  Investigating Friedel oscillations in ultracold gases would complement the
studies performed on solid state samples with scanning-tunneling microscopes.
In atomic quantum gases interactions and external potentials can be tuned
freely and the inherently slower dynamics allow to access non-equilibrium
dynamics following a potential or interaction quench. Here, we examine how
Friedel oscillations can be observed in current ultracold gas experiments under
realistic conditions. To this aim we numerically calculate the amplitude of the
Friedel oscillations which a potential barrier provokes in a 1D Fermi gas and
compare it to the expected atomic and photonic shot noise in a density
measurement. We find that to detect Friedel oscillations the signal from
several thousand one-dimensional systems has to be averaged. However, as up to
100 parallel one-dimensional systems can be prepared in a single run with
present experiments, averaging over about 100 images is sufficient.
