Chasing the thermodynamical noise limit in whispering-gallery-mode resonators for ultrastable laser frequency stabilization

Abstract: Ultrastable high-spectral-purity lasers have served as the cornerstone behind optical atomic clocks, quantum measurements, precision optical-microwave generation, high resolution optical spectroscopy and sensing. Hertz-level lasers stabilized to high finesse Fabry-P\'erot mirror cavities are typically used for these studies but are large and fragile such that they have remained laboratory instruments. There is a clear demand in rugged miniaturized lasers operating potentially at comparable stabilities to those bulk lasers. Over the past decade, ultrahigh-Q optical whispering-gallery-mode (WGM) resonators have served as a platform for low-noise microlasers but have not yet reached the ultimate stabilities defined by their fundamental noise. Here, we show the noise characteristics of WGM resonators and demonstrate a resonator-stabilized laser at the fundamental limit by compensating the intrinsic thermal expansion of a WGM resonator, allowing a sub-25 Hz linewidth and a 32 Hz Allan deviation on the 191 THz carrier in 100 ms integration. We also reveal the environmental sensitivities of the resonator at the thermodynamical noise limit and long-term frequency drifts governed by random-walk-noise statistics.

Overview of Whispering-Gallery-Mode Resonators in Laser Frequency Stabilization

This paper presents a significant advancement in the development and characterization of ultrastable laser frequency stabilization using whispering-gallery-mode (WGM) resonators. The purpose of this research is to address the limitations of conventional Fabry-Pérot (FP) mirror cavities, which are large and delicate, by presenting a robust miniaturized alternative that achieves comparable stability. WGM resonators provide a promising platform due to their potential for low noise operations. However, previous implementations have not reached the ultimate stability defined by fundamental noise limits—specifically, the thermodynamical noise limit.

In tackling this challenge, the authors of the paper designed a thermal-compensation WGM resonator system. They effectively reduced the thermal expansion of a crystalline MgF₂ WGM resonator by incorporating laminated Zerodur layers. This design choice is guided by numerical simulations to minimize the thermal sensitivity and resulted in resonator stability characterized by a linewidth of less than 25 Hz and a fractional frequency instability of 1.67×10⁻¹³ on a 191 THz carrier with a 0.1 s integration time. Notably, this stability was achieved without stringent ambient temperature control, setting a benchmark among WGM resonators of comparable size and morphology.

Key Numerical Results and Claims

1. Linewidth and Frequency Instability: The laser stabilized using the thermal-compensated WGM resonator exhibited a spectral linewidth of less than 25 Hz and an Allan deviation of 32 Hz at 100 ms integration. This is noted as the best performance for resonators of this size.

2. Thermal Sensitivity Improvement: The thermal-compensation design resulted in approximately a sevenfold improvement in thermal sensitivity over traditional MgF₂ WGM resonators.

3. Residual Environmental Sensitivity: Despite thermal compensation, the resonator showed susceptibility to ambient environmental perturbations with long-term frequency drifts attributable to random walk noise statistics.

4. Pressure and Temperature Relationship: For the compensated WGM resonator, a pressure variation of less than 0.154 mPa correlated with a necessary ambient temperature control of below 2.7 mK to approach the thermorefractive noise limit.

Implications and Future Developments

The implications of this work are profound in the fields of precision metrology, atomic clocks, and spectrally pure laser oscillators, offering the possibility of transferring such laser systems from laboratory settings to portable, field-ready instruments. The adaptability of WGM resonators for achieving low-noise microcomb generation further highlights their potential.

The paper hints at future research directions, including improving the dual-mode temperature compensation techniques to further stabilize the WGM resonator against environmental fluctuations. Additionally, refining the accuracy of the temperature sensing mechanism and controlling ambient temperature more effectively are proposed measures to enhance long-term frequency stability.

As this study demonstrates a significant leap towards the thermodynamical noise limit of WGM resonators, subsequent efforts would further explore materials and designs to enhance the resonator's robustness and adaptability across various practical applications in AI and beyond.