Qubit Seminar: Dr. Roman Riwar

PGI-2

Fractional charges in conventional sequential electron tunneling - Part II: topological numbers in open quantum systems

Abstract: In a previous talk, I discussed topological braid transitions in the full counting statistics of standard sequential electron tunneling, and argued that they can lead to an effective fractionalization of charge, even in the absence of exotic quantum correlations. Here, I want to dive deeper into a framework that can describe the braid topology in terms of generalized notions of geometric phases defined along the counting field. In fact, I show that there exists a quantized geometric phase whose value is directly related to the effective fractional charges.

In doing so, I propose a way to generalize the notion of topology to nonequilibrium open quantum systems, by using the detector degrees of freedom. Then, I use this geometric phase to demonstrate a deep analogy between fractional charges in dissipative transport and the fractional Josephson effect.

To formally demonstrate the quantization of the geometric phase, I need to introduce the notion of a complex counting field. In this complex space, there appear so-called exceptional points, to which one can assign braid generators. These exceptional points in the complex plane first of all define the topology of the spectrum along the real counting field, a fact that can be loosely regarded as a bulk-boundary correspondence. Secondly, each exceptional point contributes to the geometric phase with half a winding, thus giving rise to the quantization of the geometric phase.

Kontakt

Mohammad Ansari

Telefon: +49 2461 61-4676

Fax:  +49 2461 61-2620

E-Mail: m.ansari@fz-juelich.de