🔬 materials science

Coupling between CaWO $_4$ phonons and Er $^{3+}$ dopants

This study uses inelastic neutron scattering and density-functional perturbation theory to characterize the phonon dispersion of $\text{CaWO}_4$ and identify specific Raman-active modes, such as a 9.1 meV $B_g$ mode, that couple to $\text{Er}^{3+}$ ions and influence spin-lattice relaxation in quantum memory applications.

Original authors: Mikhael T. Sayat, Federico Pisani, Hin Lok Chang, Yaroslav Zhumagulov, Kirrily C. Rule, Tom Fennell, Jakob Nunnendorf, Chee Kwan Gan, Oleg V. Yazyev, Ping Koy Lam, Jian-Rui Soh

Published 2026-02-10

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CC BY 4.0

Original authors: Mikhael T. Sayat, Federico Pisani, Hin Lok Chang, Yaroslav Zhumagulov, Kirrily C. Rule, Tom Fennell, Jakob Nunnendorf, Chee Kwan Gan, Oleg V. Yazyev, Ping Koy Lam, Jian-Rui Soh

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Quantum "Noise" Problem: Tuning the Orchestra of Atoms

Imagine you are trying to record a very delicate, beautiful violin solo in the middle of a busy city. Even if you have the best violin in the world (the Erbium ion) and a perfect recording studio (the CaWO4 crystal), your recording will be ruined if the city's traffic, construction, and wind keep vibrating the building.

In the world of quantum computing, scientists are trying to use tiny atoms called Erbium to store information. These atoms are like our "violin solo"—they are incredibly precise and hold quantum data perfectly. But there is a problem: the crystal they live in isn't perfectly still. It is constantly vibrating. These vibrations are called phonons.

This paper is essentially a "noise map" that helps scientists understand exactly what kind of "traffic noise" is shaking their quantum violin.

1. The Map: Finding the "Traffic" (Phonons)

The researchers wanted to know every single way the CaWO4 crystal can vibrate. They used two high-tech methods:

Computer Simulations: Like using a flight simulator to predict how a plane moves.
Neutron Scattering: Like throwing tiny, high-speed marbles (neutrons) at a structure and watching how they bounce off to see where the "wobbles" are.

By doing this, they created a complete map of the crystal's vibrations, ranging from low-energy "rumbles" to high-energy "shouts."

2. The Culprit: The "Bad" Vibrations

Not all vibrations are equal. Some are just background hums, but others are "resonant"—meaning they hit the Erbium atom at just the right frequency to knock it out of its quantum state. This is like a heavy truck driving by your house at the exact frequency that makes your windows rattle and crack.

The researchers used math (symmetry analysis) to figure out which specific vibrations are the "window-rattlers." They identified eight specific modes that are most likely to interfere with the Erbium.

One specific vibration, a low-energy mode at 9.1 meV, was flagged as a major troublemaker. This is the "heavy truck" that is most likely to cause the quantum information to "leak" out and disappear.

3. The Solution: Phononic Engineering

Now that they know which "trucks" are causing the trouble, how do they fix it? They can't just tell the trucks to stop driving, so they have to change the "road."

The paper suggests Phononic Engineering. This is like building a soundproof room or a specialized highway to manage the noise:

Nanostructuring: They could carve the crystal into tiny, microscopic shapes (like a sponge or a lattice) that physically prevent those specific 9.1 meV vibrations from traveling through the material. It’s like building a "silence zone" around the violin.
Heat Management: They also suggest building tiny "cooling pipes" (waveguides) into the crystal to whisk away the heat and vibration before they can disturb the Erbium.

Why does this matter?

To build a global "Quantum Internet," we need quantum memories that can hold onto information for a long time without it decaying. This paper provides the blueprints for building a quieter, more stable home for quantum information. By understanding the "noise" of the crystal, we can finally learn how to silence it.

