Ultrastable Optical Cavities

• Ultrastable optical cavities are precision-engineered Fabry–Pérot resonators that maintain laser frequency stability near fundamental thermal and quantum noise limits.
• They utilize advanced materials such as ULE glass, crystalline silicon, and AlGaAs/GaAs coatings to reduce thermal noise and mechanical dissipation.
• Innovations like vibration-insensitive mounting and in-vacuum bonding enable compact, field-deployable systems critical for atomic clocks and precision metrology.

Ultrastable optical cavities are precision-engineered Fabry–Pérot resonators whose dimensional and environmental stability support laser frequency stabilization at instability levels approaching the fundamental limits set by thermal and quantum noise. These cavities are central to advanced optical frequency metrology, state-of-the-art atomic clocks, ultra-low-noise microwave generation, and fundamental tests of physics. By combining low-thermal-expansion materials, vibration-insensitive geometries, and—recently—innovations such as in-vacuum optical bonding for operation outside vacuum chambers, ultrastable optical cavities achieve fractional frequency instabilities below $10^{-16}$, in some cases defeating the need for bulky vacuum hardware (Liu et al., 19 Jun 2024, Liu et al., 2023).

1. Fundamental Principles and Materials

A Fabry–Pérot optical cavity is composed of two highly reflective mirrors separated by a spacer of fixed length. The resonance frequencies are determined by the cavity length $L$ and the index of refraction $n$ according to: $\nu_{\mathrm{FSR}} = \frac{c/n}{2L}$ where $c$ is the speed of light. High finesse ($\mathcal{F}$), typically $10^5$–$10^6$, is achieved with dielectric or crystalline coatings to yield ultra-narrow cavity resonances (Boyd et al., 2023). Most ultrastable cavities use ultra-low expansion (ULE) glass or crystalline silicon for the spacer due to their minimal coefficient of thermal expansion (CTE). Fused silica, sapphire, and, more recently, crystalline AlGaAs/GaAs mirror coatings are employed to minimize thermal noise and mechanical dissipation (Lee et al., 16 Sep 2025, Ma et al., 3 Apr 2024).

Mirror coatings are critical; the move from conventional SiO$_2$/Ta$_2$O$_5$ to AlGaAs/GaAs coatings has reduced mechanical loss by over an order of magnitude, directly lowering coating Brownian noise and enabling frequency instability below $3\times 10^{-17}$ (Lee et al., 16 Sep 2025, Ma et al., 3 Apr 2024). Crystalline coatings also exhibit photo-modified birefringence effects and enhanced stability under appropriately controlled conditions.

2. Innovations in Cavity Mounting and Vibration Insensitivity

Environmental vibration is a principal destabilizing influence. Cavity designs minimize vibration-induced cavity length changes ($\delta L/L$) through geometric optimization, strategic support placement, and finite element modeling. Notable advances include:

• Horizontally or vertically mounted cylindrical cavities with support points configured to cancel translation and tilt-induced noise, yielding vibration sensitivities as low as $1.5 \times 10^{-11}$ per m · s$^{-2}$ (0901.4717).
• Airy point and notched support techniques, optimizing the cavity’s resistance to bending and compressional deformations under vertical acceleration (Zhang et al., 2012).
• Short, large-diameter cavities engineered with specific holding “squeeze-insensitivity” points where axial compression and rim bulging cancel, critical for transportable systems (Davila-Rodriguez et al., 2017).
• Pyramidal and double-tetrahedral spacers, as well as optically contacted and monolithically fabricated cavities, for symmetric stress and further reduction of vibration-to-frequency transduction (Didier et al., 2019).

Vibration sensitivity is parameterized by coefficients $k_i$ ($i = x,y,z$) expressed as

$\delta L/L = \vec{k}\cdot\vec{a}$

with $k_i$ containing both translation and tilt-induced contributions. Suppressing $k_i$ to below $10^{-11}$ (m s$^{-2}$)$^{-1}$ enables thermal noise–limited operation even in less-controlled environments.

