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

TL;DR

This paper explores the many-body orthogonality catastrophe in Luttinger liquids by analyzing the Loschmidt echo after interaction changes, revealing universal decay behavior and proposing an experimental measurement method.

Contribution

It introduces a universal decay law for the Loschmidt echo in Luttinger liquids after interaction quenches and proposes an experimental setup to measure it.

Findings

Exponential decay of Loschmidt echo with system size.

Universal behavior of steady state exponent after multiple quenches.

Numerical validation using matrix-product state methods.

Abstract

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.