Charge distribution in quantum shot noise

We analyze the shot noise in a voltage biased superconducting quantum point contact. Results are presented for the single channel case with arbitrary transmission. In the limit of very low transmission it is found that the effective charge, defined from the noise-current ratio, exhibits a steplike behavior as a function of voltage with well-defined plateaus at integer values of the electronic charge. This multiple charge corresponds to the transmitted charge in a multiple Andreev reflection (MAR) process. This effect gradually disappears for increasing transmission due to interference between different MAR processes.We analyze the shot noise in a voltage biased superconducting quantum point contact. Results are presented for the single channel case with arbitrary transmission. In the limit of very low transmission it is found that the effective charge, defined from the noise-current ratio, exhibits a steplike behavior as a function of voltage with well-defined plateaus at integer values of the electronic charge. This multiple charge corresponds to the transmitted charge in a multiple Andreev reflection (MAR) process. This effect gradually disappears for increasing transmission due to interference between different MAR processes.

arXiv:cond-mat/9812175Physical Review LettersMay 17, 1999102 citations

An open problem in quantum shot noise

Gerhard C. Hegerfeldt

Lecture notes in mathematicsJan 1, 19900 citations

Tunneling and quantum noise in one-dimensional Luttinger liquids

Claudio Chamon, Denise E. Freed, Xiao-Gang Wen

We study nonequilibrium noise in the transmission current through barriers in one-dimensional Luttinger liquids and in the tunneling current between edges of fractional quantum Hall liquids. The distribution of tunneling events through narrow barriers can be described by a Coulomb gas lying in the time axis along a Keldysh (or nonequilibrium) contour. We show that the charges tend to reorganize as a dipole gas,which we use to describe the tunneling statistics. The dipole-gas picture allows us to have a unified description of the low-frequency shot noise and the high-frequency Josephson noise. The correlation between the charges within a dipole (intradipole) contributes to the high-frequency Josephson noise, which has an algebraic singularity at \ensuremath{\omega}= ${\mathit{e}}^{\mathrm{*}}$ V/\ensuremath{\Elzxh}, whereas the correlations between dipoles (interdipole) are responsible for the low-frequency noise. We show that an independent or noninteracting dipole approximation gives a Poisson distribution for the locations of the dipole centers of mass, which gives a flat noise spectrum at low frequencies and corresponds to uncorrelated shot noise. Including interdipole interactions gives an additional 1/ ${\mathit{t}}^{2}$ correlation between the tunneling events that results in an \ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} singularity in the noise spectrum. We present a diagrammatic technique to calculate the correlations in perturbation theory, and show that contributions from terms of order higher than the dipole-dipole interaction should only affect the strength of the \ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} singularity, but its form should remain \ensuremath{\sim}\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} to all orders in perturbation theory. A counting argument also suggests that the leading algebraic singularity at ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$ should be \ensuremath{\propto}\ensuremath{\Vert}\ensuremath{\omega}-${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$${\mathrm{\ensuremath{\Vert}}}^{2\mathit{g}\mathrm{\ensuremath{-}}1}$ to all orders in perturbation theory.We study nonequilibrium noise in the transmission current through barriers in one-dimensional Luttinger liquids and in the tunneling current between edges of fractional quantum Hall liquids. The distribution of tunneling events through narrow barriers can be described by a Coulomb gas lying in the time axis along a Keldysh (or nonequilibrium) contour. We show that the charges tend to reorganize as a dipole gas,which we use to describe the tunneling statistics. The dipole-gas picture allows us to have a unified description of the low-frequency shot noise and the high-frequency Josephson noise. The correlation between the charges within a dipole (intradipole) contributes to the high-frequency Josephson noise, which has an algebraic singularity at \ensuremath{\omega}=${\mathit{e}}^{\mathrm{*}}$V/\ensuremath{\Elzxh}, whereas the correlations between dipoles (interdipole) are responsible for the low-frequency noise. We show that an independent or noninteracting dipole approximation gives a Poisson distribution for the locations of the dipole centers of mass, which gives a flat noise spectrum at low frequencies and corresponds to uncorrelated shot noise. Including interdipole interactions gives an additional 1/${\mathit{t}}^{2}$ correlation between the tunneling events that results in an \ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} singularity in the noise spectrum. We present a diagrammatic technique to calculate the correlations in perturbation theory, and show that contributions from terms of order higher than the dipole-dipole interaction should only affect the strength of the \ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} singularity, but its form should remain \ensuremath{\sim}\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} to all orders in perturbation theory. A counting argument also suggests that the leading algebraic singularity at ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$ should be \ensuremath{\propto}\ensuremath{\Vert}\ensuremath{\omega}-${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$${\mathrm{\ensuremath{\Vert}}}^{2\mathit{g}\mathrm{\ensuremath{-}}1}$ to all orders in perturbation theory.

arXiv:cond-mat/9408064Physical review. B, Condensed matterJan 15, 1995157 citations

Qualitative View of Quantum Shot Noise

Rolf W. Landauer

Annals of the New York Academy of SciencesApr 1, 199513 citations

{\mathit{e}}^{\mathrm{*}}

V/\ensuremath{\Elzxh}, whereas the correlations between dipoles (interdipole) are responsible for the low-frequency noise. We show that an independent or noninteracting dipole approximation gives a Poisson distribution for the locations of the dipole centers of mass, which gives a flat noise spectrum at low frequencies and corresponds to uncorrelated shot noise. Including interdipole interactions gives an additional 1/

{\mathit{t}}^{2}

correlation between the tunneling events that results in an \ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} singularity in the noise spectrum. We present a diagrammatic technique to calculate the correlations in perturbation theory, and show that contributions from terms of order higher than the dipole-dipole interaction should only affect the strength of the \ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} singularity, but its form should remain \ensuremath{\sim}\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert} to all orders in perturbation theory. A counting argument also suggests that the leading algebraic singularity at ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$ should be \ensuremath{\propto}\ensuremath{\Vert}\ensuremath{\omega}-${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$${\mathrm{\ensuremath{\Vert}}}^{2\mathit{g}\mathrm{\ensuremath{-}}1}$ to all orders in perturbation theory.