Electronic Shot Noise Research Articles

Recent progress in open quantum systems: Non‐Gaussian noise and decoherence in fermionic systems

AbstractWe review our recent contributions to two topics that have become of interest in the field of open, dissipative quantum systems: non‐Gaussian noise and decoherence in fermionic systems. Decoherence by non‐Gaussian noise, i.e. by an environment that cannot be approximated as a bath of harmonic oscillators, is important in nanostructures (e.g. qubits) where there might be strong coupling to a small number of fluctuators. We first revisit the pedagogical example of dephasing by classical telegraph noise. Then we address two models where the quantum nature of the noise becomes essential: “quantum telegraph noise” and dephasing by electronic shot noise. In fermionic systems, many‐body aspects and the Pauli principle have to be taken care of when describing the loss of phase coherence. This is relevant in electronic quantum transport through metallic and semiconducting structures. Specifically, we recount our recent results regarding dephasing in a chiral interacting electron liquid, as it is realized in the electronic Mach–Zehnder interferometer. This model can be solved employing the technique of bosonization as well as a physically transparent semiclassical method (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Neuronal Shot Noise and Brownian 1/f2 Behavior in the Local Field Potential

We demonstrate that human electrophysiological recordings of the local field potential (LFP) from intracranial electrodes, acquired from a variety of cerebral regions, show a ubiquitous 1/f2 scaling within the power spectrum. We develop a quantitative model that treats the generation of these fields in an analogous way to that of electronic shot noise, and use this model to specifically address the cause of this 1/f2 Brownian noise. The model gives way to two analytically tractable solutions, both displaying Brownian noise: 1) uncorrelated cells that display sharp initial activity, whose extracellular fields slowly decay in time and 2) rapidly firing, temporally correlated cells that generate UP-DOWN states.

Nonalgebraic length dependence of transmission through a chain of barriers with a Lévy spacing distribution

The recent realization of a ``L\'evy glass'' (a three-dimensional optical material with a L\'evy distribution of scattering lengths) has motivated us to analyze its one-dimensional analog: A linear chain of barriers with independent spacings $s$ that are L\'evy distributed: $p(s)\ensuremath{\propto}{s}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\alpha}}$ for $s\ensuremath{\rightarrow}\ensuremath{\infty}$. The average spacing diverges for $0<\ensuremath{\alpha}<1$. A random walk along such a sparse chain is not a L\'evy walk because of the strong correlations of subsequent step sizes. We calculate all moments of conductance (or transmission), in the regime of incoherent sequential tunneling through the barriers. The average transmission from one barrier to a point at a distance $L$ scales as ${L}^{\ensuremath{-}\ensuremath{\alpha}}\text{ }\text{ln}\text{ }L$ for $0<\ensuremath{\alpha}<1$. The corresponding electronic shot noise has a Fano factor ($\ensuremath{\propto}$ average noise power/average conductance) that approaches 1/3 very slowly, with $1/\text{ln}\text{ }L$ corrections.

An atomic-resolution nanomechanical mass sensor

Mechanical resonators are widely used as inertial balances to detect small quantities of adsorbed mass through shifts in oscillation frequency. Advances in lithography and materials synthesis have enabled the fabrication of nanoscale mechanical resonators, which have been operated as precision force, position and mass sensors. Here we demonstrate a room-temperature, carbon-nanotube-based nanomechanical resonator with atomic mass resolution. This device is essentially a mass spectrometer with a mass sensitivity of 1.3 x 10(-25) kg Hz(-1/2) or, equivalently, 0.40 gold atoms Hz(-1/2). Using this extreme mass sensitivity, we observe atomic mass shot noise, which is analogous to the electronic shot noise measured in many semiconductor experiments. Unlike traditional mass spectrometers, nanomechanical mass spectrometers do not require the potentially destructive ionization of the test sample, are more sensitive to large molecules, and could eventually be incorporated on a chip.

Theory of shot noise in high-current space-charge-limited field emission

This paper studies the electron shot noise of high current space-charge limited (SCL) field emission, including the effects of both quantum partitioning and Coulomb correlation of the emitted tunneling electrons inside a gap. The Fano factor $(\ensuremath{\gamma})$ is calculated over a wide range of applied voltages, gap spacings, and electron pulse lengths in classical, quantum and relativistic regimes. It is found that the effect of space charge smoothing (observed in thermionic emission) is no longer valid for high current field emission, as the space charge field will increase the potential barrier and thus decrease the degree of quantum partitioning (larger $\ensuremath{\gamma}$). However, the shot noise of SCL field emission in a nanogap may be suppressed due to the combination of Coulomb repulsion and exchange-correlation potential among the tunneling electrons, where the dynamics of the electrons inside the gap are treated by using a quantum mean field model. Coulomb correlation can be ignored when the pulse length of the electron beam is much smaller than the gap transit time. Possible experimental settings are discussed in order to observe the shot noise suppression of field emission with and without the space charge effects.

