  We investigate the many-body generalization of the orthogonality catastrophe
by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a
global change of interaction. It decays exponentially with system size and
exhibits universal behaviour: the steady state exponent after quenching back
and forth n-times between 2 LLs (bang-bang protocol) is 2n-times bigger than
that of the adiabatic overlap, and depends only on the initial and final LL
parameters. These are corroborated numerically by matrix-product state based
methods of the XXZ Heisenberg model. An experimental setup consisting of a
hybrid system containing cold atoms and a flux qubit coupled to a Feshbach
resonance is proposed to measure the Loschmidt echo using rf spectroscopy or
Ramsey interferometry.
