Electron counting probability

Seiji Saito, Junji Endo, Tetsuji Kodama +3 more

Donald J Hinson

I M Every

The probability P(n,t 1 ,T 2 ) of counting n electrons in the time interval from t 1 to t 2 is derived from a quantum-electrodynamic treatment of an electron multiplier. Although the expressions obtained are similar to those obtained by Glauber for photons there remain fundamental differences. The interest of these results for existing and proposed experiments on electron beams is outlined.

D A Simmons, Donald J Hinson, A. Ioannidou-Phili

Fabio Taddei, Rosario Fazio

The counting statistics (CS) for charges passing through a coherent conductor comprise the most general quantity that characterizes electronic transport. The CS depend not only on the transport properties of the conductor, but also on the correlations among particles which compose the incident beam. In this paper we present general results for the CS of entangled electron pairs traversing a beam splitter, and we show that the probability that Q charges have passed is not binomial, as in the uncorrelated case, but is symmetric with respect to the average transferred charge. We furthermore consider the joint probability for transmitted charges of a given spin, and we show that the signature of entanglement distinctly appears in a correlation which is not present for a nonentangled case.

Masashi Ban

A theory of electron-counting processes is formulated in terms of the Liouville space method. The developed model is based on the quantum Markov processes developed by Davies and Srinivas. The time evolution of an electron system interacting with an electron counter and the counting probability distribution are investigated. The average value, fluctuation, and correlation function of the electron number registered by the counter are calculated, and the sub-Poissonian distribution and antibunching correlation of the electrons are obtained for an arbitrary noncorrelated initial state of electrons. For a correlated initial state, depending on the initial correlation among the electrons and on the electron counters used in the measurement, the statistics for the electron number registered by the counter is characterized as a sub-Poissonian, Poissonian, or super-Poissonian distribution, and the intensity correlation function exhibits antibunching or bunching correlation. As an example, the state with correlation between the up-spin and down-spin electrons is considered. The electron counting processes under the influence of a chaotic electron source are also considered, and the effect of the chaotic electron source on the counting statistics is investigated.