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Mechanical loss and stability analysis of NEXCERA in ultra-stable optical cavities

This study demonstrates that the ceramic material NEXCERA is a highly promising candidate for ultra-stable optical cavities by measuring its low mechanical loss at room temperature and showing that its resulting thermal noise performance rivals or exceeds that of established materials like ULE and Zerodur.

Original authors: Nico Wagner, Mateusz Narożnik, Marcin Bober, Steffen Sauer, Michał Zawada, Stefanie Kroker

Published 2026-03-27

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CC BY 4.0

Original authors: Nico Wagner, Mateusz Narożnik, Marcin Bober, Steffen Sauer, Michał Zawada, Stefanie Kroker

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

Imagine you are trying to build the world's most perfect ruler. Not a ruler made of plastic or metal that expands in the heat or shrinks in the cold, but a ruler so precise it can measure changes smaller than the width of an atom. Scientists use these "rulers" (called ultra-stable optical cavities) to keep time for atomic clocks, detect gravitational waves from colliding black holes, and test the fundamental laws of the universe.

However, there's a problem: even the best rulers vibrate. They shake due to the heat of the room itself (a phenomenon called Brownian thermal noise). If the ruler shakes too much, your measurements become blurry.

This paper is about testing a new material called NEXCERA to see if it can make a better, quieter ruler than the ones we use today.

Here is the story of their discovery, broken down simply:

1. The Problem: The "Shaky" Ruler

Think of the cavity as a hallway with two mirrors at the ends. A laser bounces back and forth between them. To keep the laser's frequency (its "pitch") perfectly stable, the distance between the mirrors must never change.

The Spacer: The thing holding the mirrors apart is called a "spacer."
The Old Guard: For years, scientists have used special glass materials like ULE and Zerodur. They are great because they don't expand much when the temperature changes.
The New Contender: NEXCERA is a ceramic material. It's like a super-stiff, high-tech ceramic tile. It doesn't expand much, and it's much stiffer (harder to bend) than glass. But, nobody knew if it was "quiet" enough. Does it vibrate less than glass?

2. The Experiment: The "Gentle Nod"

To find out if NEXCERA is quiet, the scientists had to measure its mechanical loss.

The Analogy: Imagine you have a bell. If you hit it, it rings for a long time. If the bell is made of a "lossy" material (like rubber), it stops ringing quickly because the energy turns into heat. If it's made of a "low-loss" material (like high-quality steel), it rings for a very long time.
The Challenge: Measuring this is hard. If you hold the bell with your hand, your hand absorbs the vibration, and you get a wrong answer.
The Solution: The scientists used a technique called "Gentle Nodal Suspension." Imagine balancing a spinning top on the very tip of a needle. They balanced tiny disks of NEXCERA on a tiny steel ball, letting gravity hold them in place without touching the sides. This way, the only thing stopping the vibration was the material itself, not the holder.

3. The Results: A Quiet Champion

They tapped the NEXCERA disks and listened to how they "rang."

The Score: They found that NEXCERA has a mechanical loss of 1.89 × 10⁻⁵.
The Comparison:
- Zerodur (Old Glass): Very "noisy" (high loss).
- ULE (Standard Glass): Very quiet.
- NEXCERA (New Ceramic): Almost as quiet as ULE, but slightly better in some ways.
The Big Win: Because NEXCERA is so much stiffer (like a steel beam vs. a rubber band), it resists vibrations even better than the glass, even though its "ringing" quality is similar.

4. The Future: Building the Ultimate Ruler

The scientists then did some math to predict how a real laser cavity would behave if built with NEXCERA.

The Prediction: A cavity using NEXCERA would be twice as quiet (less thermal noise) than one using the current best glass (ULE).
The Mirror Trick: They also realized that the mirrors themselves matter. If you pair the NEXCERA spacer with mirrors made of Fused Silica (a very pure glass) instead of ULE, the whole system becomes even quieter.
Drift: They also checked if the material changes shape over time (aging). NEXCERA is very stable, meaning the ruler won't slowly get longer or shorter over the years.

Why Does This Matter?

Think of this like upgrading from a wooden ruler to a diamond ruler.

Current Tech: Good enough for most things, but limited by tiny vibrations.
NEXCERA Tech: Offers a path to even more precise measurements.

This new material could help scientists:

Build better atomic clocks (so precise they wouldn't lose a second in the age of the universe).
Detect gravitational waves with greater clarity.
Test Einstein's theories of gravity with extreme precision.
Search for dark matter or new particles that we can't see yet.

In a nutshell: The scientists proved that this new ceramic, NEXCERA, is incredibly stiff and quiet. It's a strong candidate to replace the glass materials we've used for decades, potentially leading to a new generation of scientific instruments that can see the universe with unprecedented clarity.

1. Problem Statement

Ultra-stable optical cavities are critical for precision metrology, including optical lattice clocks, gravitational wave detection, and fundamental physics tests. The ultimate sensitivity of these systems is limited by Brownian thermal noise arising from the mechanical loss (dissipation) of cavity components: mirror substrates, coatings, and the spacer.

