Electron counting statistics and coherent states of electric current

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 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.

arXiv:cond-mat/9607137Journal of Mathematical PhysicsOct 1, 1996947 citations

Quantum Measurement in Electric Circuit

Leonid S Levitov, Gordey B. Lesovik

We study fluctuations of electric current in a quantum resistor and derive a general quantum-mechanical formula for the distribution of transmitted charge. For that we introduce a scheme of current measurement that involves a spin $1/2$ coupled to the current so that it precesses at the rate proportional to the current. Our approach allows the study of charge transfer without breaking the circuit. We analyze a single channel conductor and derive electron counting statistics for arbitrary relation between temperature and voltage. For a perfectly transmitting channel the counting distribution is gaussian, both for zero-point fluctuations and at finite temperature. At constant voltage and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics.We study fluctuations of electric current in a quantum resistor and derive a general quantum-mechanical formula for the distribution of transmitted charge. For that we introduce a scheme of current measurement that involves a spin $1/2$ coupled to the current so that it precesses at the rate proportional to the current. Our approach allows the study of charge transfer without breaking the circuit. We analyze a single channel conductor and derive electron counting statistics for arbitrary relation between temperature and voltage. For a perfectly transmitting channel the counting distribution is gaussian, both for zero-point fluctuations and at finite temperature. At constant voltage and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics.

arXiv:cond-mat/9401004Jan 3, 19944 citations

Counting statistics for entangled electrons

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.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.

arXiv:cond-mat/0107504Physical review. B, Condensed matterFeb 1, 200248 citations

Counting statistics of tunneling current

Leonid S Levitov, M. Reznikov

The form of electron counting statistics of the tunneling current noise in a generic many-body interacting electron system is obtained and universal relations between its different moments are derived. A generalized fluctuation-dissipation theorem providing a relation between current and noise at arbitrary bias-to-temperature ratio $eV∕{k}_{B}T$ is established in the tunneling Hamiltonian approximation. The third correlator of current fluctuations ${S}_{3}$ (the skewness of the charge counting distribution) has a universal Schottky-type relation with the current and quasiparticle charge that holds in a wide bias voltage range, both at large and small $eV∕{k}_{B}T$ . The insensitivity of ${S}_{3}$ to the Nyquist-Schottky crossover represents an advantage compared to the Schottky formula for the noise power. We discuss the possibility of using the correlator ${S}_{3}$ for detecting quasiparticle charge at high temperatures.The form of electron counting statistics of the tunneling current noise in a generic many-body interacting electron system is obtained and universal relations between its different moments are derived. A generalized fluctuation-dissipation theorem providing a relation between current and noise at arbitrary bias-to-temperature ratio $eV∕{k}_{B}T$ is established in the tunneling Hamiltonian approximation. The third correlator of current fluctuations ${S}_{3}$ (the skewness of the charge counting distribution) has a universal Schottky-type relation with the current and quasiparticle charge that holds in a wide bias voltage range, both at large and small $eV∕{k}_{B}T$. The insensitivity of ${S}_{3}$ to the Nyquist-Schottky crossover represents an advantage compared to the Schottky formula for the noise power. We discuss the possibility of using the correlator ${S}_{3}$ for detecting quasiparticle charge at high temperatures.

arXiv:cond-mat/0111057Physical Review BSep 13, 2004197 citations

Coherent dynamics in stochastic systems revealed by full counting statistics

Philipp Stegmann, Jürgen König, S. Weiss

Stochastic systems feature, in general, both coherent dynamics and incoherent transitions between different states. We propose a method to identify the coherent part in the full counting statistics for the transitions. The proposal is illustrated for electron transfer through a quantum-dot spin valve, which combines quantum-coherent spin precession with electron tunneling. We show that by counting the number of transferred electrons as a function of time, it is possible to distill out the coherent dynamics from the counting statistics even in transport regimes, in which other tools such as the frequency-dependent current noise and the waiting-time distribution fail.Stochastic systems feature, in general, both coherent dynamics and incoherent transitions between different states. We propose a method to identify the coherent part in the full counting statistics for the transitions. The proposal is illustrated for electron transfer through a quantum-dot spin valve, which combines quantum-coherent spin precession with electron tunneling. We show that by counting the number of transferred electrons as a function of time, it is possible to distill out the coherent dynamics from the counting statistics even in transport regimes, in which other tools such as the frequency-dependent current noise and the waiting-time distribution fail.

arXiv:1803.02175Physical review. B./Physical review. BJul 6, 201820 citations

Full Counting Statistics of a Luttinger Liquid Conductor

D. B. Gutman, Yuval Gefen, A. D. Mirlin

Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.

arXiv:1003.5433Physical Review LettersDec 13, 201044 citations

1/2

coupled to the current so that it precesses at the rate proportional to the current. Our approach allows the study of charge transfer without breaking the circuit. We analyze a single channel conductor and derive electron counting statistics for arbitrary relation between temperature and voltage. For a perfectly transmitting channel the counting distribution is gaussian, both for zero-point fluctuations and at finite temperature. At constant voltage and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics.

eV∕{k}_{B}T

is established in the tunneling Hamiltonian approximation. The third correlator of current fluctuations

{S}_{3}

(the skewness of the charge counting distribution) has a universal Schottky-type relation with the current and quasiparticle charge that holds in a wide bias voltage range, both at large and small

eV∕{k}_{B}T

. The insensitivity of

{S}_{3}

to the Nyquist-Schottky crossover represents an advantage compared to the Schottky formula for the noise power. We discuss the possibility of using the correlator

{S}_{3}

for detecting quasiparticle charge at high temperatures.