Wave-packet approach to full counting statistics

Abstract

Traditionally, (charge) transport phenomena describe the average current flow in response to a constant applied driving force. Additional information is provided by current-current correlations or noise, telling about the granularity, the statistical properties, and the interactions between the particles. The complete characterization of transport is given by the full counting statistics, quantifying the probability that n particles pass the device during a time window t. The desire for a complete characterization of transport in a mesoscopic device goes together with the development of new single-particle sources and the availability of quantum bits as measurement devices. In this thesis, we will describe how to combine these three elements, full counting statistics, single-particle sources, and qubit measurement devices and how these concepts relate to the description of charge transport of noninteracting electrons in a mesoscopic device. In the work on full counting statistics, we develop a new wave-packet formalism that provides access to an entire class of interesting results. The wavepacket formalism is derived from an insight regarding the equivalence between the fidelity of a quantum system and the generating function of full counting statistics; furthermore, we show how qubits can be used to measure both quantities, fidelity and full counting statistics, exploiting the induced ‘decoherence’ as a signal; thereby, we transfer the measurement of the fidelity and of the full counting statistics from the realm of a ‘Gedanken’ experiment to a practical proposal realizable with today’s qubit technology. Subsequently, we study the full counting statistics for the transmission of two identical particles with positive or negative symmetry under exchange, for the situation where the scattering depends on energy. We make use of our firstquantized wave-packet formalism and find interesting results. While it is expected that the noise as well as higher-order correlators will be sensitive to the exchange symmetry, we find the astounding result that exchange can hugely enhance (or suppress) the average charge already. The effect is a consequence of the symmetry-induced reshuffling of weight in the momentum distribution of the