🔬 optics

Absolute Length Sensing in a Long-Baseline, High-Finesse Optical Cavity

This paper demonstrates a technique for continuously measuring the absolute length of a 123-meter high-finesse optical cavity with sub-micron precision by monitoring the phase offset of a second laser relative to a resonant first laser, thereby enabling the detection of transient seismic events and earth tides with a strain sensitivity of $10^{-10} \, - \, 10^{-9}$ m/m.

Original authors: Todd Kozlowski, Henry Frädrich, Aaron D. Spector

Published 2026-06-09

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CC BY 4.0

Original authors: Todd Kozlowski, Henry Frädrich, Aaron D. Spector

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 have a giant, super-reflective hallway made of mirrors, stretching 123 meters long (about the length of a football field). This hallway is part of a particle physics experiment called ALPS II, but the scientists in this paper decided to use it as an incredibly sensitive "ruler" to measure how the ground beneath it stretches and shrinks.

Here is how they did it, explained simply:

The "Tuning Fork" Trick

Normally, if you want to measure the length of a hallway, you might use a tape measure. But the ground moves too much for a tape measure to catch tiny shifts. Instead, the scientists used light.

Think of the hallway as a giant musical instrument, like a flute. When you blow air into a flute, it only makes a clear sound at specific notes (frequencies). If the flute gets slightly longer or shorter, that "perfect note" changes.

The scientists used two lasers (beams of light) acting like two singers:

Singer A (Laser 1): This singer is perfectly tuned to the hallway's current "note." They stay locked in perfect harmony with the hallway.
Singer B (Laser 2): This singer is tuned to a note that is a specific distance away from Singer A. They are singing a note that should also be a perfect match for the hallway, but only if the hallway stays exactly the same size.

The "Phase Shift" Clue

As long as the hallway stays the same size, both singers sound perfect. But, if the ground moves even a tiny bit (stretching or shrinking the hallway by less than the width of a human hair), the hallway's "perfect note" changes.

Singer A stays locked in because the scientists actively adjust them to follow the changing note.
Singer B, however, gets slightly "out of tune." Because they are no longer hitting the perfect note, the light they send through the hallway gets a little "delayed" or shifted in its timing (this is called a phase shift).

By measuring exactly how much Singer B is out of step compared to Singer A, the scientists can calculate exactly how much the hallway stretched or shrank. It's like noticing that a clock is running a fraction of a second slow and knowing exactly how much the temperature changed to cause that drift.

What They Found

Using this "laser ruler," they turned the particle physics tunnel into a super-sensitive seismometer. They caught three very different types of ground movements:

The Taylor Swift Effect (Anthropogenic Noise):
When Taylor Swift performed in a stadium just 1.1 km away, the ground didn't just shake; it danced. The scientists could see the exact rhythm of the concert. When the crowd jumped to a song with a fast beat, the ground vibrated at that same speed. They even noticed that the crowd's jumping patterns were so consistent that the seismic "fingerprint" of the concert was nearly identical on two different nights. It was as if the ground itself was keeping time with the music.
The Earthquake:
They detected a massive earthquake in Tibet, thousands of miles away. The signal from the earthquake arrived at their tunnel at the exact same moment it hit a standard seismometer nearby. The two recordings matched so perfectly (over 90% similarity) that it proved their laser ruler was just as good as traditional earthquake detectors at catching big, distant tremors.
The Moon's Pull (Earth Tides):
The Moon pulls on the Earth, causing the ground to stretch and squeeze like a rubber band twice a day. The scientists saw this slow, rhythmic breathing of the Earth in their data. Interestingly, because their tunnel is located at a specific latitude and runs East-West, the "stretch" caused by the Moon was almost zero (a natural "sweet spot" where the effect cancels out), which matched their scientific predictions perfectly.

Why This Matters

The paper concludes that they successfully turned a piece of high-tech particle physics equipment into a precise tool for measuring the Earth's movement. They didn't just measure big earthquakes; they measured the tiny vibrations of a concert crowd and the slow pull of the moon.

The authors note that while this worked well, they could make it even better in the future by making the hallway longer, using better mirrors, and controlling the temperature more strictly. But for now, they proved that a 123-meter laser tunnel can listen to the Earth's heartbeat with incredible precision.

