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 states with quantum-mechanical coherent states.
A weakly biased normal-metal-superconductor junction is considered as a potential device injecting entangled pairs of quasi-particles into a normal-metal lead. The two-particle states arise from Cooper pairs decaying into the normal lead and are characterized by entangled spin-and orbital degrees of freedom. The separation of the entangled quasi-particles is achieved with a fork geometry and normal leads containing spin-or energy-selective filters. Measuring the current-current cross-correlator between the two normal leads allows to probe the efficiency of the entanglement (cond-mat/0009193).PACS 03.67.Hk,72.70.+m,74.50.+r The nonlocal nature of quantum mechanics has been demonstrated theoretically [1] using entangled pairs of particles several decades ago. Recently, potential applications of this entanglement have been found in quantum cryptography [2], in quantum teleportation [3], and in quantum computing [4]. It is thus necessary to search for practical ways to produce such pairs given a specific interaction between particles. While past experiments have focused on pairs of photons [5] propagating in vacuum, attention is now turning to electronic systems [6], where this entanglement interaction can be stronger while coherence can still be maintained over appreciable distances in mesoscopic conductors. A scheme was recently presented [7] which discussed the entanglement of electrons via the exchange interaction in pairs of quantum dots. Here, we propose a rather robust electronic entanglement scheme based on the Andreev reflection of electrons and holes at the boundary between a normal metal and a superconductor.The basic concept underlying the microscopic description of superconductivity is the formation of Cooper pairs. A normal metal in vicinity to a superconductor bears the trace of this phenomenon through the presence of Bogoliubov quasi-particles, or through the non-vanishing of the Gor'kov Green function [8] F = c k↑ c −k↓ (c kσ denote the usual electron annihilation operators). While in a superconductor F = ∆/λ is a consequence of a nonzero gap parameter ∆ (λ is the pairing potential), the coherence surviving in the adjacent normal metal can be understood through the presence of evanescent Cooper pairs. These involve two electrons with entangled spin-and orbital degrees of freedom, carrying opposite spins in the case of usual s-wave pairing and with kinetic energies above and below the superconductor chemical potential. This proximity effect has been illustrated in several recent experiments [9].In order to detect this entanglement and implement it for applications, it is necessary to achieve a spatial separation between the two constituent electrons. The entanglement apparatus which is proposed here consists of a mesoscopic normal-metal-superconductor (NS) junction with normal leads arranged in a fork geometry (see Fig. 1). Using appropriate spin-or energy-selective filters in the two normal leads the quasi-particle pairs are properly separated and their entanglement can be quantified through a c...
Bell-inequality checks constitute a probe of entanglement -given a source of entangled particles, their violation are a signature of the non-local nature of quantum mechanics. Here, we study a solid state device producing pairs of entangled electrons, a superconductor emitting Cooper pairs properly split into the two arms of a normal-metallic fork with the help of appropriate filters. We formulate Bell-type inequalities in terms of current-current cross-correlators, the natural quantities measured in mesoscopic physics; their violation provides evidence that this device indeed is a source of entangled electrons.
We consider a measurement of finite-frequency current fluctuations, using a resonance circuit as a model for the detector. We arrive at an expression for the measurable response in terms of the current-current correlators which differs from the standard ͑symmetrized͒ formula. The possibility of detection of vacuum fluctuations is discussed.PACS numbers: 05.40.ϩj, 07.50. Hp, 72.70.ϩm Finite-frequency ͑FF͒ current fluctuations at zero temperature ͑vacuum fluctuations, VFs͒ have been discussed for a long time 1 in connection with the analogous question of electromagnetic vacuum fluctuations. Recently there has been renewed interest in the noise at finite frequency in connection with the supposed possibility of observing the Fermi edge singularity in noninteracting 1,2 and interacting 3 systems.In the present letter we consider a realistic model for an FF measurement and show that, in a very close analogy with the electromagnetic vacuum fluctuations, a certain measurability limitation appears.There are different practical and theoretical approaches to FF measurements:1. Making repeated measurements of the instantaneous values of the current over a long time interval and later Fourier transforming the data obtained.2. Making a single measurement of the charge transmitted during a given time interval. In that case the information about the FF fluctuation appears through an integral over all frequencies. Ideally that can be done by making two measurements of the charge in the reservoir, the initial ͑during system preparation͒ and final. An alternative measurement can be made with a ''Larmor clock'' ͑the spin rotating in the magnetic field produced by the current͒; this method, which is described in Ref. 4, can perhaps be implemented.3. Making a time-averaged measurement of the response of a resonance circuit, which can be an ordinary LC element, i.e., an inductive element coupled to the quantum wire, a capacitor whose charge is the quantity to be measured as a response, and the resistance of the circuit.The last approach, we believe, is the most relevant for FF measurements.We model our detector ͑the resonator, which we will refer to as LC) by an oscillator 1
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