Laser fractional frequency instability at $\mathbf{4\times 10^{-17}}$ with a room temperature optical reference cavity

This paper demonstrates a record-breaking laser fractional frequency instability of $4\times 10^{-17}$ and a 12 mHz linewidth using a 68 cm room-temperature optical reference cavity, proving that state-of-the-art spectral purity is achievable without cryogenic cooling.

The Gist

Imagine you are trying to measure time with a stopwatch so precise that if it had started ticking at the beginning of the universe, it would only be off by a fraction of a second today. This is the goal of ultra-stable lasers, which are the heartbeats of modern timekeeping.

For a long time, the best of these lasers required a "cryogenic" environment—essentially a super-cold freezer using liquid helium or complex cooling machines—to keep them steady. It was like trying to keep a delicate glass sculpture from shaking by putting it in a block of ice. While effective, these setups were expensive, bulky, and hard to keep running continuously.

This paper describes a breakthrough: the team at the National Physical Laboratory (UK) built a laser system that is just as stable as the best frozen ones, but it operates at room temperature. They achieved this without the need for a freezer, making high-precision timekeeping accessible to more people.

Here is how they did it, explained through simple analogies:

1. The "Super-Ruler" (The Optical Cavity)

At the core of their system is a 68-centimeter-long glass tube called an optical cavity. Think of this as a hallway with two perfect mirrors at each end. A laser beam bounces back and forth inside this hallway millions of times. The length of this hallway determines the "note" (frequency) of the laser.

To keep the laser stable, the hallway must not change length even by the width of an atom. If the hallway expands or shrinks due to heat or vibration, the laser's "note" wavers, and the clock becomes inaccurate.

2. The Shape Shift: From Cylinder to Box

Previous attempts to make long, stable glass tubes used a cylindrical shape (like a rolling pin). However, making a long, perfect cylinder out of a special glass called ULE (Ultra-Low Expansion) is like trying to carve a perfect statue out of soap while it's spinning on a lathe; it's prone to chipping and cracking.

The team switched to a cuboid shape (a rectangular box).

• The Analogy: Imagine trying to carve a block of wood. It is much easier and safer to hold a block steady on a table and run a saw over it (milling) than to try to spin it and carve it while it rotates (lathe).
• The Result: This box shape allowed them to machine the glass without defects, creating a near-perfect "hallway" that is incredibly resistant to the vibrations that usually ruin these measurements.

3. The "Self-Balancing" Chair

Even with a perfect box, the glass still needs to sit on something. If you put a heavy box on four legs, one leg might be slightly shorter, or the floor might be uneven, causing the box to tilt or wobble.

The team designed a self-balancing support system.

• The Analogy: Think of a four-legged table on a wobbly floor. If you put a heavy book on one corner, the table might tip. But imagine if the table sat on a special "floating" base that automatically adjusted the pressure on all four legs so they all pushed back equally.
• The Execution: They used soft rubber pads (Viton) and added small weights (tuning masses) to the top of the cavity. By carefully adjusting these, they "tuned" the system so that the cavity was perfectly balanced against gravity and vibrations, effectively canceling out the shake.

4. The "Three-Way Conversation" (Measuring the Stability)

How do you know your new laser is the best if you don't have a better clock to compare it to? You can't just look at it; you need a reference.

The team used a clever trick called the "Three-Cornered Hat" method.

• The Analogy: Imagine three people (Laser A, Laser B, and Laser C) trying to tell the time. You can't know who is right just by listening to one. But if you listen to the conversation between A and B, then B and C, and then A and C, you can mathematically figure out exactly how much each person is drifting, even if you don't know the "true" time.
• The Result: By comparing their new 68cm laser (ULE68a) against two other high-quality lasers (ULE48a and ULE48b), they proved that their new room-temperature laser was the most stable one ever recorded for a system not using a freezer.

The Bottom Line

The team achieved a frequency instability of 4 × 10⁻¹⁷.

• What that means: If this laser were used as a clock, it would lose or gain less than one second over 800 million years.
• The Linewidth: The laser is so pure that its "color" is incredibly narrow (12 millihertz), comparable to the best lasers in the world that require cryogenic cooling.

Why this matters (according to the paper):
This work proves that you don't need a complex, expensive, liquid-nitrogen-cooled freezer to get the world's most precise lasers. By using a cleverly shaped glass box and a self-balancing chair, they made this level of precision achievable at room temperature. This opens the door for these lasers to be used more widely, including as a continuous "flywheel" to help bridge gaps in timekeeping data for the future redefinition of the second.

Technical Summary

Technical Summary: Laser Fractional Frequency Instability at 4 × 10⁻¹⁷ with a Room Temperature Optical Reference Cavity

Problem and Motivation
Ultrastable lasers are critical for optical frequency metrology, determining the stability and accuracy of optical frequency standards. While state-of-the-art stability is often achieved using cryogenic optical reference cavities (operating ≤130 K) to minimize Brownian thermal noise, these systems introduce significant drawbacks: complexity, cost, large equipment footprint, acoustic and acceleration noise from cryocoolers, and limitations on continuous operation due to coolant refilling and maintenance.