Effects of Electron Shot Noise and Quantum Field Fluctuations on the Photon Statistics of the Coherent Spontaneous Harmonic Radiation

We present a theoretical analysis of the statistical fluctuations in the coherent spontaneous harmonic radiation (CSHR) generated by a free electron laser (FEL) under the conditions applicable in a previously published experiment [1] where sub-Poisson optical fluctuations were observed. The numerical analyses presented here document the conclusion that the emission of CSHR can serve as a useful test bed for analyses of the nonclassical aspects of electron beam formation and radiation. Two possible explanations for the observed fluctuations in the CSHR are investigated as limiting physical mechanisms: the fluctuations in the number density of the radiating electrons, the so-called and the quantum fluctuations in the radiation field. When the uncertainties in the radiation field are considered as the only noise source as in the analysis, the statistical fluctuations in the CSHR would result in Poisson statistics. On the other hand, when the electron shot noise is regarded as the only noise contribution as assumed by the shot-noise model, we find numerically and analytically that the fluctuations, as characterized by the Fano factor, would be much smaller than those due to the quantum uncertainties in the radiation field in the analysis. The experimentally observed fluctuations are larger than those due to shot noise, but smaller than those due to quantum fluctuations in the field. Hence, neither the classical shot-noise model nor the quasi-classical analysis can explain the experimental results. Given the results presented in this report, it is clear that attention must be given to the other phenomena-including the quantum fluctuations in the electromagnetic field and the nonclassical electron correlation, which contributed to the observed laser fluctuations.

Current Shot Noise and Bunching of Electrons in Multilevel Quantum Dots

Currents and their fluctuations in multilevel quantum dots are studied theoretically in the limit of sequential tunneling. The spin degrees of freedom, many-body electronic states (singlet and triplet) as well as relaxation processes between the levels of the quantum dots are considered. In general, due to the rapid relaxation processes the shot noise is sub-Poissonian, however for a large polarization of the outgoing currents from the singlet and triplet states one gets the super-Poissonian type of the shot noise due to the bunching of tunneling events.

Experimental Test of the High-Frequency Quantum Shot Noise Theory in a Quantum Point Contact

We report on direct measurements of the electronic shot noise of a quantum point contact at frequencies nu in the range 4-8 GHz. The very small energy scale used ensures energy independent transmissions of the few transmitted electronic modes and their accurate knowledge. Both the thermal energy and the quantum point contact drain-source voltage V_{ds} are comparable to the photon energy hnu leading to observation of the shot noise suppression when V_{ds}<hnu/e. Our measurements provide the first complete test of the finite frequency shot noise scattering theory without adjustable parameters.

Observation of the [formula omitted] shot noise singularity in a quantum point contact

We report on direct measurements of the electronic shot noise of a quantum point contact (QPC) at frequencies ν in the range 4–8 GHz. Both the thermal energy and the QPC drain–source voltage V are comparable to the photon energy leading to observation of the shot noise suppression when V < h ν / e .

Frequency-Selective Single-Photon Detection Using a Double Quantum Dot

We use a double quantum dot as a frequency-tunable on-chip microwave detector to investigate the radiation from electron shot-noise in a near-by quantum point contact. The device is realized by monitoring the inelastic tunneling of electrons between the quantum dots due to photon absorption. The frequency of the absorbed radiation is set by the energy separation between the dots, which is easily tuned with gate voltages. Using time-resolved charge-detection techniques, we can directly relate the detection of a tunneling electron to the absorption of a single photon.

Coulomb effects on electron transport and shot noise in hybrid normal-metal–superconducting metallic structures

We analyze the effect of electron-electron interactions on Andreev current and shot noise in diffusive hybrid structures composed of a normal metal attached to a superconductor via a weakly transmitting interface. We demonstrate that at voltages/temperatures below the Thouless energy of a normal metal, Coulomb interaction yields a reduction of both Andreev current and its noise by a constant factor which essentially depends on the system dimensionality. For quasi-one-dimensional (1D) structures this factor is $\ensuremath{\sim}{N}_{\mathrm{Ch}}^{8∕g}$, where ${N}_{\mathrm{Ch}}$ and $g$ are, respectively, the number of conducting channels and dimensionless conductance of a normal metal. At voltages above the Thouless energy the interaction correction to Andreev current and shot noise acquires an additional voltage dependence which turns out to be a power-law in the quasi-1D limit.

