Over the past years, ultrafast lasers with average powers in the 100 W range have become a mature technology, with a multitude of applications in science and technology. Nonlinear temporal compression of these lasers to few- or even single-cycle duration is often essential, yet still hard to achieve, in particular at high repetition rates. Here we report a two-stage system for compressing pulses from a 1030 nm ytterbium fiber laser to single-cycle durations with 5 ${mu}$J output pulse energy at 9.6 MHz repetition rate. In the first stage, the laser pulses are compressed from 340 to 25 fs by spectral broadening in a krypton-filled single-ring photonic crystal fiber (SR-PCF), subsequent phase compensation being achieved with chirped mirrors. In the second stage, the pulses are further compressed to single-cycle duration by soliton-effect self-compression in a neon-filled SR-PCF. We estimate a pulse duration of ~3.4 fs at the fiber output by numerically back-propagating the measured pulses. Finally, we directly measured a pulse duration of 3.8 fs (1.25 optical cycles) after compensating (using chirped mirrors) the dispersion introduced by the optical elements after the fiber, more than 50% of the total pulse energy being in the main peak. The system can produce compressed pulses with peak powers >0.6 GW and a total transmission exceeding 70%.
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