Optical two-way time and frequency transfer over free space (1211.4902v1)

Abstract: The transfer of high-quality time-frequency signals between remote locations underpins a broad range of applications including precision navigation and timing, the new field of clock-based geodesy, long-baseline interferometry, coherent radar arrays, tests of general relativity and fundamental constants, and the future redefinition of the second [1-7]. However, present microwave-based time-frequency transfer [8-10] is inadequate for state-of-the-art optical clocks and oscillators [1,11-15] that have femtosecond-level timing jitter and accuracies below 1E-17; as such, commensurate optically-based transfer methods are needed. While fiber-based optical links have proven suitable [16,17], they are limited to comparisons between fixed sites connected by a specialized bidirectional fiber link. With the exception of tests of the fundamental constants, most applications instead require more flexible connections between remote and possibly portable optical clocks and oscillators. Here we demonstrate optical time-frequency transfer over free-space via a two-way exchange between coherent frequency combs, each phase-locked to the local optical clock or oscillator. We achieve femtosecond-scale timing deviation, a residual instability below 1E-18 at 1000 s and systematic offsets below 4E-19, despite frequent signal fading due to atmospheric turbulence or obstructions across the 2-km link. This free-space transfer would already enable terrestrial links to support clock-based geodesy. If combined with satellite-based free-space optical communications, it provides a path toward global-scale geodesy, high-accuracy time-frequency distribution, satellite-based relativity experiments, and "optical GPS" for precision navigation.

• The paper introduces an optical TWTFT method that enables bidirectional femtosecond-scale synchronization over a 2-km free-space link.
• It employs coherent frequency combs and linear optical sampling to achieve residual instability below 1e-18 at 1000 seconds and systematic offsets under 4×10^-19.
• The approach effectively cancels optical path-length variations below 300 nm, setting the stage for advanced terrestrial geodesy and satellite-based optical communications.

Optical Two-Way Time and Frequency Transfer Over Free Space: An Analysis

This paper presents a rigorous exploration of optical two-way time and frequency transfer (TWTFT) across a free-space medium, which addresses the limitations of conventional microwave-based methods for high-precision time-frequency signal dissemination. The primary challenge addressed is the synchronization of optical clocks and oscillators over free space, particularly over significant distances where traditional methods fall short.

The authors demonstrate this by employing coherent frequency combs locked to local optical clocks or oscillators, facilitating a bidirectional exchange of femtosecond-scale timing signals. The paper achieves an impressive timing deviation at the femtosecond level, residual instability less than $10^{-18}$ at 1000 seconds, and systematic offsets below $4 \times 10^{-19}$. These metrics are noteworthy, demonstrating the system's robustness even amid atmospheric turbulence or signal obstruction over a 2-km link. Notably, the implications for terrestrial clock-based geodesy are significant, and potential applications include satellite-based optical communications, offering pathways to global-scale geodesy, high-accuracy time-frequency distribution, and advanced experiments concerning relativity and navigation.

In fiber-based optical links, continuously operating links have been demonstrated successfully over extended distances, as shown with Germany's 920-km link. However, such a setup is incompatible with free-space transmission, where turbulence causes significant and frequent signal interruptions. In this regard, the authors pursue an optical analog to microwave-based TWTFT, focusing on elapsed time interval comparisons between sites rather than continuous frequency measurements. This method circumvents the need for an uninterrupted link, only requiring pulse exchanges for site synchronization at specific time intervals.

The optical TWTFT leverages linear optical sampling between pulse trains of optical frequency combs to achieve the desired precision, as conventional pulse detection would introduce picosecond-level jitter or worse. Importantly, the authors highlight the cancellation of optical path-length variations to below 300-nm across various time scales due to free-space single-mode link reciprocity. This setup effectively mitigates atmospheric effects, platform motions, and other environmental factors that could otherwise degrade performance. The results indicate potential scalability beyond the tested 2-km distance without significant degradation in transfer performance.

Experimental evidence is provided through data covering a 24-hour acquisition period, demonstrating the performance of the optical TWTFT. A notable finding is the modified Allan deviation achieving a figure below $10^{-18}$ around 1000-second measurement intervals. This is critical as it indicates that the system's limitations are rooted in transceiver noise rather than in path-length variations intrinsic to free-space traversal.

The paper explores one-way noise contributions, distinguishing sources such as detector and shot noise above 100 Hz, fiber-induced vibration noise between 20 Hz and 100 Hz, and atmospheric piston effect noise below 20 Hz. In the contrast, two-way residual timing differences reveal significantly lower noise levels, suggesting efficacy in the transceiver mechanism and phase locking consistency.

To conclude, the paper posits that current demonstration extends to the tested 2-km link, indicating feasibility for longer terrestrial links with maintained performance levels. Achieving very long-distance coverage or global implementation will necessitate satellite integration while handling extended delays and Doppler effects. The presented results and methodologies offer a conduit toward enhancing ultra-precise time/frequency distribution, with significant ramifications for fields such as global geodesy and satellite-based relativistic measurements. This research opens avenues for leveraging existing and emerging technologies in optical communication to explore these advanced applications further.