  Pulse trains emitted from dual-comb systems are designed to have low relative
timing jitter, making them useful for many optical measurement techniques such
as optical ranging and spectroscopy. However, the characterization of
low-jitter dual-comb systems is challenging because it requires measurement
techniques with high sensitivity. Motivated by this challenge, we developed a
technique based on an optical heterodyne detection approach for measuring the
relative timing jitter of two pulse trains. The method is suitable for
dual-comb systems with essentially any repetition rate difference. Furthermore,
the proposed approach allows for continuous and precise tracking of the
sampling rate. To demonstrate the technique, we perform a detailed
characterization of a single-mode-diode pumped $\mathrm{Yb:CaF_2}$ dual-comb
laser from a free-running polarization-multiplexed cavity. This new laser
produces 115 fs pulses at 160 MHz repetition rate, with 130 mW of average power
in each comb. The detection noise floor for the relative timing jitter between
the two pulse trains reaches $8.0 \times 10^{-7} \, \mathrm{fs}^2/\mathrm{Hz}
\; ( \sim 896 \: \mathrm{zs}/\sqrt{\mathrm{Hz}} )$, and the relative root mean
square (rms) timing jitter is 13 fs when integrating from 100 Hz to 1 MHz. This
performance indicates that the demonstrated laser is highly compatible with
practical dual-comb spectroscopy, ranging, and sampling applications.
Furthermore, our results show that the relative timing noise measurement
technique can characterize dual-comb systems operating in free-running mode or
with finite repetition rate differences while providing a sub-attosecond
resolution, which was not feasible with any other approach before.
