  Intertwining charge density wave (CDW) with spin and pairing order parameters
is a major focus of contemporary condensed matter physics. Lattice distortions
and local symmetry breaking resulted from CDWs are crucial for the emergence of
correlated and topological states in quantum materials in general. While the
presence of CDWs can be detected by diffraction or spectroscopic techniques,
atomic visualization of the CDW induced lattice distortions remains limited to
CDW with short wavelengths. In this letter, we realized the imaging of
incommensurate long-wavelength CDWs based on cryogenic four-dimensional
scanning transmission electron microscopy (cryo-4DSTEM). By visualizing the
incommensurate CDW induced lattice modulations in a skyrmion magnet EuAl4, we
discover two out-of-phase intra-unit cell shear modulations that specifically
break the local inversion-symmetry. Our results provide direct evidence for the
intertwined spin and charge orders in EuAl4 and key information about local
symmetry. Furthermore, we establish cryo-4DSTEM as an indispensable approach to
understand CDW induced new quantum states of matter.
