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We investigate the many-body generalization of the orthogonality catastropheby studying the generalized Loschmidt echo of Luttinger liquids (LLs) after aglobal change of interaction. It decays exponentially with system size andexhibits universal behaviour: the steady state exponent after quenching backand forth n-times between 2 LLs (bang-bang protocol) is 2n-times bigger thanthat of the adiabatic overlap, and depends only on the initial and final LLparameters. These are corroborated numerically by matrix-product state basedmethods of the XXZ Heisenberg model. An experimental setup consisting of ahybrid system containing cold atoms and a flux qubit coupled to a Feshbachresonance is proposed to measure the Loschmidt echo using rf spectroscopy orRamsey interferometry.

Loschmidt echo and the many-body orthogonality catastrophe in a qubit-coupled Luttinger liquid