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Physics Letters A

Electron counting theory

Seiji Saito, Junji Endo, Tetsuji Kodama, Akira Tonomura, Akira Fukuhara, Kohji Ohbayashi

Published Mar 1, 1992• 20 citations
Publisher
DOI
10.1016/0375-9601(92)90003-5

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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.
A theory of electron counting statistics in quantum transport is presented. It involves an idealized scheme of current measurement using a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current. Within such an approach, counting charge without breaking the circuit is possible. As an application, we derive the counting statistics in a single channel conductor at finite temperature and bias. For a perfectly transmitting channel the counting distribution is gaussian, both for zero-point fluctuations and at finite temperature. At constant bias and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics. Another application considered is the noise due to short current pulses that involve few electrons. We find the time-dependence of the driving potential that produces coherent noise-minimizing current pulses, and display analogies of such current stateswith quantum-mechanical coherent states.