Frequency dispersion of photon-assisted shot noise in mesoscopic conductors

We calculate the low-frequency current noise for AC biased mesoscopic chaotic cavities and diffusive wires. Contrary to what happens for the admittance, the frequency dispersion is not dominated by the electric response time (the "RC" time of the circuit), but by the time that electrons need to diffuse through the structure (dwell time or diffusion time). Frequency dispersion of noise stems from fluctuations of the Fermi distribution function that preserve charge neutrality. Our predictions can be verified with present experimental technology.Comment: 5 pages, 3 Figure

High Frequency Dynamics and Third Cumulant of Quantum Noise

The existence of the third cumulant $S_{3}$ of voltage fluctuations has demonstrated the non-Gaussian aspect of shot noise in electronic transport. Until now, measurements have been performed at low frequency, \textit{i.e.} in the classical regime $\hbar \omega < eV, k_BT$ where voltage fluctuations arise from charge transfer process. We report here the first measurement of $S_3$ at high frequency, in the quantum regime $\hbar \omega > eV, k_BT$. In this regime, experiment cannot be seen as a charge counting statistics problem anymore. It raises central questions of the statistics of quantum noise: 1) the electromagnetic environment of the sample has been proven to strongly influence the measurement, through the possible modulation of the noise of the sample. What happens to this mechanism in the quantum regime? 2) For $\hbar \omega > eV$, the noise is due to zero point fluctuations and keeps its equilibrium value: $S_2= G \hbar \omega$ with $G$ the conductance of the sample. Therefore, $S_2$ is independent of the bias voltage and no photon is emitted by the conductor. Is it possible, as suggested by some theories, that $S_3 \neq 0$ in this regime? With regard to these questions, we give theoretical and experimental answers to the environmental effects showing that they involve dynamics of the quantum noise. Using these results, we investigate the question of the third cumulant of quantum noise in the a tunnel junction

Minimal excitation states for heat transport in driven quantum Hall systems

We investigate minimal excitation states for heat transport into a fractional quantum Hall system driven out of equilibrium by means of time-periodic voltage pulses. A quantum point contact allows for tunneling of fractional quasi-particles between opposite edge states, thus acting as a beam splitter in the framework of the electron quantum optics. Excitations are then studied through heat and mixed noise generated by the random partitioning at the barrier. It is shown that levitons, the single-particle excitations of a filled Fermi sea recently observed in experiments, represent the cleanest states for heat transport, since excess heat and mixed shot noise both vanish only when Lorentzian voltage pulses carrying integer electric charge are applied to the conductor. This happens in the integer quantum Hall regime and for Laughlin fractional states as well, with no influence of fractional physics on the conditions for clean energy pulses. In addition, we demonstrate the robustness of such excitations to the overlap of Lorentzian wavepackets. Even though mixed and heat noise have nonlinear dependence on the voltage bias, and despite the non-integer power-law behavior arising from the fractional quantum Hall physics, an arbitrary superposition of levitons always generates minimal excitation states.Comment: 15 pages, 7 figure

Electron waiting times in coherent conductors are correlated

We evaluate the joint distributions of electron waiting times in coherent conductors described by scattering theory. Successive electron waiting times in a single-channel conductor are found to be correlated due to the fermionic statistics encoded in the many-body state. Our formalism allows us also to investigate the waiting times between charge transfer events in different outgoing channels. As an application we consider a quantum point contact in a chiral setup with one or both input channels biased by either a static or a time-dependent periodic voltage described by Floquet theory. The theoretical framework developed here can be applied to a variety of scattering problems and can in a straightforward manner be extended to joint distributions of several electron waiting times.Comment: 14 pages, 7 figure

Negativity of the excess noise in a quantum wire capacitively coupled to a gate

The electrical current noise of a quantum wire is expected to increase with increasing applied voltage. We show that this intuition can be wrong. Specifically, we consider a single channel quantum wire with impurities and with a capacitive coupling to nearby metallic gates and find that its excess noise, defined as the change in the noise caused by the finite voltage, can be negative at zero temperature. This feature is present both for large ($c \gg c_q$) and small ($c \ll c_q$) capacitive coupling, where $c$ is the geometrical and $c_q$ the quantum capacitance of the wire. In particular, for $c \gg c_q$, negativity of the excess noise can occur at finite frequency when the transmission coefficients are energy dependent, i.e. in the presence of Fabry-P\'erot resonances or band curvature. In the opposite regime $c \lesssim c_q$, a non trivial voltage dependence of the noise arises even for energy independent transmission coefficients: at zero frequency the noise decreases with voltage as a power law when $c < c_q/3$, while, at finite frequency, regions of negative excess noise are present due to Andreev-type resonances.Comment: 11 pages, 5 figures. Revised version, references and technical details added, typos correcte

Shot noise of photon-excited electron-hole pairs in open quantum dots

We investigate shot noise of photon-excited electron-hole pairs in open multi-terminal, multi-channel chaotic dots. Coulomb interactions in the dot are treated self-consistently giving a gauge-invariant expression for the finite frequency correlations. The Coulomb interactions decrease the noise, the strong interaction limit coincides with the non-interacting adiabatic limit. Inelastic scattering and dephasing in the dot are described by voltage and dephasing probe models respectively. We find that dephasing leaves the noise invariant, but inelastic scattering decreases correlations eventually down to zero.Comment: 4 pages, 1 figure; minor changes, 3 references adde

Numerical simulations of time resolved quantum electronics

This paper discusses the technical aspects - mathematical and numerical - associated with the numerical simulations of a mesoscopic system in the time domain (i.e. beyond the single frequency AC limit). After a short review of the state of the art, we develop a theoretical framework for the calculation of time resolved observables in a general multiterminal system subject to an arbitrary time dependent perturbation (oscillating electrostatic gates, voltage pulses, time-vaying magnetic fields) The approach is mathematically equivalent to (i) the time dependent scattering formalism, (ii) the time resolved Non Equilibrium Green Function (NEGF) formalism and (iii) the partition-free approach. The central object of our theory is a wave function that obeys a simple Schrodinger equation with an additional source term that accounts for the electrons injected from the electrodes. The time resolved observables (current, density. . .) and the (inelastic) scattering matrix are simply expressed in term of this wave function. We use our approach to develop a numerical technique for simulating time resolved quantum transport. We find that the use of this wave function is advantageous for numerical simulations resulting in a speed up of many orders of magnitude with respect to the direct integration of NEGF equations. Our technique allows one to simulate realistic situations beyond simple models, a subject that was until now beyond the simulation capabilities of available approaches.Comment: Typographic mistakes in appendix C were correcte