Technical Summary: Coupling between $\text{CaWO}_4$ Phonons and $\text{Er}^{3+}$ Dopants

Problem Statement

The development of scalable quantum networks requires long-lived quantum memories. Rare-earth-ion-doped crystals, specifically erbium ( $\text{Er}^{3+}$ ), are leading candidates because their optical transitions ( $\sim 1.5\,\mu\text{m}$ ) are compatible with existing telecommunications infrastructure. However, a major limiting factor for the coherence and storage time of these quantum states is spin-lattice relaxation.

While magnetic noise can be suppressed via specific techniques (e.g., zero first-order Zeeman conditions), lattice vibrational noise (phonons) is an intrinsic property of the host crystal. Specifically, the "direct process"—the resonant absorption or emission of a single phonon—persists even at millikelvin temperatures, setting an upper bound on coherence. To mitigate this, one must identify the specific phonon modes that couple to the $\text{Er}^{3+}$ crystal-field manifold to enable "phononic engineering" (e.g., creating phonon band gaps). Previous studies were limited by either being restricted to the zone center ( $\Gamma$ -point) via optical spectroscopy or lacking the energy range/momentum resolution to map the full Brillouin zone.

Methodology

The researchers employed a dual approach combining computational modeling and advanced experimental scattering:

Computational Modeling: They used Density-Functional Perturbation Theory (DFPT) via the QUANTUM ESPRESSO package. They employed norm-conserving pseudopotentials within the Local Density Approximation (LDA) to calculate the full phonon dispersion across the Brillouin zone.
Experimental Mapping: To validate the theory, they performed Inelastic Neutron Scattering (INS) on high-quality $\text{CaWO}_4$ $CaWO_{4}$ single crystals.
- Low-energy modes (2–60 meV): Measured using the EIGER triple-axis spectrometer at SINQ (PSI), Switzerland.
- High-energy modes (80–130 meV): Measured using the Taipan spectrometer at ANSTO, Australia.
Symmetry Analysis: They performed group-theoretical analysis to determine which phonon eigenmodes (based on their irreducible representations) could linearly couple to the $\text{Er}^{3+}$ crystal-field (CEF) operators under the local $S_4$ site symmetry.

Key Contributions

Comprehensive Phonon Mapping: Provided the first complete experimental and theoretical mapping of the $\text{CaWO}_4$ phonon spectrum, spanning from low-energy acoustic modes to high-energy optical branches across the full Brillouin zone.
Symmetry-Based Coupling Identification: Identified the specific Raman-active phonon modes that are symmetry-allowed to couple directly to the $\text{Er}^{3+}$ crystal-field manifold.
Microscopic Framework: Established a theoretical basis for understanding how lattice vibrations drive decoherence in $\text{Er}^{3+}$ -doped scheelite structures.

Results

Phonon Dispersion: The phonon bands extend up to $130\,\text{meV}$ , with a distinct phonon band gap between $60$ and $80\,\text{meV}$ . The experimental INS data showed excellent agreement with DFPT calculations, with slight energy softening observed in experiments due to anharmonic effects at $200\,\text{K}$ compared to $0\,\text{K}$ calculations.
Coupling Modes: The symmetry analysis identified eight Raman-active modes capable of direct coupling to $\text{Er}^{3+}$ $Er^{3 +}$ :
- Three $A_g$ modes (coupling to axial operators $O_k^0$ ).
- Five $B_g$ modes (coupling to fourfold operators $O_k^4$ ).
Critical Mode: A low-energy $B_g$ mode at $9.1\,\text{meV}$ was identified as a dominant contributor to phonon-assisted spin-lattice relaxation.

Significance

This work provides the "blueprints" for phononic engineering in $\text{Er}^{3+}:\text{CaWO}_4$ quantum memories. By understanding exactly which modes cause decoherence, researchers can now pursue two specific engineering pathways:

Nanostructuring: Creating phononic crystals to induce band gaps at specific frequencies (e.g., shifting the $9.1\,\text{meV}$ mode) to suppress the local density of states available for relaxation.
Thermal/Optical Management: Utilizing the natural $60\text{--}80\,\text{meV}$ phonon gap to design waveguides that guide optical modes while minimizing phonon-induced heating, thereby allowing higher repetition rates and more intense control pulses for quantum operations.