Feb. 15, 2006

Correlations and entanglement in nanostructures

K. Kinderman

Rapid experimental progress over the past two decades has made available electronic systems with an effectively reduced spatial dimensionality. In such structures electron-electron interactions generically induce strong correlations that are able to change their properties drastically. A thorough characterization of these correlations is essential for a clear understanding of electronic systems at the nanoscale. Electronic structures are typically probed by measurements of electrical currents. Interaction-induced correlations in these systems may thus be studied experimentally by measurements of correlations of electrical currents. Several fascinating correlation effects in nanostructures have been discovered by such measurements. I will give a brief overview of these effects and discuss one of them in more detail: a recently observed suppression of current correlations in strongly interacting quantum wires. In many situations, however, standard current correlation measurements are insensitive to interaction-induced correlations. It has for instance been shown by Levitov and Reznikov that current correlations of conductors in the generic tunneling regime carry no information at all about many-body interactions. Motivated by this I will propose an alternative experimental probe that aims at more subtle correlations than these conventional measurements. It is based on an experimentally accessible measure of the interaction-induced ground state entanglement of fermionic systems. This many-body entanglement quantifies selectively interaction-induced correlations in the ground state wave function. It vanishes in the absence of interactions. I will discuss properties of the proposed entanglement measure with two examples of typical electronic nanostructures: an interacting quantum dot and a superconducting tunnel conductor.