Optical-Frequency Transfer over a Single-Span 1840 km Fiber Link

To compare the increasing number of optical frequency standards, highly stable optical signals have to be transferred over continental distances. We demonstrate optical-frequency transfer over a 1840-km underground optical fiber link using a single-span stabilization. The low inherent noise introduced by the fiber allows us to reach short term instabilities expressed as the modified Allan deviation of $2\times {10}^{-15}$ for a gate time $\tau$ of 1 s reaching $4\times {10}^{-19}$ in just 100 s. We find no systematic offset between the sent and transferred frequencies within the statistical uncertainty of about $3\times {10}^{-19}$. The spectral noise distribution of our fiber link at low Fourier frequencies leads to a ${\tau }^{-2}$ slope in the modified Allan deviation, which is also derived theoretically.

Figure 1

Schematic of the optical fiber link. Light of a commercial cw fiber laser locked to an optical cavity is launched into an underground telecommunication fiber at MPQ. After a 1840-km loop the light arrives back at MPQ where a fraction of it is retroreflected. The round-trip light is used to derive an error signal for a servo loop with AOM 1 as the actuator. EDFA: erbium-doped fiber amplifier, FBA: fiber Brillouin amplifier, AOM: acousto-optic modulator, PC: polarization controller, FM: Faraday mirror, PD: photo diode.

Figure 2

Fractional frequency instability of the 1840-km free-running fiber link (open circles) and the stabilized link (squares) derived from a nonaveraging ($\Pi$-type) frequency counter and expressed as the ADEV. To obtain a significantly shorter measurement time and to distinguish between white phase, flicker phase, and other noise types [29], averaging (overlapping $\Lambda$-type) frequency counters may be used for which the modified ADEV (filled circles) measures the instability. Also shown is the measured noise floor of the interferometer (diamonds). The transferred frequency is subject to phase noise at measurement times of up to 20 ms that cannot be compensated for by the control loop due to the signal delay in the fiber.

Figure 3

Three-day frequency comparison between sent and transferred frequency after 1840 km. Data were taken with a dead-time free $\Lambda$-type frequency counter with 1-s gate time (green data points). The arithmetic means of all cycle-slip free 100 s intervals have been computed. From the resulting 1367 data points (black dots, right frequency axis, enlarged scale) a fractional difference between sent and transferred frequency of $(-0.14\pm 2.6)\times {10}^{-19}$ is calculated.

Figure 4

Phase noise power spectral density $S_{\varphi }(f)$ of the free-running (thick black line) and the stabilized (green line) 1840-km link. The servo bump around 27 Hz is in agreement with the bandwidth limit due to the propagation delay. Also shown is the Doppler noise suppression limit [22] (dashed gray line).