The authors aim to demonstrate that state-of-the-art frequency stability and spectral purity are achievable at room temperature. This would eliminate cryogenic drawbacks and enable full continuous operation, supporting optical clocks in meeting targets for the redefinition of the SI second and providing a continuous "optical flywheel" to bridge data gaps in optical timescales. Theoretical scaling laws indicate that room temperature stability can be maximized by utilizing long optical cavities with large optical beam diameters to suppress thermal noise.

Methodology
The authors developed a 68 cm long optical reference cavity, designated "ULE68a," constructed from ultra-low-expansion (ULE) glass. Key design and experimental strategies include:

• Geometry and Machining: Unlike previous cylindrical ULE cavities (e.g., 48.5 cm systems) which suffered from machining defects and flaking due to rotational stress, ULE68a utilizes a cuboid geometry. This allows for milling rather than lathing, ensuring the cavity remains stationary during machining and distributing mechanical forces over a larger area to avoid glass defects.
• Optical Parameters: The cavity features two optically contacted mirrors with a 10.2 m radius of curvature (ROC) on Suprasil 312 fused silica substrates. This configuration yields a beam diameter of 1.9 mm on the mirrors and a finesse of 410,000. The mirrors are coated with a dielectric ion-beam-sputtering high-reflectivity coating, chosen for uniformity and reproducibility, resulting in a calculated thermal noise limit of 2.5 × 10⁻¹⁷.
• Acceleration Sensitivity Minimization:
  • Design: Finite-element-method (FEM) simulations guided the placement of support points (Airy points) and the vertical position of the support plane to nullify angular tilts and create anti-symmetric longitudinal displacements.
  • Support Structure: The cavity rests on four Viton disks (4.5 mm diameter) which mediate contact with PEEK supports. A self-balancing structure, inspired by previous work and utilizing Zerodur bars and compliant Viton materials, ensures symmetrical reaction forces.
  • Tuning: Transverse sensitivity was reduced to 3 × 10⁻¹⁰ g⁻¹ using aluminum and Viton constraints. Longitudinal sensitivity was tuned to 2 × 10⁻¹⁰ g⁻¹ using tuning masses placed on the cavity surface.
• Vibration Isolation: The vacuum chamber is mounted on a honeycomb breadboard atop a commercial active vibration isolation (AVI) system. A custom AVI configuration was implemented, combining commercial sensors with a seismometer and tiltmeter to improve isolation above 0.1 s averaging time.
• Characterization: The system operates at 1542 nm to leverage telecom components. Stability was evaluated using a three-cornered hat (TCH) scheme comparing ULE68a against two reference cavities (ULE48a and ULE48b) at 1064 nm, linked via a 1 km fiber and a frequency comb.

Key Results

• Frequency Instability: The ULE68a cavity achieved a fractional frequency instability of 4 × 10⁻¹⁷ between 5 s and 20 s averaging time. This is the lowest instability ever reported for a room temperature optical reference cavity system.
• Linewidth: The laser stabilized to this cavity exhibits a linewidth of 12 mHz (full width at half maximum), determined by integrating the phase noise power spectral density. This matches the performance of state-of-the-art cryogenic systems.
• Noise Performance: At 0.5 s averaging time, the instability is 1.2 × 10⁻¹⁶, approaching the known noise floor of the measurement system (vibrations, thermal noise, and transfer noise from the comb/fiber link).
• Drift: The linear drift of ULE68a was isolated to 19 mHz s⁻¹, typical for room temperature ULE cavities. A non-linear drift component of 2 nHz s⁻² was observed in the beat residuals.
• Acceleration Sensitivity: The vertical acceleration sensitivity was measured at 1.4 × 10⁻¹⁰ g⁻¹, in good agreement with FEM simulations. Longitudinal sensitivity stabilized at 8 × 10⁻¹⁰ g⁻¹ after six months, potentially due to deformation of supporting Viton disks.

Significance and Claims
The authors claim that this work demonstrates that the lowest fractional frequency instability and narrowest linewidth reported to date for a room temperature system are achievable without cryogenics. The results are competitive with the best cryogenic realizations.

The significance of this work lies in proving that high-performance optical frequency stability is accessible to a broader range of users by removing the barriers of cryogenic complexity, cost, and maintenance. The system supports applications requiring continuous operation, such as the redefinition of the SI second and the creation of a continuous optical timescale. The authors note that while the current instability (4 × 10⁻¹⁷) exceeds the calculated thermal noise limit (2.5 × 10⁻¹⁷), likely due to local deformations at spacer ends or low-quality factor materials in the support structure, the platform provides a robust foundation for further improvements, such as the addition of ULE compensating rings to address long-term drift and sensitivity.