The Impact of Turbulence on High Accuracy Time- Frequency Transfer across Free Space L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, I. Coddington, and N. R. Newbury National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305 laura.sinclair@nist.gov Abstract: Atmospheric optical path-length variations are measured across a 2-km optical link through a frequency comb-based system with femtosecond-level precision. Without mitigation, the turbulent piston effect will severely restrict time-frequency transfer from optical clocks. Work of the U.S. government, not subject to copyright. OCIS codes: 010.7060 (Turbulence); 010.1330 (Atmospheric Turbulence) Optically based time-frequency transfer (TFT) is necessary, as the accuracy and precision of the next generation of optical atomic clocks will far exceed the capabilities of microwave-based systems to faithfully transfer the clock signals across free-space. Because optical systems operate at much higher carrier frequencies, they are fundamentally better suited to transfer high-accuracy time-frequency signals than microwave-based systems. However, just as for free-space optical communications, atmospheric turbulence can limit optically based TFT. While the impact of turbulence on free-space laser communication is well studied [1-3], its impact on optical TFT is not. Many of the same issues arise, such as scintillation and beam wander, which cause signal fading. However, in addition, TFT is sensitive to time-of-flight variations. Time-of-flight variations originate from the coupling of the spatial variation in phase via the wind (frozen turbulence) as well as, on long timescales, changes in atmospheric conditions such as temperature and pressure. The so-called “piston” effect, which is the variation in the optical phase averaged across the receive aperture, is expected to dominate the time-of-flight variations at short timescales. This effect is closely related to angular jitter at the receive aperture, which arises from the variation in the slope of the optical phase across the aperture. For the purpose of TFT, we translate these variations in the optical phase to their effective time-of-flight variation, measured in seconds. Here we report measurements of the time-of-flight variations across a 2 km free-space link from timescales of milliseconds to hours. The measurements were made with a dual frequency-comb system that had femtosecond-level accuracy (corresponding to 300 nm fluctuations in the optical path length) and that was capable of making coherent measurements despite signal fading [4]. Our results are in reasonable agreement with predictions. Specifically, at very low Fourier frequencies (corresponding to timescales of tens of minutes to hours), the time of flight will vary with the overall air temperature and pressure. At higher frequencies, the measured variations follow the f -8/3 dependence expected from the Kolmogorov spectrum for the piston effect [5]. The measured timing fluctuations greatly exceed the uncertainty of atomic optical clocks, which can reach 10 -18 fractional uncertainty [6]. Therefore some form of two-way transfer is critical to the free-space transfer of high-accuracy time-frequency signals across free space, as demonstrated in Ref. [4]. Figure 1: Experimental setup for the measurements. A coherent pulse train from a frequency comb (blue) propagates through 500 m of optical fiber and a 2 km air-path before being sampled by a second frequency comb (red), providing femtosecond –level timing information. In order to achieve femtosecond-level timing information, a dual comb measurement technique was used as described in Ref [4]. A coherent pulse train (frequency comb) was generated by phase-locking a femtosecond Er- fiber laser to an optical oscillator. This pulse train was transmitted across the link and then sampled with a second frequency comb locked to the same oscillator but with a repetition rate offset by f r . The result is a series of interferograms, or cross correlations, that occur every 1/f r . A variation in the time-of-flight appears as a variation in the spacing of the interferograms. This method can have femtosecond-level sensitivity and is robust against interruptions of the signal. Consequently phase fluctuations can be measured for turbulence conditions that would prevent a continuous link. Environmental variables including temperature, humidity, pressure, and wind speed were also measured at two points in the link. Fast steering mirrors on both sides of the link compensated for beam wander