Statistics of the dissipated energy in driven single-electron transitions

We analyze the distribution of heat generated in driven single-electron transitions and discuss the related non-equilibrium work theorems. In the adiabatic limit, the heat distribution is shown to become Gaussian, with the heat noise that, in spite of thermal fluctuations, vanishes together with the average dissipated energy. We show that the transitions satisfy Jarzynski equality for arbitrary drive and calculate the probability of the negative heat values. We also derive a general condition on the heat distribution that generalizes the Bochkov-Kuzovlev equality and connects it to the Jarzynski equality.Comment: 5 pages, 2 figure

Probing quasiparticle excitations in a hybrid single electron transistor

We investigate the behavior of quasiparticles in a hybrid electron turnstile with the aim of improving its performance as a metrological current source. The device is used to directly probe the density of quasiparticles and monitor their relaxation into normal metal traps. We compare different trap geometries and reach quasiparticle densities below 3um^-3 for pumping frequencies of 20 MHz. Our data show that quasiparticles are excited both by the device operation itself and by the electromagnetic environment of the sample. Our observations can be modelled on a quantitative level with a sequential tunneling model and a simple diffusion equation

Experimental Observation of the Role of Mutual Information in the Nonequilibrium Dynamics of a Maxwell Demon

We validate experimentally a fluctuation relation known as generalized Jarzynski equality governing the work distribution in a feedback-controlled system. The feedback control is performed on a single electron box analogously to the original Szilard engine. In the generalized Jarzynski equality, mutual information is treated on an equal footing with the thermodynamic work. Our measurements provide the first evidence of the role of mutual information in the fluctuation theorem and thermodynamics of irreversible processes.Peer reviewe

Single-electron current sources: towards a refined definition of ampere

Controlling electrons at the level of elementary charge $e$ has been demonstrated experimentally already in the 1980's. Ever since, producing an electrical current $ef$, or its integer multiple, at a drive frequency $f$ has been in a focus of research for metrological purposes. In this review we first discuss the generic physical phenomena and technical constraints that influence charge transport. We then present the broad variety of proposed realizations. Some of them have already proven experimentally to nearly fulfill the demanding needs, in terms of transfer errors and transfer rate, of quantum metrology of electrical quantities, whereas some others are currently "just" wild ideas, still often potentially competitive if technical constraints can be lifted. We also discuss the important issues of read-out of single-electron events and potential error correction schemes based on them. Finally, we give an account of the status of single-electron current sources in the bigger framework of electric quantum standards and of the future international SI system of units, and briefly discuss the applications and uses of single-electron devices outside the metrological context.Comment: 55 pages, 38 figures; (v2) fixed typos and misformatted references, reworded the section on AC pump

Spin orbit coupling at the level of a single electron

We utilize electron counting techniques to distinguish a spin conserving fast tunneling process and a slower process involving spin flips in AlGaAs/GaAs-based double quantum dots. By studying the dependence of the rates on the interdot tunnel coupling of the two dots, we find that as many as 4% of the tunneling events occur with a spin flip related to spin-orbit coupling in GaAs. Our measurement has a fidelity of 99 % in terms of resolving whether a tunneling event occurred with a spin flip or not

Environmentally activated tunneling events in a hybrid single-electron box

We have measured individual tunneling events and Coulomb step shapes in single-electron boxes with opaque superconductor–normal metal tunnel junctions. We observe anomalous broadening of the Coulomb step with decreasing temperature in a manner that is consistent with activation of first-order tunneling events by an external dissipative electromagnetic environment. We demonstrate that the rates for energetically unfavorable tunneling events saturate to finite values at low temperatures, and that the saturation level can be suppressed by more than an order of magnitude by a capacitive shunt near the device. The findings are important in assessing the performance limits of any single-electronic device. In particular, master-equation-based simulations show that the electromagnetic environment realized in the capacitively shunted devices allows for a metrologically accurate charge pump based on hybrid tunnel junctions.Peer reviewe

Leakage current of a superconductor–normal metal tunnel junction connected to a high-temperature environment

We consider a voltage-biased normal metal-insulator-superconductor (NIS) tunnel junction, connected to a high-temperature external electromagnetic environment. This model system features the commonly observed subgap leakage current in NIS junctions through photon-assisted tunneling which is detrimental for applications. We first consider a NIS junction directly coupled to the environment and analyze the subgap leakage current both analytically and numerically; we discuss the link with the phenomenological Dynes parameter. Then, we focus on a circuit where a low-temperature lossy transmission line is inserted between the NIS junction and the environment. We show that the amplitude of the transmitted frequencies relevant for the photon-assisted tunneling is exponentially suppressed as the length ℓ and the resistance per unit length R0 of the line are increased. Consequently, the subgap current is reduced exponentially as well. This property can not be obtained by means of lumped circuit elements. We finally discuss our results in view of the performance of NIS junctions in applications.Peer reviewe