# Decoherence

### From Institute for Theoretical Physics II / University of Erlangen-Nuremberg

## Interaction effects and decoherence

A main focus of our research centers on the effects of interactions in electronic transport experiments. This involves, in particular, the destruction of quantum-mechanical interference phenomena, often called "decoherence" or "dephasing".

In the picture shown here, two wave packets interfere to form interference fringes. However, the action of some fluctuating environment (represented by the wavy orange lines) leads to dephasing and thus blurs the interference pattern (see the 'observed' pattern to the right of the red line, in contrast to the undisturbed pattern at the left). In a sense, dephasing produces the gradual crossover between wave-like phenomena (interference) and particle-like behaviour (classical, localized particles with well-defined trajectories). It is brought about by the interactions among the particles or with some external environment (phonons, photons, spins, or other degrees of freedom).

In the following, we discuss a few examples of our research topics in the field of decoherence.

## The Mach-Zehnder interferometer

The most basic two-way interference setup - the Mach-Zehnder interferometer - has been invented for light about 100 years ago. However, for electrons it has been realized in ideal form only recently, by an experimental group at the Weizmann institute - read their Nature 422, 415 - 418 (2003). This opens interesting possibilities to explore the interference of electrons (tunable via a magnetic flux), and its destruction by fluctuations in the environment. It also represents a challenge for theorists: While dephasing of a single particle under the influence of an environment has been discussed quite thoroughly in the past, the presence of a Fermi sea adds important features, particularly Pauli blocking. In addition, the experimentalists measured the shot noise to learn more about dephasing, thus combining two modern topics in mesoscopic physics.

In our theoretical work, we have analyzed fermions moving through such a Mach-Zehnder setup, subject to a fluctuating quantum field representing phonons or Nyquist noise or other sources of dephasing (read Europhysics Letters 72, 788 (2005) ). We have introduced a novel and physically transparent equations-of-motion approach, calculated the loss of interference contrast (fully capturing Pauli blocking effects), and made connections to the theory of dephasing in weak localization. Besides, the technically most challenging part of this work is the calculation of the shot noise in the interferometer output current. This extends our previous analysis, where we had studied the considerably simpler limit of classical external noise - see Phys. Rev. Lett. 92, 056805 (2004) and Phys. Rev. B 70, 125305 (2004)

## Dissipation and relaxation in a many-particle system: A many-fermion version of the Caldeira-Leggett model

A single particle coupled via springs to an infinite number of other particles: That is the simplest possible generic model in which friction and fluctuations act on a quantum-mechanical particle. It is called the "Caldeira-Leggett model" and represents a cornerstone of the theory of quantum-dissipative systems. Its applications range from the diffusion of particles in a crystal to dissipation in superconducting Josephson junctions. However, in many other interesting problems involving dissipation and dephasing, one does not consider a single particle, but rather an electron being part of a Fermi sea of electrons. Then, additional effects due to the Pauli principle drastically change the picture.

Together with Dmitri Golubev (Karlsruhe), we have constructed the simplest nontrivial many-fermion extension of the Caldeira-Leggett model. Our model deals with fermions moving inside a harmonic oscillator, subject to a fluctuating quantum force. This force leads to relaxation and dephasing, which we have analyzed using bosonization techniques.

See: *Relaxation and Dephasing in a Many-Fermion Generalization of the Caldeira-Leggett Model, F. Marquardt and D. S. Golubev, Phys. Rev. Lett. 93, 130404 (2004) Journal PDF Cite*

You will learn about the failure of the naive picture of a single particle undergoing energy relaxation until it reaches the Fermi surface, how relaxation and dephasing are revealed in the time-evolution of the density matrix, what are the consequences of the bath-induced effective interaction between the fermions, how the coupling to the bath smears the Fermi surface, and how the Pauli principle affects all this.