3. Vacuum Techniques and Transition to Air Operation

Traditionally, ultrastable cavities operate in vacuum chambers (often $\leq 10^{-5}$ hPa) to eliminate refractive index fluctuations and to preclude contamination or condensation on optical surfaces (Boyd et al., 2023, Heinz et al., 2020). Innovations have now eliminated the need for large vacuum enclosures:

• In-vacuum Bonded Cavities: Superpolished ULE mirrors and spacers are optically contact–bonded inside a vacuum chamber at sub-Pa pressure (Liu et al., 2023, Liu et al., 19 Jun 2024). The miniaturized vacuum (e.g., 9.7 mL or even 0.5 mL) persists for years after bonding, forming an intrinsic vacuum-gap cavity that remains stable when operated in air.
• Residual Gas-Induced Noise: For $(P < 0.1{-}0.3)$ hPa, the fundamental phase noise from gas refractive index fluctuation is negligible, as quantified by

$$\mathscr{L}(f) \approx \sqrt{\frac{m}{2} \frac{8\pi^2 \alpha^2}{L w_0} \frac{P}{(k_BT)^{3/2}} \frac{\nu^2}{f^2}}$$

demonstrating that, for these vacuum-sealed cavities, residual noise from gases remains well below the thermal noise floor over relevant offset frequencies (Liu et al., 19 Jun 2024).

• Thermal and Acoustic Shields: By placing the in-vacuum bonded cavity within a temperature-controlled air-tight enclosure, environmental perturbations are further mitigated without active pumping.

This shift in paradigm enables compact, lightweight, fieldable ultrastable laser references with demonstrated phase noise and instability at the previous state-of-the-art (Liu et al., 2023, Liu et al., 19 Jun 2024).

4. Measurement Techniques and Stability Benchmarks

Laser stabilization is performed via the Pound–Drever–Hall (PDH) technique, locking laser frequency to the cavity resonance. Key performance metrics include phase noise spectral density and the Allan deviation ($\sigma_y$). State-of-the-art results:

• Phase noise: thermal-noise-limited over 0.1 Hz to 10 kHz, e.g., $\sim$\,$-105$ dBc/Hz at 10 kHz offset for a 9.7 mL cavity operated in air (Liu et al., 19 Jun 2024, Liu et al., 2023).
• Fractional frequency instability (Allan deviation): measured as low as

$\sigma_y(1\,\mathrm{s}) = 2.4\times10^{-14}$

for a small in-vacuum bonded cavity, and $5\times10^{-14}$ for similar designs (Liu et al., 19 Jun 2024, Liu et al., 2023).

Other systems with larger and cryogenic cavities have reported

• $\sigma_y(1\,\mathrm{s})\lesssim10^{-16}$ at 4 K (Zhang et al., 2017),
• Stability down to $2.5\times10^{-17}$ at 10 s with 6 cm silicon cavities and crystalline coatings at 17 K (Lee et al., 16 Sep 2025).

Long-term drift rates of $<5\times10^{-19}$/s and even $9\times10^{-21}$/s over week-long intervals have been achieved by precise tuning of temperature close to the CTE zero crossing and by minimizing optical power (Hagemann et al., 2014, Robinson et al., 2018). For coating-limited cavities, modified Allan deviation and frequency noise spectral density are used to identify and separate Brownian noise, technical noise, and flicker frequency noise regimes.

