Shot noise in tunneling transport through molecules and quantum dots

We consider electrical transport through single molecules coupled to metal electrodes via tunneling barriers. Approximating the molecule by the Anderson impurity model as the simplest model which includes Coulomb charging effects, we extend the ``orthodox'' theory to expand current and shot noise systematically order by order in the tunnel couplings. In particular, we show that a combined measurement of current and shot noise reveals detailed information of the system even in the weak-coupling limit, such as the ratio of the tunnel-coupling strengths of the molecule to the left and right electrode, and the presence of the Coulomb charging energy. Our analysis holds for single-level quantum dots as well.Comment: 8 page

Influence of a Random Telegraph Process on the Transport through a Point Contact

We describe the transport properties of a point contact under the influence of a classical two-level fluctuator. We employ a transfer matrix formalism allowing us to calculate arbitrary correlation functions of the stochastic process by mapping them on matrix products. The result is used to obtain the generating function of the full counting statistics of a classical point contact subject to a classical fluctuator, including extensions to a pair of two-level fluctuators as well as to a quantum point contact. We show that the noise in the quantum point contact is a sum of the (quantum) partitioning noise and the (classical) noise due to the two-level fluctuator. As a side result, we obtain the full counting statistics of a quantum point contact with time-dependent transmission probabilities.Comment: 8 pages, 2 figure; a new section about experiments and a figure showing the crossover from sub- to superpoissonian noise have been adde

Adiabatic non-equilibrium steady states in the partition free approach

Consider a small sample coupled to a finite number of leads, and assume that the total (continuous) system is at thermal equilibrium in the remote past. We construct a non-equilibrium steady state (NESS) by adiabatically turning on an electrical bias between the leads. The main mathematical challenge is to show that certain adiabatic wave operators exist, and to identify their strong limit when the adiabatic parameter tends to zero. Our NESS is different from, though closely related with the NESS provided by the Jak{\v s}i{\'c}-Pillet-Ruelle approach. Thus we partly settle a question asked by Caroli {\it et al} in 1971 regarding the (non)equivalence between the partitioned and partition-free approaches

Full counting statistics of information content

We review connections between the cumulant generating function of full counting statistics of particle number and the R\'enyi entanglement entropy. We calculate these quantities based on the fermionic and bosonic path-integral defined on multiple Keldysh contours. We relate the R\'enyi entropy with the information generating function, from which the probability distribution function of self-information is obtained in the nonequilibrium steady state. By exploiting the distribution, we analyze the information content carried by a single bosonic particle through a narrow-band quantum communication channel. The ratio of the self-information content to the number of bosons fluctuates. For a small boson occupation number, the average and the fluctuation of the ratio are enhanced.Comment: 16 pages, 5 figure

Optimal control of shot noise and Fano factor by external fields

A method is devised to control the current, shot noise and Fano factor in a molecular junction using external fields. The tunneling of electrons through a molecular junction weakly coupled to two leads in the presence of a time-dependent external field is studied using a quantum master equation approach. By combining optimal control theory and assuming a predefined time-dependent current pattern, an external field can be determined which does generate a current pattern close to the requested one. With this approach the current flow pattern in time can be chosen in an almost arbitrary fashion. The same technique can be applied to control the shot noise. For minimizing the current, the corresponding shot noise decreases but does not vanish. By minimizing the shot noise, the corresponding current also approaches zero for the present model of spinless electrons. Within certain limits the proposed strategy even works well for the control of the Fano factor. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010