Tunable coherence laser interferometry: demonstrating 40dB of straylight suppression and compatibility with resonant optical cavities

This paper experimentally demonstrates a tunable coherence technique using pseudo-random-noise phase modulation to suppress parasitic stray light by 40 dB in laser interferometers while maintaining compatibility with resonant optical cavities.

The Gist

Imagine you are trying to listen to a very faint whisper (a gravitational wave) in a giant, echoing cathedral. The problem isn't just that the whisper is quiet; it's that the cathedral is full of annoying echoes, dust motes dancing in the light, and random noises bouncing off the walls. These "ghost sounds" are so loud that they drown out the whisper you are trying to hear.

In the world of physics, scientists use giant laser interferometers (like the ones used to detect gravitational waves) to listen to the universe. But just like in the cathedral, stray light bounces off mirrors, dust, and screws, creating "ghost beams" that interfere with the real signal. This is a huge problem for future, more sensitive detectors.

This paper presents a clever new trick to silence these ghosts without building a better cathedral. They call it "Tunable Coherence."

Here is the breakdown of how it works, using simple analogies:

1. The Problem: The "Echo Chamber"

Normally, laser light is like a perfectly synchronized marching band. Every soldier (photon) steps in perfect time. Because they are so synchronized, if a soldier takes a wrong turn, bounces off a wall, and comes back late, they still march in step with the main band. This creates a confusing interference pattern (noise) that ruins the measurement.

2. The Solution: The "Random Code"

The researchers decided to break the synchronization, but only for the "wrong" paths.

Imagine the laser light is a song. Normally, the song is a smooth, continuous melody.

• The Trick: They take that melody and chop it up into tiny, rapid-fire snippets. They then scramble the order of these snippets using a Pseudo-Random Noise (PRN) code. It's like taking a sentence and shuffling the words so fast that it sounds like static to anyone listening from a distance, but if you know the exact code, you can unscramble it.
• The Effect:
  • The Main Path: The light that goes straight through the interferometer (the intended path) travels a specific distance. When it arrives, the "scrambler" at the end knows the code and unscrambles it perfectly. The signal is clear.
  • The Ghost Path: The light that bounces off a stray mirror (the ghost) takes a slightly different, longer path. Because the light was chopped into tiny pieces, by the time this "ghost" light returns, its tiny pieces are out of sync with the main beam. They don't match the code anymore. To the detector, this ghost light looks like random static noise and effectively disappears.

3. The "Magic Length"

The researchers found a sweet spot. They made the "chips" (the tiny pieces of the code) so short that the light has to travel a very specific distance to stay in sync.

• If the ghost light travels even a little bit too far (more than about 30 centimeters in their experiment), it falls out of sync and gets silenced.
• If the main light travels the exact right distance, it stays in sync and is heard loud and clear.

4. The Results: Silencing the Noise

They tested this in a lab with a setup called a Michelson interferometer (a standard "Y" shaped laser setup).

• The Test: They injected a fake "ghost" signal that was supposed to ruin their measurement.
• The Result: When they turned on their "random code" trick, the ghost signal dropped by 40 decibels.
  • Analogy: Imagine a person shouting in your ear. Turning on this trick is like putting on noise-canceling headphones that specifically target that one voice. The shout becomes a whisper.
• The Catch: They also had to prove this wouldn't break the laser's ability to stay locked in a resonant cavity (a box where light bounces back and forth thousands of times to get stronger). They proved that as long as the "box" is the exact right size to match their code, the laser works perfectly.

Why This Matters

Currently, scientists have to spend years building incredibly clean rooms and polishing mirrors to the atomic level just to stop stray light. It's expensive and difficult.

This new technique is like a software update for the laser. Instead of trying to physically stop every single photon from bouncing off the wrong thing, they just make the laser "forget" about the bounces that take the wrong path.

The Bottom Line:
They successfully demonstrated a way to make a laser "tunable." It can be perfectly coherent (synchronized) for the path we want, but instantly incoherent (scrambled) for any path we don't want. This could allow future gravitational wave detectors to be much more sensitive, potentially hearing the "whispers" of the universe that are currently drowned out by the "noise" of the lab.

Technical Summary

1. Problem Statement

Laser interferometers, particularly those used in ground-based gravitational wave detectors (e.g., LIGO, Virgo, KAGRA), rely on high spatial coherence to achieve extreme sensitivity. However, this high coherence makes them vulnerable to parasitic light fields (straylight, scattered light, or "ghost beams").

• Mechanism of Noise: Photons that scatter off optical components and re-enter the main beam path via unintended trajectories can couple back into the measurement signal.
• Impact: These parasitic fields cause non-linear noise. Low-frequency disturbances (e.g., seismic or acoustic motion) affecting the scattering path can be "up-converted" into the sensitive measurement band (10 Hz – 10 kHz) as phase and amplitude noise.
• Limitation of Current Solutions: Existing mitigation techniques (baffles, beam dumps, active subtraction) are insufficient for next-generation detectors (like the Einstein Telescope) aiming for sensitivities below 10 Hz, where even single scattered photons can be problematic.

