Demonstration of length control for a filter cavity with coherent control sidebands

This paper experimentally demonstrates a new length and alignment control scheme for a 300-meter filter cavity using coherent control sidebands, successfully reducing the cavity's length noise from 6.8 to 2.1 pm to enable frequency-dependent squeezing for advanced gravitational-wave detectors.

The Gist

Imagine you are trying to listen to a whisper in a hurricane. That is essentially what scientists do when they try to detect gravitational waves—ripples in space-time caused by massive cosmic events like colliding black holes. The "whisper" is the tiny signal from a distant event, and the "hurricane" is the background noise that drowns it out.

One of the biggest sources of this noise is quantum noise, which is like the static on an old radio. To fix this, scientists use a trick called "squeezing." Imagine a balloon filled with air (the noise). Usually, the air pushes out equally in all directions. "Squeezing" is like squeezing the balloon so the air pushes out less in one direction (reducing noise there) but more in another.

However, for this to work perfectly across all frequencies (both high and low pitches of the cosmic "whisper"), the scientists need a special tool called a filter cavity. Think of this cavity as a very long, 300-meter hallway with mirrors at both ends. It acts like a tuning fork that filters the noise.

The Problem: Keeping the Tuning Fork in Tune

The problem is that this 300-meter hallway is incredibly sensitive. If it moves even a tiny bit—smaller than the width of an atom—it gets out of tune, and the noise reduction fails.

Previously, scientists tried to keep this hallway in tune using a "green laser" (a different color of light) as a guide. But this was like trying to steer a car by looking at a reflection in a side mirror that might be slightly crooked. The green laser and the actual signal (the squeezed light) weren't perfectly aligned, so the hallway would drift out of tune, and the noise would come back.

The Solution: The "Coherent Control Sidebands"

The authors of this paper introduced a new, smarter way to keep the hallway in tune. Instead of using a separate green laser, they used "coherent control sidebands."

Here is the analogy:
Imagine you are trying to tune a guitar string.

• The Old Way: You have a separate person humming a note to help you tune. But sometimes the hummer is slightly out of sync with the guitar, so you tune the guitar to the hummer, not the actual song you want to play.
• The New Way (This Paper): You attach a tiny, perfect tuning fork directly to the guitar string itself. Because the tuning fork is part of the string, it always knows exactly where the string should be.

In the experiment, these "tuning forks" (the sidebands) are generated right alongside the squeezed light inside the same machine. Because they are born together, they are perfectly matched. They tell the scientists exactly how to adjust the 300-meter hallway to keep it perfectly aligned with the signal they want to catch.

What They Did

The team built a 300-meter-long vacuum tunnel (the filter cavity) and tested this new "tuning fork" method. They compared it to the old green laser method.

• The Result: The new method was much more stable.
• The Numbers: They reduced the "jitter" or movement of the hallway from 6.8 picometers down to 2.1 picometers.
  • To visualize this: A picometer is one-trillionth of a meter. If the hallway were the size of the Earth, the old method let it wiggle by the width of a human hair, while the new method reduced the wiggle to the width of a single atom.

Why It Matters

By keeping the filter cavity perfectly still and aligned, the scientists can reduce the quantum noise much more effectively. This means future gravitational wave detectors (like Advanced LIGO and Advanced Virgo) will be able to "hear" much fainter whispers from the universe, potentially finding more black hole collisions and neutron star crashes than ever before.

In short, the paper demonstrates a new, highly precise way to keep a giant, sensitive scientific instrument perfectly tuned, allowing us to listen to the universe with much clearer ears.

Technical Summary

Technical Summary: Demonstration of Length Control for a Filter Cavity with Coherent Control Sidebands

Problem Statement
Gravitational-wave (GW) detectors, such as Advanced LIGO and Advanced Virgo, require broadband quantum noise reduction to increase detection rates. The most promising technique for this is the injection of a frequency-dependent squeezed vacuum field, realized using a 300-meter filter cavity. However, effective implementation requires precise length and alignment control of the filter cavity relative to the squeezed vacuum field.

