We demonstrate the stable and flexible light delivery of multi-{\mu}J, sub-200-fs pulses over a ~10-m-long vacuumized anti-resonant hollow-core fiber (AR-HCF), which was successfully used for high-performance pulse synchronization. Compared with the pulse train launched into the AR-HCF, the transmitted pulse train out of the fiber exhibits excellent stabilities in pulse power and spectrum, with pointing stability largely improved. The walk-off between the fiber-delivery and the other free-space-propagation pulse trains, in an open loop, was measured to be <6 fs root-mean-square (RMS) over 90 minutes, corresponding to a relative optical-path variation of <2x10-7. This walk-off can be further suppressed to ~2 fs RMS simply using an active control loop, highlighting the great application potentials of this AR-HCF set-up in large-scale laser and accelerator facilities.
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