  We synchronize a 8.06-GHz microwave signal from a voltage-controlled
oscillator with an optical pulse train from a 77.5- MHz mode-locked Er-fiber
laser using a fiber-based optical-microwave phase detector. The residual phase
noise between the optical pulse train and the synchronized microwave signal is
-133 dBc/Hz (-154 dBc/Hz) at 1 Hz (5 kHz) offset frequency, which results in
838 as integrated rms timing jitter [1 Hz - 1 MHz]. The long-term residual
phase drift is 847 as (rms) measured over 2 hours, which reaches
4\times10^{-19} fractional frequency instability at 1800 s averaging time. This
method has a potential to provide both sub-fs-level short-term phase noise and
long-term phase stability in microwave extraction from mode-locked fiber
lasers.