Conventional control schemes utilize an auxiliary "green field" (532 nm) to generate error signals, while the squeezed field operates at the carrier wavelength (1064 nm). This approach presents two critical limitations:

1. Drift: The relative alignment between the green and squeezed fields can drift, meaning the green field's control does not guarantee the squeezed field is properly aligned.
2. Phase Fluctuations: Anisotropies in the cavity mirror coatings cause relative phase delay fluctuations between the green and squeezed fields, leading to detuning fluctuations.

Furthermore, because the squeezed vacuum state lacks coherent amplitude, it cannot directly provide the error signals necessary for control. Previous attempts to solve this using a Resonant Locking Field (RLF) required an additional auxiliary field.

Methodology
The authors experimentally demonstrate a new control scheme, termed CCFC (Coherent Control Filter Cavity), which utilizes Coherent Control Sidebands (CCSBs) already present in squeezed vacuum sources for GW detectors.

• Principle: CCSBs are generated within the Optical Parametric Oscillator (OPO) alongside the squeezed vacuum. They share the same mode-matching conditions and have a frequency offset (approx. 7 MHz) from the carrier that is negligible regarding mirror coating phase shifts.
• Error Signal Generation: The filter cavity length signal is derived from the beat note of the CCSBs reflected by the cavity. By demodulating this signal at $2\Omega_{cc}$, an error signal is obtained that is zero-crossing at the optimal cavity detuning.
• Experimental Setup: The experiment utilized an in-vacuum 300-meter filter cavity and an in-air squeezed vacuum source.
  • A 532 nm green field was used for conventional control and alignment.
  • Two auxiliary lasers phase-locked to the main laser provided the CCSBs and OPO length control.
  • A beam splitter (80% transmissivity) in the infrared reflection path picked off the CCSBs for detection by a resonant photodetector.
  • The CCFC error signal was mixed with the green field error signal. The control loop fed back to the main laser frequency above 10 Hz and the filter cavity end mirror below 10 Hz, with a crossover frequency around 2 kHz.

Key Contributions

1. Experimental Demonstration: This is the first experimental demonstration of controlling a 300-meter filter cavity length using CCSBs, validating the theoretical framework proposed in [Phys. Rev. D 102, 042003 (2020)].
2. Noise Reduction: The study successfully reduced the filter cavity length noise (root mean square) from 6.8 pm to 2.1 pm by integrating the CCFC scheme with conventional green field control.
3. Validation of Error Signal: The measured CCFC error signal was shown to be consistent with theoretical predictions, including the effects of mode mismatch between the squeezed field and the filter cavity.

Results

• Locking Precision: The addition of CCFC improved the locking precision (rms) from 6.4 Hz to 2 Hz. Analysis of the noise spectrum revealed that while increasing the gain of the green control reduced laser frequency noise, it did not reduce filter cavity length noise below 10 Hz. The CCFC scheme specifically addressed this low-frequency length noise.
• Frequency-Dependent Squeezing: The system successfully demonstrated frequency-dependent squeezing. The measured cavity detuning fluctuation was approximately 9 Hz, which is an improvement over the ~30 Hz fluctuation observed in previous experiments without CCFC and alignment control.
• Squeezing Degradation: The current squeezing degradation budget is dominated by propagation losses (52%), primarily due to the 20% loss introduced by the pick-off beam splitter used in the experiment. The authors note that in actual GW detectors, this loss can be avoided by extracting the CCSB signal from an output mode cleaner reflection.

Significance and Claims
The paper claims that the CCFC scheme is a necessary advancement for the fourth observing run of Advanced LIGO and Advanced Virgo, where frequency-dependent squeezing is planned. The significance lies in the ability to control the filter cavity length and alignment directly with respect to the squeezed vacuum field, eliminating the drift and phase instability issues inherent in green-field-only control.

The authors modestly conclude that while the current experiment achieved a significant reduction in length noise, the full potential of the scheme will be realized in GW detectors where:

• The squeezer laser is locked to the more stable interferometer laser, reducing frequency noise.
• The pick-off beam splitter is removed, reducing propagation losses.
• Alignment control using CCFC is implemented to stabilize detuning fluctuations caused by infrared alignment drifts.

The paper does not claim to have solved all alignment issues or achieved the final target squeezing levels for GW detectors, but rather demonstrates the viability and immediate performance benefits of the CCFC control scheme as a critical step toward those goals.