Effects and detection of quantum noise

Effects and detection of quantum noise

Tobiska, J.

Nazarov, Yu.V. (promotor)

Applied Sciences

2006-01-30

This thesis is about random fluctuations over time (or noise) of electric currents and voltages occuring in small (mesoscopic) electronic devices with typical sizes of micro- to nanometre. Even though the theory presented is of a more general nature, research into such systems has been greatly pushed forward by the prospect of building a quantum computer. There are two important aspects to noise which are addressed in this work. The first can be summarised as detection and refers to the idea, that the fluctuations carry information about the microscopic details (geometric design, scattering, temperature) of transport which causes them. The theoretical problem we investigate is then to relate detector signals to fundamental properties of the sample. Secondly, fluctuations can trigger a variety of processes in the environment. Depending on the system one may wish to enhance or diminish such effects. To achieve this goal we study noise-induced effects and the coupling between noise sources and their environment. The precise way in which these fluctuations occur can be found from the theory of Full Counting Statistics (FCS) which provides a cornerstone for this thesis. In chapter 3 the effect of a weak electromagnetic environment on the Full Counting Statistics of a coherent conductor is investigated. We obtain explicit expressions for the correction to the FCS which are further studied by analytical and numerical means. We also present a reinterpretation of the correction in terms of elementary physical events. The major result in that chapter is a universal relation for Full Counting Statistics which holds at arbitrary voltage, temperature and with no regard to the concrete realization of the contact. For FCS this relation takes the form of detailed balance. In chapter 4 we investigate the detection of finite frequency noise using a quantum tunnelling detector. We focus on a concrete experimental setup consisting of a coherent conductor taking the role of the noise source and a tunnel junction (the detector) which is capacitively coupled to it. We show that the detector rate in a certain parameter range is dominated by a two-photon process and a process involving two interacting electrons in the coherent conductor. We find an explicit analytical expression for the detector signal in terms of system parameters: tunnel coupling, transmissions, environment, voltage over the conductor and coupling parameter. Our results facilitate the detection of many-particle events in the context of quantum transport, particularly electron-electron interactions. The non-Gaussian higher moments of the distribution of current fluctuations in a mesoscopic conductor contain more information than is present in average current and noise. However they are inherently difficult to measure. In order to facilitate such experiments, we propose a completely new way for measuring the Full Counting Statistics in chapter 5. We study threshold detection with a Josephson junction coupled to a mesoscopic conductor. We show that the detailed dependence of the junction's escape rate is sensitive to the distinct FCS of specific conductors (tunnel junction, diffusive, ballistic). We also address issues related to the measurement procedure notably feedback and dispersiveness of the detector. Our theoretical results facilitate a new type of electric noise measurement: direct measurement of the full distribution of transferred charge.

quantum noise
detection
Josephson junction
quantum point contact
photon assisted tunneling
quantum dot
full counting statistics
coherent conductor

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doctoral thesis

(c) 2006 J. Tobiska