  Superfluid helium confined to nanofluidic systems is emerging as an important
system for studies of two-dimensional turbulence and as the basis for novel
quantum technologies. In fully enclosed nanofluidic geometries only the fourth
sound can propagate, which we show can be used for probing quantized vortices
pinned in well-defined slab geometry. We show that similarly to
well-established second sound attenuation, fourth sound attenuation can be used
to infer the number of quantized vortices in a unit area. We experimentally
verify fourth sound attenuation as a probe of vortex line density by injecting
a known number of quantized vortices into a nanofluidic slab using a rotating
cryostat.
