Loschmidt echo and the many-body orthogonality catastrophe in a qubit-coupled Luttinger liquid.
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 behavior: 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.
BME-MTA Exotic Quantum Phases Research Group, Budapest University of Technology and Economics, Budapest 1521, Hungary. dora@eik.bme.hu
Balázs
B
Dóra
Frank
F
Pollmann
József
J
Fortágh
Gergely
G
Zaránd