Quantum Model Cuts Parameters in Erbium-Doped GdVO4 Optical Spectrum

Researchers have developed a new model detailing how erbium ions interact within a gadolinium vanadate crystal, revealing that each erbium ion directly couples to its four nearest gadolinium neighbors. This cluster-based approach, detailed in a recent paper, moves beyond previous models by explicitly accounting for this immediate interaction and utilizing fewer parameters to describe the system’s complex optical spectrum. The work demonstrates that the model successfully captures the most important interactions within the Er:GdVO4 crystal, suggesting its potential for predicting microwave-to-optical transduction in future experiments. This improved understanding of rare-earth dopants builds on recent findings showing magnetically ordered crystals can provide a quiet environment for long optical coherence times. Measurements of the magnons in GdVO4 suggest that at zero applied field, the magnon frequency is 30.61 GHz, well within the microwave regime. The gadolinium vanadate structure has an easy axis, where spins prefer to align. Er-Gd and Gd-Gd exchange interactions (J and I) are central to the model. Masaya Hiraishi is now at Basic Research Laboratories, NTT, Inc. Zachary H. Roberts is one of the authors of the paper.

Er:GdVO4 Crystal Structure and Magnetic Ordering

Unlocking Microwave-Optical Links with Crystal Structure The precise arrangement of atoms within the Er:GdVO₄ crystal dictates its potential as a crucial component in future quantum technologies, with new modeling revealing a surprisingly direct interplay between erbium and its gadolinium neighbors. Researchers have moved beyond previous theoretical approaches by detailing how each erbium ion is directly coupled to four nearest gadolinium ions, a connection not previously included in simpler models. The significance of this proximity lies in the material’s magnetic properties. Gadolinium vanadate is antiferromagnetic, ordering below a Néel temperature of K. This magnetic order isn’t simply a background effect; the new model demonstrates that the erbium ions actively participate in this ordering through direct Er-Gd and Gd-Gd exchange interactions. The Hamiltonian for this system incorporates these interactions.

This detailed consideration of local interactions, combined with the broader mean field of the crystal, allows for a more accurate prediction of the material’s optical spectrum. The refined model achieves its accuracy using fewer parameters than its predecessors. Previous attempts to model the optical spectrum of Er:GdVO₄ relied on adjustments to account for the gadolinium spin lattice, but did not include excitations of the gadolinium spin lattice. By directly incorporating the nearest-neighbor gadolinium ions into the core Hamiltonian, the new model streamlines the fitting process and offers a more physically intuitive representation of the system. This improved understanding has implications beyond academic research.

The ultimate goal is to enhance microwave-to-optical transduction, a process vital for linking quantum information stored in microwave frequencies to optical frequencies for long-distance transmission. Er:GdVO₄, with its long optical coherence times and potential for strong coupling between magnons and rare-earth ions, is a promising candidate for this task. Measurements of the magnons in GdVO₄ suggest that at zero applied field, the magnon frequency is 30.61 GHz, well within the microwave regime.

Rare-Earth Ion Interactions in Antiferromagnetic Hosts

The pursuit of robust quantum technologies increasingly focuses on solid-state materials, specifically crystals doped with rare-earth ions, due to their potential for long coherence times and efficient microwave-to-optical transduction. Recent advances move beyond simply embedding these ions within a host lattice; instead, researchers are meticulously modeling the complex interplay between the rare-earth ion and its immediate magnetic environment. A new cluster-based model, focusing on erbium-doped gadolinium vanadate (Er:GdVO₄), details how erbium ions interact with surrounding gadolinium ions, offering a more accurate representation of the system than previous approaches. This work builds on findings demonstrating magnetically ordered crystals provide a quieter environment for sensitive quantum states. Central to this refined understanding is the explicit consideration of interactions between the erbium ion and its nearest neighbors, as well as interactions between the gadolinium ions.

