  We report observational evidence of highly turbulent ionized gas kinematics
in a sample of 20 Lyman continuum (LyC) emitters (LCEs) at low redshift ($z\sim
0.3$). Detailed Gaussian modeling of optical emission line profiles in
high-dispersion spectra consistently shows that both bright recombination and
collisionally excited lines can be fitted as one or two narrow components with
intrinsic velocity dispersion of $\sigma$ $\sim$ 40-100 km s$^{-1}$, in
addition to a broader component with $\sigma \sim$ 100-300 km s$^{-1}$, which
contributes up to $\sim$40% of the total flux and is preferentially blueshifted
from the systemic velocity. We interpret the narrow emission as highly ionized
gas close to the young massive star clusters and the broader emission as a
signpost of unresolved ionized outflows, resulting from massive stars and
supernova feedback. We find a significant correlation between the width of the
broad emission and the LyC escape fraction, with strong LCEs exhibiting more
complex and broader line profiles than galaxies with weaker or undetected LyC
emission. We provide new observational evidence supporting predictions from
models and simulations; our findings suggest that gas turbulence and outflows
resulting from strong radiative and mechanical feedback play a key role in
clearing channels through which LyC photons escape from galaxies. We propose
that the detection of blueshifted broad emission in the nebular lines of
compact extreme emission-line galaxies can provide a new indirect diagnostic of
Lyman photon escape, which could be useful to identify potential LyC leakers in
the epoch of reionization with the JWST.