Current Limitations: State-of-the-art cavities typically use Ultra-Low Expansion (ULE) glass or Zerodur® as spacer materials. While these have low coefficients of thermal expansion (CTE), their mechanical loss limits the thermal noise floor.
The Gap: NEXCERA, a ceramic developed by Krosaki Harima, offers ultra-low thermal expansion, high stiffness (Young's modulus of 140 GPa), and low linear drift. However, its mechanical loss ( $\phi$ ) had not been measured at room temperature. Without this value, the potential thermal noise performance of NEXCERA-based cavities could not be accurately predicted or compared to established materials.

2. Methodology

The authors employed a two-pronged approach: experimental measurement of mechanical loss and theoretical performance projection.

A. Experimental Measurement of Mechanical Loss

Technique: The study utilized the gentle nodal suspension technique to minimize extrinsic damping from the suspension system.
Setup:
- Three NEXCERA N117B disks (50.077 mm diameter, ~0.54 mm thickness) were suspended on a 4.5 mm steel sphere under high vacuum ( $10^{-7}$ mbar) to eliminate gas damping.
- Excitation: A non-contact comb electrode excited mechanical eigenmodes via a high-voltage amplifier (up to 800 V).
- Readout: A 635 nm laser diode and a quadrant photodetector (QPD) monitored the disk's oscillation amplitude and frequency.
Analysis: Mechanical loss ( $\phi$ ) was calculated from the spectral linewidth ( $\Delta f$ ) and resonance frequency ( $f_0$ ) using the relation $\phi = \Delta f / f_0$ . The team verified that measurements were independent of excitation voltage and accounted for surface roughness and suspension tilt effects.

B. Theoretical Performance Projection

Thermal Noise Modeling: Using the Fluctuation-Dissipation Theorem, the authors calculated the Brownian thermal noise and thermoelastic noise for a cavity with a NEXCERA spacer.
Comparisons: The performance was modeled against ULE and Zerodur spacers.
Mirror Substrate Analysis: The study evaluated the total cavity noise by combining the NEXCERA spacer with different mirror substrate options (ULE, Fused Silica, and Silicon) and crystalline coatings.

3. Key Contributions

First Mechanical Loss Measurement: This work provides the first experimental determination of the mechanical loss for NEXCERA N117B at room temperature.
Noise Floor Characterization: It establishes that NEXCERA's intrinsic mechanical loss is low enough to make the spacer's thermal noise contribution negligible compared to mirror substrates in standard configurations.
Design Optimization: The paper demonstrates that pairing NEXCERA spacers with Fused Silica (FS) mirror substrates yields superior thermal noise performance compared to the traditional NEXCERA/ULE combination.

4. Key Results

Mechanical Loss Measurements

Minimum Loss: The lowest measured mechanical loss was $\phi = 1.89 \times 10^{-5}$ at a resonance frequency of ~3.2 kHz.
Comparison:
- NEXCERA: $\approx 1.89 \times 10^{-5}$
- ULE: $\approx 1.6 \times 10^{-5}$ (slightly lower, but comparable)
- Zerodur: $\approx 3.2 \times 10^{-4}$ (significantly higher)
Variability: Variations up to 36% were observed across different disks and resonances, attributed to surface roughness and suspension conditions, but the minimum value represents the intrinsic material limit.
Thermoelastic Loss: Calculated to be negligible ( $< 1 \times 10^{-10}$ ) due to NEXCERA's low CTE.

Thermal Noise and Stability Projections

Spacer Performance: A cavity with a NEXCERA spacer exhibits Brownian thermal noise approximately two times lower than a ULE spacer and significantly lower than Zerodur. This is attributed to NEXCERA's high Young's modulus (140 GPa vs. 67.6 GPa for ULE).
Allan Deviation (ADEV): The projected ADEV for NEXCERA spacers is orders of magnitude lower than the previously reported experimental limit of $\sigma_y \approx 10^{-15}$ , suggesting that previous limitations were technical rather than fundamental.
Mirror Substrate Impact:
- Replacing ULE mirrors with Fused Silica (FS) or Silicon mirrors in a NEXCERA cavity improves total thermal noise by more than an order of magnitude.
- While Silicon offers the lowest noise, its high CTE at room temperature makes it less practical for room-temperature operation compared to Fused Silica, which offers a versatile balance of low loss and manageable CTE.

Drift Rate

NEXCERA exhibits a linear drift rate of $1.738 \times 10^{-17} \text{ s}^{-1}$ , which is lower than the best-reported ULE values ( $4.572 \times 10^{-17} \text{ s}^{-1}$ ) and significantly lower than Zerodur.

5. Significance and Conclusion

This study validates NEXCERA as a premier candidate for next-generation ultra-stable optical cavities.

Low Noise: Its combination of low mechanical loss and high stiffness ensures that the spacer does not limit the cavity's frequency stability, even when compared to the best ULE systems.
Long-Term Stability: The material's ultra-low drift rate and high stiffness make it ideal for experiments requiring long integration times, such as dark matter searches, tests of Lorentz invariance, and constraints on quantum fluctuations.
System Design: The findings suggest that future ultra-stable cavities should utilize NEXCERA spacers paired with Fused Silica mirror substrates to achieve the lowest possible thermal noise floor at room temperature.

In summary, NEXCERA overcomes the trade-off between thermal expansion and mechanical loss found in traditional materials, offering a robust path toward frequency references with stability approaching the fundamental limits of mirror coatings.