A sub-40 mHz linewidth laser based on a silicon single-crystal optical cavity (1112.3854v2)

Abstract: State-of-the-art optical oscillators based on lasers frequency stabilized to high finesse optical cavities are limited by thermal noise that causes fluctuations of the cavity length. Thermal noise represents a fundamental limit to the stability of an optical interferometer and plays a key role in modern optical metrology. We demonstrate a novel design to reduce the thermal noise limit for optical cavities by an order of magnitude and present an experimental realization of this new cavity system, demonstrating the most stable oscillator of any kind to date. The cavity spacer and the mirror substrates are both constructed from single crystal silicon and operated at 124 K where the silicon thermal expansion coefficient is zero and the silicon mechanical loss is small. The cavity is supported in a vibration-insensitive configuration, which, together with the superior stiffness of silicon crystal, reduces the vibration related noise. With rigorous analysis of heterodyne beat signals among three independent stable lasers, the silicon system demonstrates a fractional frequency stability of 1E-16 at short time scales and supports a laser linewidth of <40 mHz at 1.5 \mu m, representing an optical quality factor of 4E15.

• The paper achieves a sub-40 mHz linewidth by using a cryogenic silicon single-crystal cavity that minimizes thermal noise for exceptional frequency stability.
• It employs a nitrogen-cooled cryostat at 124 K to exploit silicon’s zero-crossing thermal expansion, yielding a fractional frequency stability of 1 × 10⁻¹⁶.
• Experimental validation via a three-cornered hat measurement confirms an optical quality factor exceeding 4 × 10¹⁵, setting a new benchmark for precision oscillators.

Sub-40 mHz Linewidth Laser Utilizing Silicon Single-Crystal Optical Cavity

This paper presents a substantial advancement in the design and implementation of an optical cavity-stabilized laser system, achieving a sub-40 mHz linewidth, which marks a notable progression in optical metrology. The research introduces an innovative approach employing a silicon single-crystal cavity, which significantly minimizes thermal noise — a fundamental limitation for frequency stability in optical interferometers.

Core Contributions

The key novelty of this work is the successful reduction of thermal noise by using a cavity system where both the spacer and mirror substrates are constructed from mono-crystalline silicon, operating at 124 K. This temperature exploits the zero-crossing of silicon's thermal expansion coefficient and benefits from the material's low mechanical loss at this temperature. Such a configuration not only substantially decreases thermal noise but also reduces the contributions from environmental vibrations due to silicon’s superior stiffness.

• Fractional Frequency Stability: The paper reports a fractional frequency stability of $1 \times 10^{-16}$ and an exceptionally low laser linewidth of under 40 mHz at a wavelength of 1.5 μm. This is achieved by employing a novel nitrogen gas-based cryostat to maintain the cryogenic temperatures, minimizing vibrational effects on the cavity.
• Optical Quality Factor: The optical quality factor achieved exceeds $4 \times 10^{15}$, setting a new benchmark for stability in oscillators, whether optical or microwave.
• Experimental Validation: The stability of the laser frequency was evaluated against two state-of-the-art ULE-based optical systems, with performance assessed through a three-cornered hat measurement. This approach confirmed the superiority of the silicon cavity-stabilized system.

Implications and Future Outlook

The implications of this research are profound for precision measurement science, including time and frequency metrology, and open new possibilities in quantum measurement and gravitational wave detection. The ability to maintain such low instability suggests improvements in the performance of optical atomic clocks and could enhance experiments reliant on high coherence lengths.

Future Directions:

• Coating Thermal Noise: The authors acknowledge the current limitations imposed by the optical coatings and propose exploration into alternative coating technologies such as microstructured gratings or III/V semiconductor materials, like gallium-arsenide, to further minimize noise beyond the cavity's current baseline.
• Comparative Studies: The implementation of a second silicon cavity system is anticipated to address potential limitations and validate theoretical predictions about drift and stability over extended timescales.

In conclusion, this silicon single-crystal cavity technique represents a significant advancement in the pursuit of ultra-stable optical frequency references, promoting development opportunities in diverse applications requiring high precision and stability.