Quantum Thermodynamics away from Equilibrium: Entanglement, Brownian Motors and Nonergodicity

• Applicant: Professor Dr. Eric Lutz
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2005 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 17546756

• Final Report Year: 2012

Final Report Abstract

The aim of the project was to investigate two complementary aspects of the quantum-mechanical properties of nonequilibrium systems, entanglement and decoherence, and examine the potential applications for the design of nanotechnological devices such as Brownian motors. In the first part, we have developed a general framework to study the properties of nonequilibrium quantum systems. In particular, we have generalized the work relation of Jarzynski and proposed an experimental protocol to verify it in ions traps. Moreover, we have determined the microscopic entropy production in quantum systems, and investigated nonequilibrium entanglement generation in harmonic and spin chains. We have additionally shown that quantum correlations can be used to increase the efficiency of quantum heat engines and put forward a nanoengine using a single trapped ion. In the second part of the project, we have examined decoherence in nonergodic systems. Specifically, we have shown that decoherence in the quantum kicked rotator can be controlled by properly engineering its environment; we have identified a regime of nonexponential decay where the classical limit is never reached. We have further investigated anomalous transport, ergodicity breaking and the multifractal properties of cold atoms in shallow dissipative optical lattices.

Publications

• Collective current rectification, Physica A 377, 429 (2007)
  S. Denisov
  
• Controlled decoherence in a quantum Lévy kicked rotator, Phys. Rev A 77, 062113 (2008)
  H. Schomerus and E. Lutz
  
• Nonequilibrium work distribution of a quantum harmonic oscillator, Phys. Rev. E 77, 021128 (2008)
  S. Deffner and E. Lutz
  
• Quantum discord and quantum phase transition in spin chains, Phys. Rev. B 78, 224413 (2008)
  R. Dillenschneider
  
• Energy cost and optimal entanglement production in harmonic chains, Phys. Rev. A 79 032327 (2009)
  F. Galve and E. Lutz
  
• Entanglement resonance in driven spin chains, Phys. Rev. A 79, 032332 (2009)
  F. Galve, D. Zueco, S. Kohler, E. Lutz, and P. Hänggi
  
• Nonequilibrium thermodynamic analysis of squeezing, Phys. Rev. A 79, 055804 (2009)
  F. Galve and E. Lutz
  
• Quantum Smoluchowski equation for driven systems, Phys. Rev. E 80 042101 (2009)
  R. Dillenschneider and E. Lutz
  
• Quantum work statistics of linear and nonlinear parametric oscillators, Chem. Phys. 375, 200 (2010)
  S. Deffner, O. Abah, and E. Lutz
  
• Hamiltonian of mean force for a damped quantum oscillator, Phys. Rev. A 84 031110 (2011)
  S. Hilt, B. Thomas and E. Lutz
  
• Quantum walk with jumps, Eur. J. Phys. B 64, 119 (2011)
  H. Lavicka, V. Potocek, T. Kiss, E. Lutz, and I. Jex
  
• Solution of the Fokker-Planck equation with a logarithmic potential, J. Stat. Phys. 145, 1524 (2011)
  A. Dechant, E. Lutz, E. Barkai, and D. Kessler
  
• Statistical mechanics of entanglement mediated by a thermal reservoir I, Phys. Rev. A 85, 042318 (2012)
  E. Kajari, A. Wolf, E. Lutz, and G. Morigi
  (See online at https://doi.org/10.1103/PhysRevA.85.042318)
• Super-aging correlation function and ergodicity breaking in logarithmic potentials, Phys. Rev. E 85, 051124 (2012)
  Andreas Dechant, Eric Lutz, David Kessler, and Eli Barkai