2. Methodology: Tunable Coherence

The authors propose a technique called Tunable Coherence, which artificially controls the coherence length of the laser light to suppress interference from unintended paths while preserving it for the intended path.

• Core Mechanism: The laser light is phase-modulated using a Pseudo-Random Noise (PRN) binary sequence at a high frequency ($f_{PRN}$).
  • The sequence consists of "chips" (logical 0s and 1s) that flip the light phase by $180^\circ$.
  • This modulation effectively creates a "pseudo-white-light" interferometer.
• Key Length Scales:
  1. Coherence Length ($d_{chip}$): Determined by the chip duration ($1/f_{PRN}$). Interference is suppressed if the path difference between the main beam and a parasitic beam exceeds this length.
  2. Recoherence Length ($d_{coh}$): The distance at which coherence is restored, defined as $n_{chips} \times d_{chip}$. Coherence is only restored for path differences that are integer multiples of this length.
• Demodulation: The system uses photodetectors with bandwidths lower than the sequence repetition rate ($f_{PRN}/n_{chips}$). This filters out the high-frequency modulation, leaving the standard interferometric signal intact, provided the main arms are delay-matched.

3. Experimental Setup

The authors validated the concept through two distinct experimental setups:

A. Michelson Interferometer (Straylight Suppression)

• Setup: A 1-meter arm-length Michelson interferometer.
• Parasitic Simulation: A low-reflectivity mirror ($R \approx 0.2$) in one arm created a "parasitic" beam path. This path included a delay line and a piezo-actuated mirror to simulate scattered light with variable delay ($\tau_{sc}$) and phase modulation.
• Signal Injection:
  • A "gravitational wave" signal simulated at 172.4 kHz.
  • A "scattered light" signal simulated at 170 kHz.
• Modulation: A 20 GHz electro-optic modulator (EOM) applied PRN sequences (lengths ranging from 7 to 2047 chips) at $f_{PRN} = 1$ GHz.

B. Optical Resonator (Cavity Compatibility)

• Setup: A folded linear optical cavity (Finesse $\approx 696$).
• Goal: To prove that PRN modulation does not destroy the ability to lock and operate high-finesse cavities.
• Conditions: The cavity round-trip length ($l_{cav}$) was matched to the PRN recoherence length ($d_{coh}$) and its integer multiples/halves.
• Locking: The cavity was locked using the Pound-Drever-Hall (PDH) technique with an additional RF sideband.

4. Key Results

Straylight Suppression in Michelson Interferometer:

• Suppression Level: Achieved 41.7 dB of noise suppression for the parasitic tone (scattered light) while maintaining the desired signal.
• Delay Dependency: Suppression was effective once the parasitic delay exceeded the chip length ($d_{chip} < 30$ cm). The suppression followed theoretical predictions based on the autocorrelation of the PRN sequence.
• Sequence Length: Suppression generally improved with longer sequences (up to 2047 chips), though the 63-chip sequence was an outlier. The suppression saturated around 40 dB, limited by experimental noise floors and imperfect phase flips.

Compatibility with Optical Resonators:

• Resonance Recovery: When the cavity length matched the PRN recoherence length (integer multiples), the cavity exhibited standard resonant behavior (power buildup) identical to the unmodulated case.
• Mismatch Effects:
  • Half-integer mismatch: Resulted in a 50% reduction in power buildup (destructive interference for every second round-trip).
  • Detuning: A new resonance width (FWHM) of $\approx 710$ $\mu$m was observed for macroscopic length matching.
• PDH Locking: The Pound-Drever-Hall error signal remained valid and usable for small detunings ($\pm 50$ kHz). Only significant mismatches ($\pm 250$ kHz) degraded the error signal, but the system could maintain a lock over a 1 MHz detuning range.

5. Significance and Implications

• State-of-the-Art Improvement: This technique demonstrates a suppression level (40 dB) that is an order of magnitude better than previous methods (e.g., opto-mechanical frequency shifting) without requiring complex post-processing or identification of specific scatter sources.
• Tolerance Increase: A 40 dB suppression implies that the tolerable power of parasitic beams can increase by a factor of 10,000. This significantly relaxes the mechanical and optical cleanliness requirements for future detectors.
• Scalability: The method is compatible with complex interferometer topologies involving multiple optical resonators (Fabry-Perot cavities, mode cleaners), which are essential for quantum noise reduction in gravitational wave detectors.
• Future Potential: By utilizing faster electronics (telecom-grade components) and longer PRN sequences, coherence lengths could be reduced to the centimeter or millimeter scale, further enhancing suppression capabilities for next-generation observatories like the Einstein Telescope.

Conclusion

The paper successfully demonstrates that tunable coherence via PRN phase modulation is a viable, fundamental solution to the straylight problem in precision laser interferometry. It effectively suppresses parasitic noise by orders of magnitude while maintaining full compatibility with high-finesse optical cavities and standard locking techniques, paving the way for more sensitive gravitational wave detectors.