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AIP conference proceedings

Current fluctuations in a dissipative environment

Alessandro Braggio, Christian Flindt, Tomáš Novotný, Massimo Macucci, Giovanni Basso

Published Jan 1, 2009• 2 citations
Publisher

Abstract

We have recently developed methods for calculating the statistics of a single counted quantity in a stochastic transport process described by a non‐Markovian generalized master equation. Here, we expand on these ideas and extend our formalism to several counted quantities, allowing us to study cross‐correlations between different variables. As an illustrative example, we consider charge transport through a double quantum dot capacitively coupled to a quantum point contact. We calculate the cross‐correlations between the current through the double quantum dot and the current through the quantum point contact, and demonstrate the sensitivity of this cross‐correlator to measurement quantum back‐action.

DOI
10.1063/1.3140491

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We have recently developed methods for calculating the statistics of a single counted quantity in a stochastic transport process described by a non‐Markovian generalized master equation. Here, we expand on these ideas and extend our formalism to several counted quantities, allowing us to study cross‐correlations between different variables. As an illustrative example, we consider charge transport through a double quantum dot capacitively coupled to a quantum point contact. We calculate the cross‐correlations between the current through the double quantum dot and the current through the quantum point contact, and demonstrate the sensitivity of this cross‐correlator to measurement quantum back‐action.
We consider the counting statistics of electron transport through a double quantum dot with special emphasis on the dephasing induced by a nearby charge detector. The double dot is embedded in a dissipative enviroment, and the presence of electrons on the double dot is detected with a nearby quantum point contact. Charge transport through the double dot is governed by a non-Markovian generalized master equation. We describe how the cumulants of the current can be obtained for such problems, and investigate the difference between the dephasing mechanisms induced by the quantum point contact and the coupling to the external heat bath. Finally, we consider various open questions of relevance to future research.
We present a formalism for studying the behavior of quantum systems coupled to nonequilibrium environments exhibiting non-Gaussian fluctuations. We discuss the role of a qubit as a detector of the statistics of environmental fluctuations, as well as non-Markovian effects in both weak and strong-coupling limits. We also discuss the differences between the influences of classical and quantum environments. As examples of the application of this formalism we study the dephasing and relaxation of a charge qubit coupled to nonequilibrium electron transport through single and double quantum dots.
We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.
We formulate a quantum theory of electron waiting time distributions for charge transport in nanostructures described by non-Markovian generalized master equations. We illustrate our method by calculating the waiting time distribution of electron transport through a dissipative double quantum dot, where memory effects are present due to a strongly coupled heat bath. We consider the influence of non-Markovian dephasing on the distribution of electron waiting times and discuss how spectral properties of the heat bath may be detected through measurements of the electron waiting time.
Nonequilibrium transport properties of quantum systems have recently become experimentally accessible in a number of platforms in so-called full-counting experiments that measure transient and steady-state nonequilibrium transport dynamics. We show that the effect of the measurement back-action can be exploited to establish general relationships between transport coefficients in the transient regime which take the form of fluctuation-dissipation theorems in the steady state. This result becomes most conspicuous in the transient dynamics of open quantum systems under strong-coupling to non-Markovian environments in nonequilibrium settings. In order to explore this regime, a new simulation method based in a hierarchy of equations of motion has been developed. We instantiate our proposal with the study of energetic conductance between two baths connected via a few level system.
We investigate the trajectory-level stochastic dynamics of a double quantum dot system using the formalism of stochastic excursions. An excursion is a sub-trajectory that begins when the system leaves a chosen reference state (or more generally, a set of states)---here, the empty double dot---and ends upon its first return to it. Filtering trajectories into excursions extends full counting statistics and gives access to the correlations between thermodynamic currents and excursion durations. The main objects of study are counting observables, defined as weighted sums of transition counts within a single excursion. For three main counting observables---charge current, dynamical activity, and entropy production---we compute averages and noise contributions and show how they provide insights into the operation of the double quantum dot system. At the trajectory level, we analyze outcome distributions for transport and connect the results with trade-offs between successful and unsuccessful events that shape the overall performance of the double quantum dot as a transport device. We then discuss the populations of the two dots, as well as their correlations. Finally, we illustrate how the framework provides insights into the thermodynamics of precision through the Fano factor and thermo-kinetic uncertainty relations, where different regimes are fundamentally constrained either by entropy production or by dynamical activity. Altogether, our work is a case study that highlights the utility of the excursion framework as a toolkit to analyze many quantities of interest and to uncover the structure of nonequilibrium fluctuations. Moreover, it also suggests new avenues for refining uncertainty relations and understanding transport in mesoscopic systems.