Femtosecond Timekeeping: Slip-Free Clockwork for Optical Timescales

The generation of true optical time standards will require the conversion of the highly stable optical-frequency output of an optical atomic clock to a high-fidelity time output. We demonstrate a comb-based clockwork that phase-coherently integrates $\sim 7\times {10}^{20}$ optical cycles of an input optical frequency to create a coherent time output. We verify the underlying stability of the optical timing system by comparing two comb-based clockworks with a common input optical frequency and show $<20\mathrm{fs}$ total time drift over the 37-day measurement period. Both clockworks also generate traditional timing signals including an optical pulse per second and a 10-MHz rf reference. The optical pulse-per-second time outputs remain synchronized to 240 attoseconds (240 as) at 1000 s. The phase-coherent 10-MHz rf outputs are stable to near a part in ${10}^{19}$. Fault-free timekeeping from an optical clock to femtosecond level over months is an important step in replacing the current microwave time standard by an optical standard.

Figure 1

(a) Experimental setup. Each comb-based clockwork converts the common optical frequency of 191 THz (${\nu }_{\mathrm{cw}}$) to three outputs: (1) a 160-MHz optical pulse train, (2) an optical PPS signal, and (3) a 10-MHz rf output. To evaluate the clockwork performance, we compare these three outputs of the two clockworks, as discussed in the text. (b) Phase-locking scheme to enable the timing comparison. All lock frequencies between the combs are the same sign but offset such that $f_{\mathrm{CEO},1}-f_{\mathrm{CEO},2}=f_{\mathrm{opt},1}-f_{\mathrm{opt},2}=5\mathrm{MHz}$. The shaded regions labeled $f_{1577}$ and $f_{1536}$ indicate the bands used for the synthetic wavelength measurement (direct comparison of two optical pulse trains). OC, optical coupler; DWDM, dense wavelength division multiplexer; MZM, Mach-Zehnder modulator, “$÷16$,” rf divider; $f_{\mathrm{CEO}}$, carrier-envelope offset frequency; $f_{\mathrm{opt}}$, offset frequency between the cw laser and one optical comb tooth; $f_{\mathrm{rep}}$, comb repetition rate.

Figure 2

(a) Time offset between the two optical pulse trains (red line) as measured for 37 days using the synthetic wavelength technique. After high-pass filtering (gray line) the data show the clear absence of phase slips. (b) Setup of the pulse-train optical timing comparison. BPF, optical band-pass filter. (c) Time offset between the PPS clock outputs (blue line) over the same 37-day period. (d) Setup of the PPS optical timing comparison.

Figure 3

Top panel: Relative humidity (%RH) (black) and temperature (gray) data for the last two weeks of timing comparison experiment during which humidity data were available. Temperature data have been smoothed with a 10-min window. Bottom panel: Pulse-train timing (red) and PPS timing (blue). The strong correlation between humidity and timing offsets is clearly evident.

Figure 4

Fractional frequency instability (MDEV) for our 10-MHz rf generator as measured with a test set capable of long-term operation (purple down-pointing triangle) and as measured with a low-noise test set [orange up-pointing triangle; scaled from Allan deviation (ADEV) values reported by test set]. Noise floor of the long-term test set is plotted in gray. Also shown are the MDEV values for a state-of-the-art, commercial hydrogen maser (black). A factor of $\sqrt{2}$ has been removed from the comb-generated instability data assuming an equal contribution from each clockwork.

Figure 5

Time deviation (TDEV) of the optical pulse-train timing comparison (red down-pointing triangle) and the 1 PPS timing comparison (blue up-pointing triangle) over 37 days. The gray region represents the best possible TDEV supported by current optical clocks [32, 33]. Values have been divided by $\sqrt{2}$ assuming equal contribution from each comb.