Technical Summary: Absolute Length Sensing in a Long-Baseline, High-Finesse Optical Cavity

Problem Statement
Long-baseline Fabry-Perot cavities are traditionally utilized to measure relative length changes between mirrors, such as in gravitational wave detectors. However, obtaining continuous, absolute length measurements with sub-micron precision over long durations presents a challenge. While techniques exist using double modulation of resonant sidebands to determine absolute length, there is a need for methods that can continuously monitor absolute cavity length to detect transient seismic events, anthropogenic noise, and long-term earth tides without requiring complex dual-laser stabilization on the cavity itself.

Methodology
The authors present a technique for measuring the absolute length of a Fabry-Perot cavity using a phase-sensitive heterodyne readout in transmission. The method employs two continuous-wave lasers (1064 nm Nd:YAG):

Laser 1 (L1): Actively stabilized to the cavity resonance using a Pound-Drever-Hall (PDH) loop.
Laser 2 (L2): Phase-locked to L1 with a fixed frequency separation ( $f_{PLL}$ ) initially set to be an integer multiple ( $N$ ) of the cavity's Free Spectral Range (FSR, $f_0$ ).

As the cavity length ( $L$ ) changes, the FSR ( $f_0 = c/2L$ ) shifts. Consequently, L2 detunes slightly from resonance. This detuning induces a phase shift ( $\Delta\phi$ ) in the transmission of L2 relative to L1. The relative phase between the two lasers in transmission is measured using a lock-in amplifier. The strain ( $\Delta L/L$ ) is derived from this phase offset according to the relation $\Delta L/L = -\Delta\phi / (2F \cdot N)$ , where $F$ is the cavity finesse.

The system was implemented on the 123-meter long ALPS II Regeneration Cavity (RC), located 26 meters underground in the former HERA tunnel at DESY, Hamburg. The setup utilizes a fiber-based beam splitter to combine the lasers, with one port directed to the cavity and the other to a photodetector for the phase-lock loop. A third photodetector on the opposite side of the cavity measures the transmission beat-note. All RF signals are synchronized to a rubidium master oscillator referenced to GPS time, ensuring timing accuracy better than $10^{-14}$ .

Key Contributions and Results
The application of this technique to the ALPS II RC transformed the facility into a strainmeter with an effective sensitivity to transient seismic events of $10^{-10}$ to $10^{-9}$ m/m. The study reports the following specific observations:

Anthropogenic Noise: The system detected ground motion associated with Taylor Swift concerts at the nearby Volksparkstadion (approx. 1.1 km away) on July 23 and 24, 2024. The measured strain spectra matched the published beats-per-minute (BPM) tempos of the songs, indicating coordinated crowd motion. The seismic signatures of the two separate nights were highly correlated (up to 0.96), demonstrating the consistency of crowd behavior and the system's ability to resolve specific temporal features of cultural events.
Earthquake Detection: On January 7, 2025, the system recorded the magnitude 7.1 Southern Tibetan Plateau Earthquake. The strain data from the RC showed a correlation coefficient exceeding 0.90 with data from the nearby BGR Seismology Station (Hamburger Sternwarte), with seismic waves arriving simultaneously (within 0.1 s).
Earth Tides: Over a 21-day period in October 2024 and January 2025, the system measured long-term strain variations. The data revealed a clear semidiurnal lunar earth tide signal (period of 12 hours 25 minutes) with an amplitude of approximately $3 \times 10^{-9}$ strain RMS. The authors note that the amplitude is lower than typical ocean-less earth models due to the cavity's latitude (53.6°N) and east-west orientation, which places it near a theoretical minimum for semidiurnal strain. Daily variations (24-hour period) were also observed, attributed to environmental factors such as temperature fluctuations.

Significance and Claims
The paper claims that this technique successfully demonstrates the capability to continuously measure the absolute length of a high-finesse optical cavity with sub-micron precision. By converting the ALPS II Regeneration Cavity into a strainmeter, the authors show that existing particle physics infrastructure can be repurposed to monitor diverse seismic signals, ranging from local cultural events to distant earthquakes and global tidal forces.

The authors maintain a modest stance regarding the system's optimization. They acknowledge that the ALPS II RC was not originally designed as a dedicated seismic strainmeter. They suggest that sensitivity could be improved by utilizing the full 250-meter ALPS II baseline, upgrading mirrors for higher reflectivity and lower losses, and implementing more robust climate control to mitigate temperature-dependent length changes. The paper concludes that while the current setup is effective, future work involving distributed acoustic sensing or co-located seismometers is necessary to fully distinguish between experiment-limited sensitivity and ambient seismic conditions.

The "Tuning Fork" Trick

The "Phase Shift" Clue

What They Found

Why This Matters

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