramics to gain insights into dephasing mechanisms relevant to single crystals and suggests that ceramics may be an interesting alternative for applications in classical and quantum information processing.