5. Technological Innovations and Materials Science

Key advancements include:

• Crystalline AlGaAs/GaAs Coatings: These enable a $>10\times$ reduction of the coating mechanical loss factor ($\phi_{\mathrm{coat}}\sim 2.3\times 10^{-5}$ at 17 K), reducing the Brownian noise limit and beating the performance of Ta$_2$O$_5$/SiO$_2$ dielectric coatings (Lee et al., 16 Sep 2025). Their use enables cavity-stabilized lasers to approach the $10^{-18}$ stability domain.
• Photo-induced Birefringence Management: Power-dependent birefringence in crystalline coatings can induce excess noise (Ma et al., 3 Apr 2024). This can be suppressed via dual-polarization locking and by stabilizing intracavity power.
• Integrated Thermometry for Nanophotonic Cavities: For chip-scale high-Q microresonators, on-chip temperature sensors combined with feedback loops yield a 48 dB reduction in frequency drift and wavelength stability within $±0.5$ pm, outperforming commercial DFB standards (Dacha et al., 26 Jun 2025). This advance is critical for photonic integration with electronics and Kerr-comb stabilization.
• Microfabricated and Miniature Cavities: In-vacuum bonding and dicing of microfabricated mirrors have produced 0.5 mL cavities operating at the thermal noise limit, establishing a route towards wafer-scale production for portable frequency references (Liu et al., 19 Jun 2024).

6. Applications and Impact

Ultrastable optical cavities serve as the backbone for:

• Optical Atomic Clocks: They define the local oscillator linewidth and phase noise, directly affecting clock instability through the Dick effect (0901.4717, Zhadnov et al., 2021). Multi-cavity averaging schemes allow reduction of short-term instability by $\sqrt{N}$ (Lee et al., 16 Sep 2025).
• Low-Noise Microwave Generation: With optical frequency division, cavities support generation of microwaves with phase noise $<-100$ dBc/Hz at 1 Hz offset (e.g., for radar, quantum networks, precise time transfer) (Davila-Rodriguez et al., 2017).
• Field and Space Applications: The operation of ultrastable reference cavities without vacuum chambers dramatically reduces volume, mass, and deployment complexity, opening fieldable optical clocks, environmental sensors, and precision optical metrology in challenging environments (Liu et al., 19 Jun 2024, Liu et al., 2023).
• Fundamental Physics: Optical cavities enable high-precision tests of Lorentz invariance and relativity by monitoring cavity-stabilized laser frequencies under rotation (Michelson–Morley configurations) and through frequency drift comparisons across multiple reference systems (Nagel et al., 2011, Nagel et al., 2013).

The table below summarizes representative configurations and their performance:

Cavity Type	Operating Medium	Best $\sigma_y(1\,\mathrm{s})$
Fused Silica/ULE, 100 mm	Vacuum chamber	$5.6\times10^{-16}$ (0901.4717)
Si (AlGaAs mirrors), 6 cm	17 K, cryostat	$2.5\times10^{-17}$ (Lee et al., 16 Sep 2025)
ULE, 25 mm, in-vacuum bond	Air (enclosure)	$2.4\times10^{-14}$ (Liu et al., 19 Jun 2024)
ULE, 25 mm, pyramidal	Vacuum chamber	$7.5\times10^{-15}$ (Didier et al., 2019)

7. Future Directions and Prospects

The integration of ultrastable cavities into chip-scale photonics, the deployment of crystalline coatings, and advances in in-vacuum bonding are poised to yield <10$^{-18}$ instability and robust, field-ready systems. Research aims include:

• All-optical Timescales: By combining multiple cavity-stabilized oscillators with frequency combs, an all-optical timescale surpassing hydrogen maser stability is now realistic (Lee et al., 16 Sep 2025).
• Portability and Mass Production: Miniaturized, vacuum-sealed, or thermometrically stabilized microresonator cavities will enable new applications in quantum networking, geodesy, and satellite-borne instruments (Liu et al., 19 Jun 2024, Dacha et al., 26 Jun 2025).
• Noise Cancellation and Advanced Algorithms: Dual-polarization, cavity averaging, and machine-learning-based thermometric feedback are areas of rapid development for both bulk and on-chip cavity systems.

Ultrastable optical cavities thus remain an essential platform for the advancement of optical frequency standards, precision timing, and fundamental science, with a clear trajectory towards higher stability, reduced size, and real-world deployability.