This direct coupling, illustrated in accompanying diagrams, highlights the erbium ion surrounded by its four red-labeled gadolinium neighbors and the surrounding mean field of white gadolinium ions. The team’s Hamiltonian incorporates an Er-Gd exchange interaction (J) and a Gd-Gd exchange interaction (I), quantifying the energy coupling between the erbium and each of these immediate gadolinium neighbors. The authors write, “We build upon the model developed in Ref. [17] by considering an erbium ion directly interacting with its four nearest neighbor gadolinium ions, forming a cluster of five atoms,” emphasizing the shift towards a more localized, detailed approach. The structure has an easy axis, influencing the erbium’s energy levels. Importantly, this improved model achieves its accuracy with a reduced number of parameters compared to its predecessors. The current model streamlines this process, utilizing parameters with clearer physical origins, suggesting a more intuitive and efficient representation of the system. The researchers also incorporated the dynamic mean field created by the bulk of the gadolinium crystal, extending the model’s applicability to scenarios involving external magnetic fields and phase transitions in magnetic ordering.

Researchers at Basic Research Laboratories at NTT, Inc. in Japan note that Masaya Hiraishi is now with their organization. A cluster-based model has been developed by a team including Zachary H. Roberts at the University of Otago in New Zealand that moves beyond previous approaches by directly coupling an erbium ion to its four nearest neighbor gadolinium ions. The team’s work addresses a long-standing challenge in the field: accurately predicting the optical spectra of these doped crystals. The material has a Néel temperature of K and an easy axis along the c-axis, where spins prefer to align. The model describes Er-Gd and Gd-Gd exchange interactions (J and I, respectively).

Optical Spectrum Analysis of Er:GdVO4

Recent work with rare-earth doped crystals, specifically erbium-doped gadolinium vanadate (Er:GdVO₄), offers a promising avenue for achieving effective microwave-to-optical transduction systems. Researchers at Basic Research Laboratories at NTT, Inc. are now refining models to accurately predict and ultimately enhance the optical properties of these materials, moving beyond representations of rare-earth ion behavior. Zachary H. Roberts, Masaya Hiraishi, Luke S. Trainor, and Jevon J. Longdell developed a cluster-based model to describe erbium ions doped into a gadolinium vanadate (Er:GdVO₄) host crystal, wherein the erbium ion couples directly to its four nearest neighbor gadolinium ions, which in turn couple to the mean field of the rest of the crystal.

This detailed interaction, a departure from earlier models that did not include excitations of the gadolinium spin lattice, considers the erbium ion surrounded by its immediate environment, acknowledging that the crystal’s magnetic properties significantly influence the rare-earth dopant’s behavior. The researchers also considered the antiferromagnetic ordering of the gadolinium vanadate, acknowledging that the crystal’s structure has an easy axis and plays a critical role in suppressing spin flips and extending optical coherence times.

Mean Field Approach to Gadolinium Spin Configuration

The pursuit of stable quantum states often hinges on minimizing environmental noise, a challenge researchers are addressing through increasingly sophisticated material models. While conventional approaches adequately describe individual rare-earth ions within a crystal lattice, accurately capturing the complex interplay between these ions and their surroundings has proven elusive until now. This refined model centers on the understanding that an erbium ion isn’t isolated, but directly coupled to its four nearest gadolinium neighbors within the GdVO₄ crystal structure. This direct interaction forms the core of a “cluster” that then interacts with the broader magnetic field generated by the remaining gadolinium ions. The team’s approach builds on prior work, but significantly expands the scope of interaction considered. Crucially, this new model achieves its accuracy with streamlined computational efficiency. This is achieved by treating the gadolinium lattice as having two sublattices, aligning parallel and antiparallel to the crystal’s easy axis.

The structure has an easy axis. The Hamiltonian for this system, detailed in the paper, accounts for Er-Gd exchange interaction (J) and Gd-Gd exchange interaction (I), alongside the erbium-gadolinium interactions. The ultimate goal of this detailed modeling isn’t purely academic; it’s to enhance microwave-to-optical transduction, converting information between these different wavelengths, a vital step in building more powerful quantum technologies. The success of the model in matching experimental data suggests its potential for predicting and optimizing the optical properties of Er:GdVO₄.