VietNam 2013 

IXth Rencontres du Vietnam
Quy-Nhon, August 4-10, 2013

 QNplage

 Nanophysics: from fundamentals to applications

(the return)

 

Friday 9
Dots and wires

› 17:00 - 17:30 (30min)
Loschmidt echo and the many-body orthogonality catastrophe in a qubit-coupled Luttinger liquid
Gergely Zarand  1@  , Balázs Dóra  2@  , Frank Pollmann  3@  
1 : EQP group, Institute of Physics, Budapest University of Technology and Economics  (TU Budapest)
Budafoki út 8, H-1521 Budapest -  Hungary
2 : EQP group, Institute of Physics, Budapest University of Technology and Economics  (TU Budapest)
Budafoki út 8, 1521 Budapest -  Hungary
3 : Max Planck Institute of Complex Systems  (MPI Desden)
01187 Dresden -  Germany

The Loschmidt echo (LE) measures the "distance" between two quantum states and serves to quantify irreversibility and chaos in quantum mechanics. Furthermore, it can be used to diagnose quantum phase transitions, and is also an important quantity in various fields of physics, ranging from nuclear magnetic resonance to quantum computation and information theory. 

In this work, we study the interaction-driven LE of a genuine interacting one-dimensional system, a Luttinger liquid (LL). We evaluate the LE within the Luttinger liquid (LL) description for a time dependent Hamiltonian, and verify the predictions of the LL model numerically on the XXZ Heisenberg chain using matrix-product state (MPS) based methods. We find that back scattering plays a role only close to the Ising phases. A connection to work statistics and quantum quenches is also discussed. Finally, we propose an experimental setup to measure the LE of a Luttinger liquid, where a flux qubit coupled to a Feshbach resonance is used to control the interaction in a one-dimensional cold atom gas. In this system, the LE can be measured by performing a Ramsey sequence on the qubit. Alternatively, one could access the Fourier transform of the LE (X-ray absorbtion edge) by measuring the absorbtion spectrum of the qubit.


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