New theoretical methods for Full Counting Statistics and noise spectra in nano-scale electronic systems with long memories

• Applicant: Professor Dr. Tobias Brandes (†)
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2007 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 37945977

• Final Report Year: 2011

Final Report Abstract

With technology advancing towards the nanoscale level, the understanding of dynamical properties of small conductors becomes progressively important. The understanding and the control of quantum properties in nanoscale systems is one of the major keys for the design of new electronic devices, for example in nanoelectronics, nanophotonics, and quantum communication. Dynamical fluctuations of the electric current around its average - full counting statistics (FCS) and noise spectra - have been recognized as a potential tool for fully assessing quantum mechanical properties of electronic systems. The goal of this project was to attack some major issues: 1. Fundamental questions concerning the very definition of FCS in quantum systems and its relation to the quantum measurement. We have made some considerable progress here by applying theoretical tools that originally stem from the field of quantum optics, such as operators describing individual quantum jumps, or waiting time distributions for single electrons. The role of the detector during a transport measurement has become much clearer now, with some models allowing us to quantitatively assess the detector back-action. 2. New theoretical methods for calculating FCS and noise spectra for strongly interacting, dissipative systems with long memory times. Here, we have advanced some theoretical tools such as new versions of generalized master equations to a point of maturity, but we have made less progress in developing alternative FCS methods for strongly correlated systems. 3. The interpretation of FCS experiments. Here, a successful collaboration with a group from Hannover has helped us to apply and adapt our methods to state-of-the-art experiments.

Publications

• Waiting Times and Noise in Single Particle Transport. Ann. Phys. (Berlin) 17, No 7, 477-496 (2008)
  T. Brandes
  
• Transport Statistics of interacting double dot systems: Coherent and Non-Markovian effects. Phys. Rev. B 80, 245107 (2009)
  G. Schaller, G. Kiesslich, and T. Brandes
  
• Universal oscillations in counting statistics. Proc. Natl. Acad. Sci. U.S.A. 106, 10116 (2009)
  C. Flindt, C. Fricke, F. Hohls, T. Novotny, K. Netocny, T. Brandes, and Rolf J. Haug
  
• Weak coupling approximations in non-Markovian transport. Phys. Rev. B 80, 045309 (2009)
  P. Zedler, G. Schaller, G. Kiesslich, C. Emary, and T. Brandes
  
• Feedback Control of Quantum Transport. Phys. Rev. Lett. 105, 060602 (2010)
  T. Brandes
  
• Low-dimensional detector model for full counting statistics: Trajectories, back-action, and fidelity. Phys. Rev. B 82, 041303(R) (2010)
  G. Schaller, G. Kiesslich, and T. Brandes