Shot noise of spin-polarized electrons

The shot noise of spin polarized electrons is shown to be generically dependent upon spin-flip processes. Such a situation represents perhaps the simplest instance where the two-particle character of current fluctuations out of equilibrium is explicit, leading to trinomial statistics of charge transfer in a single channel model. We calculate the effect of spin-orbit coupling, magnetic impurities, and precession in an external magnetic field on the noise in the experimentally relevant cases of diffusive wires and lateral semiconductor dots, finding dramatic enhancements of the Fano factor. The possibility of using the shot noise to measure the spin-relaxation time in an open mesoscopic system is raised.

Experimental investigation of density fluctuations in high-speed jets and correlation with generated noise

The air density fluctuations in the plumes of fully expanded, unheated free jets were investigated experimentally using a Rayleigh-scattering-based technique. The point measuring technique used a continuous-wave laser, fibre-optic transmission and photon counting electronics. The radial and centreline profiles of time-averaged density and root-mean-square density fluctuation provided a comparative description of jet growth. To measure density fluctuation spectra a two-photomultiplier-tube (PMT) technique was used. Cross-correlation between the two PMT signals significantly reduced the electronic shot noise contribution. The density fluctuation spectra were found to be remarkably similar for all Mach number jets. A detailed survey in fully expanded Mach 0.95, 1.4 and 1.8 jets further confirmed that the distribution of various Strouhal frequency fluctuations remained similar, except for a spatial stretching with increased Mach number. In spite of this similarity in flow fluctuations the noise sources in these three jets were found to be significantly different. Spark schlieren photographs and near-field microphone measurements confirmed that Mach wave radiation was present in the Mach 1.8 jet, and was absent in the Mach 0.95 jet. Direct correlation measurement between the flow density fluctuation (cause) and far-field sound pressure fluctuation (effect) shed further light on the sound generation process. For this purpose a microphone was kept fixed at a far-field point, mostly at a distance of 50 diameters and 30° to the flow direction, and the laser probe volume was moved from point to point in the flow. In the Mach 1.8 jet, where the convective velocity of Kelvin–Helmholtz instability waves exceeded the ambient sound speed, significant correlation was measured from the peripheral shear layer, while in the Mach 0.95 jet, where the instability waves had subsonic convective speed, no correlation could be measured. Although the same instability waves were present in both Mach 1.8 and 0.95 jets, the peripheral shear layer of the former was found to be an obvious noise source, while that of the latter was not. Further correlation studies along the jet centreline showed that behaviour in the region downstream of the potential core was similar in all Mach number jets tested, 0:6[les ]M[les ]1:8. Good correlation at low Strouhal frequencies was measured from this region, which started from downstream of the potential core and extended many diameters from there.

Assessment of crossed-plane tomography for flamelet surface normal measurements

A recently introduced method for measuring three-dimensional flamelet surface normal vectors, N , in turbulent, premixed flames is described and evaluated. Crossed-plane tomography allows the determination of N from two simultaneously acquired laser-tomographic images. The method is evaluated through comparisons with data from single-plane measurements made on a vortex-street perturbed v-flame, and through an error analysis. The standard deviation of the angle between N s measured using crossed-plane tomography and a vertical image-plane aligned perpendicular to the flame stabilizing rod is 3.7°, consistent with the instantaneous, two-dimensional structure of the perturbed flame. PDFs of the orientation of the projection of N onto this vertical plane are compared to PDFs of the orientation of N s measured using single-plane tomography, and the two are found to be, for the most part, within statistical uncertainty of one another. The results of an analysis of random error due to electronic noise and marker shot noise are consistent with experimental results, and thus uncertainty can be estimated through analytic expressions. The statistical weighting of PDFs generated by crossed-plane tomography measurements is discussed, as is the evaluation of the flamelet surface density in terms of the mean inverse cosine of the angle between N and an arbitrarily oriented line η. It is shown that this PDF is weighted by the probability that the flamelet crosses the line of intersection between the two illumination planes, a crossing-weighted PDF, and that the mean inverse cosine term is also a crossing-weighted average, where η is the line crossed. The flamelet surface density is written as the product of the mean inverse cosine term and the average number of flamelet crossings of η per unit length, the flamelet crossing density. It is argued that the preferred orientation of η is perpendicular to ⟨ c ⟩ constant surfaces, and a PDF fit for the N s from previous work (Bingham, Gouldin, and Knaus, 1998) is used to evaluate the mean inverse cosine term. It is found that the maximum value for this orientation of η is slightly more than two, indicating that large burning rate flames must have large corresponding values of the flamelet crossing density.

