Bidirectional Single-Electron Counting and the Fluctuation Theorem

Physical review. B, Condensed matter (Impact Factor: 3.66). 08/2009; 81(12). DOI: 10.1103/PhysRevB.81.125331
Source: arXiv


We investigate theoretically and experimentally the full counting statistics of bidirectional single-electron tunneling through a double quantum dot in a GaAs/GaAlAs heterostructure and compare with predictions of the fluctuation theorem (FT) for Markovian stochastic processes. We observe that the quantum point contact electrometer used to study the transport induces nonequilibrium shot noise and dot-level fluctuations and strongly modifies the tunneling statistics. As a result, the FT appears to be violated. We show that it is satisfied if the back-action of the electrometer is taken into account, and we provide a quantitative estimate of this effect. Comment: 4pages, 2figures

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Available from: Gerd Schön, Oct 01, 2015
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    • "The precise meaning of these expressions will be amply clarified below. The real-valued constants a, b, contain information about the equilibrium starting points of the B and F transformations. Figure 1 depicts a probability distribution satisfying the fluctuation relation, as measured in a recent experiment of electron transport through a nano-junction (Utsumi et al., 2010). We shall analyze this experiment in detail in Sec. "
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    ABSTRACT: Two fundamental ingredients play a decisive role in the foundation of fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars we guide the reader through a self-contained exposition of the theory and applications of quantum fluctuation relations. These are exact results that constitute the fulcrum of the recent development of nonequilibrium thermodynamics beyond the linear response regime. The material is organized in a way that emphasizes the historical connection between quantum fluctuation relations and (non)-linear response theory. We also attempt to clarify a number of fundamental issues which were not completely settled in the prior literature. The main focus is on (i) work fluctuation relations for transiently driven closed or open quantum systems, and (ii) on fluctuation relations for heat and matter exchange in quantum transport settings. Recently performed and proposed experimental applications are presented and discussed.
    Review of Modern Physics 12/2010; 83(3). DOI:10.1103/RevModPhys.83.771 · 29.60 Impact Factor
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    ABSTRACT: Experiments on the direction-resolved full-counting statistics of single-electron tunneling allow testing the fundamentally important Fluctuation Theorem (FT). At the same time, the FT provides a frame for analyzing such data. Here we consider tunneling through a double quantum dot system which is coupled capacitively to a quantum point contact (QPC) detector. Fluctuations of the environment, including the shot noise of the QPC, lead to an enhancement of the effective temperature in the FT. We provide a quantitative explanation of this effect; in addition we discuss the influence of the finite detector bandwidth on the measurements. Comment: Prepared for "Perspectives of Mesoscopic Physics - Dedicated to Prof. Yoseph Imry's 70th Birthday"
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    ABSTRACT: We experimentally demonstrate the validity of nonequilibrium fluctuation relations by using a quantum coherent conductor. In equilibrium the fluctuation-dissipation relation leads to the correlation between current and current noise at the conductor, namely, the Johnson-Nyquist relation. When the conductor is voltage biased so that the nonlinear regime is entered, the fluctuation theorem has predicted similar nonequilibrium fluctuation relations, which hold true even when the Onsager-Casmir relations are broken in magnetic fields. Our experiments qualitatively validate the predictions as the first evidence of this theorem in the nonequilibrium quantum regime.
    Physical Review Letters 02/2010; 104(8):080602. DOI:10.1103/PhysRevLett.104.080602 · 7.51 Impact Factor
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