Electron transport and shot noise in double-barrier resonant diodes: The role of Pauli and Coulomb correlations

We present a theoretical study of electron transport and shot noise in double barrier resonant diodes within the sequential tunneling model. We investigate the role played by Pauli principle and Coulomb interaction on the current voltage $(I\ensuremath{-}V)$ characteristics and the Fano factor by varying carrier concentration and lattice temperature. At $4.2\mathrm{K}$ we obtain the bistable $I\ensuremath{-}V$ characteristics of Z type. In the region of low and intermediate voltages for a sufficiently low electron concentration in the contacts the Fano factor exhibits two successive suppressed regimes associated with Pauli blockade and Coulomb correlation, respectively. By further increasing the voltage shot noise enhancement is found to be a precursor indicator that the device is approaching an instability regime in analogy with the case of phase transitions. In the bistable region hysteresis effects on different transport and parameters are analyzed. At $77\mathrm{K}$ and increasing temperatures for a carrier concentration of $5\ifmmode\times\else\texttimes\fi{}{10}^{16}{\mathrm{cm}}^{\ensuremath{-}3}$ the diode exhibits the usual negative differential conductance (NDC) characteristic. For voltages below NDC only Coulomb correlation remains effective, leading to a suppressed Fano factor intermediate between $0.5--1.$ For voltages just above NDC a moderate enhancement of the Fano factor up to values around 8 is evidenced. Theoretical findings provide a detailed physical interpretation of experimental results available in the literature and predict features to be confirmed by further experiments.

Pulsed mirror electron microscope: A fast near-surface imaging probe

A pulsed mirror electron microscope was developed for imaging laser-induced processes on the nanosecond time scale. Variations of the electronic structure of the surface are imaged. The evaporation or deposition of an atomic monolayer is readily detected. Pulsed mirror electron microscopy is an alternative technique to pulsed photoelectron microscopy for tracking chemical reactions. In addition, gas flow above the surface and laser-induced ablation of absorbing layers at the back surface of a dielectric can be probed, exploiting electron scattering and capacitive coupling, respectively. Presently, the space/time resolution is limited by the competition between electron shot noise and illumination aperture to 1 μm/5 ns. The illuminating electron pulses are supplied by a laser-driven robust ZrC-covered Re cathode. This device can be operated in a high vacuum of 10−5 mbar either as a photo or a thermal electron emitter.

Observation of Sub-Poisson Fluctuations in the Intensity of the Seventh Coherent Spontaneous Harmonic Emitted by a rf Linac Free-Electron Laser

We report the observation of sub-Poisson intensity fluctuations in the coherent spontaneous harmonic radiation generated by an infrared free-electron laser in a photon counting experiment using a well-defined ensemble of electron pulses. These observations constitute the first observation of a nonclassical state of the radiation field generated by a beam of free electrons. The fluctuations observed in the experiment are smaller than those expected from semiclassical radiation theory, and larger than those expected from electron shot noise.

Electron transport and shot noise in ultrashort single-barrier semiconductor heterostructures

We present a theoretical study of electron transport and shot noise in ultrashort single barrier semiconductor structures. Calculations are applied to a simple GaAs semiconductor model in the presence of ballistic and thermalized carriers. The coupling between space charge and the dependence of the transmission coefficient on energy is found to provide the positive feedback that enhances shot noise and ultimately leads to a current instability of S type. When the strength of this feedback is weak, shot-noise suppression is observed. The occurrence of enhanced shot noise is explained in terms of a negative lifetime related to carrier escape through the collector contact. The model also predicts shot-noise enhancement in single barrier structures with constant transparency in the region of current saturation. Theoretical results are in qualitative agreement with existing current-voltage experiments and confirm recent Monte Carlo simulations evidencing shot-noise enhancement in GaAs/AlGaAs semiconductor heterostructures. Shot-noise enhancement is found to be a precursor indicator that the device is approaching an instability regime in analogy with the case of phase transitions.

Counting statistics of photons produced by electronic shot noise.

A theory is presented for the photodetection statistics of radiation produced by current fluctuations in a phase-coherent conductor. Deviations are found from the Poisson statistics that would result from a classical current. For detection in a narrow frequency interval delta omega, the photocount distribution has the negative-binomial form of blackbody radiation if e delta omega is less than the mean current I in the conductor. When electronic localization sets in, I drops below e delta omega and a different type of super-Poissonian photon statistics results.

Current instability and shot noise in nanometricsemiconductor heterostructures

We investigate electron transport and shot noise ina single-barrier GaAs/AlGaAs heterostructure of nanometric size inthe presence of ballistic and thermalized carriers. Thecoupling between space charge and the dependence of thetransmission coefficient on energy is found to provide thepositive feedback which enhances shot noise and ultimately leadsto a current instability of S type. Theoretical results arein qualitative agreement with existing experiments and confirmrecent Monte Carlo simulations evidencing shot-noise enhancementin GaAs/AlGaAs heterostructures.