Julien Gabelli

A Coherent RC Circuit

We review the first experiment on dynamic transport in a phase-coherent quantum conductor. In our discussion, we highlight the use of time-dependent transport as a means of gaining insight into charge relaxation on a mesoscopic scale. For this purpose, we studied the ac conductance of a model quantum conductor, i.e. the quantum RC circuit. Prior to our experimental work, Büttiker et al (1993 Phys. Lett. A 180 364-9) first worked on dynamic mesoscopic transport in the 1990s. They predicted that the mesoscopic RC circuit can be described by a quantum capacitance related to the density of states in the capacitor and a constant charge-relaxation resistance equal to half of the resistance quantum h/2e(2), when a single mode is transmitted between the capacitance and a reservoir. By applying a microwave excitation to a gate located on top of a coherent submicronic quantum dot that is coupled to a reservoir, we validate this theoretical prediction on the ac conductance of the quantum RC circuit. Our study demonstrates that the ac conductance is directly related to the dwell time of electrons in the capacitor. Thereby, we observed a counterintuitive behavior of a quantum origin: as the transmission of the single conducting mode decreases, the resistance of the quantum RC circuit remains constant while the capacitance oscillates.

Relaxation Time of a Chiral Quantum R-L Circuit

We report on the GHz complex admittance of a chiral one-dimensional ballistic conductor formed by edge states in the quantum Hall regime. The circuit consists of a wide Hall bar (the inductor L) in series with a tunable resistor (R) formed by a quantum point contact. Electron interactions between edges are screened by a pair of side gates. Conductance steps are observed on both real and imaginary parts of the admittance. Remarkably, the phase of the admittance is transmission independent. This shows that the relaxation time of a chiral R -L circuit is resistance independent. A current and charge conserving scattering theory is presented that accounts for this observation with a relaxation time given by the electronic transit time in the circuit.

Dynamics of quantum noise in a tunnel junction under ac excitation.

We report the first measurement of the dynamical response of shot noise (measured at frequency omega) of a tunnel junction to an ac excitation at frequency omega0. The experiment is performed in the quantum regime, variant Plancks over 2piomega approximately variant Plancks over 2piomega0>>kBT at very low temperature T=35 mK and high frequency omega0/2pi=6.2 GHz. We observe that the noise responds in phase with the excitation, but not adiabatically. The results are in very good agreement with a prediction based on a new current-current correlator.

Full counting statistics of avalanche transport: An experiment

We report the first measurement of high order cumulants of the current fluctuations in an avalanche diode run through by a stationary dc current. Such a system is archetypic of devices in which transport is governed by a collective mechanism, here charge multiplication by avalanche. We have measured the first 5 cumulants of the probability distribution of the current fluctuations. We show that the charge multiplication factor is distributed according to a power law that is different from that of the usual avalanche below breakdown, when avalanches are well separated.

Classical and quantum theory of photothermal cavity cooling of a mechanical oscillator

The optomechanical coupling between a mechanical oscillator and light trapped in a cavity has been the subject of many recent investigations. One salient feature of this coupling is the possibility to cavity-cool a mechanical oscillator down to its quantum ground state. The standard situation studied in most optomechanics experiments pictures the scenario of a Fabry-Perot cavitys end mirror light enough to undergo the mechanical force induced by photons bouncing back on the mirror. Here we are interested in scenarios where the photons are, at least partially, absorbed. As a result of the end mirror absorption, a «photothermal» force can be produced which can overcome radiation pressure by several orders of magnitude in experimental settings. This force was already shown to enable very efficient cavity-cooling or dynamical pumping of mechanical oscillators [1,2]. In this work [3] we present a classical and a quantum theory of photothermal cavity cooling of a mechanical oscillator.

Electron and electron-hole quasiparticle states in a driven quantum contact

We study the many-body electronic state created by a time-dependent drive of a mesoscopic contact. The many-body state is expressed manifestly in terms of single-electron and electron-hole quasiparticle excitations with the amplitudes and probabilities of creation which depend on the details of the applied voltage. We experimentally probe the time dependence of the constituent electronic states by using an analog of the optical Hong-Ou-Mandel correlation experiment where electrons emitted from the terminals with a relative time delay collide at the contact. The electron wave packet overlap is directly related to the current noise power in the contact. We have confirmed the time dependence of the electronic states predicted theoretically by measurements of the current noise power in a tunnel junction under harmonic excitation.

Electron-photon correlations and the third moment of quantum noise

The radiation generated by a quantum conductor should be correlated with the electrons crossing it. We have measured the correlation between the fluctuations of the high-frequency electromagnetic power generated by a tunnel junction at very low temperature and the low-frequency voltage fluctuations across it. This quantity corresponds to a third-order correlator of the electromagnetic field. At low-voltage bias, i.e. when the junction emits no radiation into the impedance-matched vacuum connected to it, we observe that the voltage fluctuations of the electric signal generated by the junction has zero third moment. Yet we show by a careful analysis of environmental contributions that the intrinsic third moment of the high-frequency current fluctuations in the junction is given by e2I.

The noise susceptibility of a coherent conductor

The complex ac conductance G(ω0) of a system measures the dynamical response of the current to a small voltage excitation at frequency ω0. It cannot in general be deduced from the only knowledge of the dc I(V ) characteristics. Similarly, we investigate the dynamical response of current noise to an ac excitation, i.e. the in-phase and out-of-phase response of current noise density S(ω) measured at frequency ω. We present a detailed calculation of this new response function χω0 (ω), that we name noise susceptibility, at arbitrary frequencies for a coherent conductor in the scattering matrix formalism. We exemplify the relevance of our calculation by the measurement of the noise susceptibility of a tunnel junction in the quantum regime &barh;ω ~ &barh;ω0> >kBT, which is in remarkable agreement with our theory.

Characterization and control of charge transfer in a tunnel junction

Charge transfer in a tunnel junction is studied under dc and ac voltage bias using quantum shot noise. Under dc voltage bias V, spectral density of noise measured within a very large bandwidth enables to deduce the current–current correlator in the time domain by Fourier transform. This correlator exhibits regular oscillations proving that electrons try to cross the junction regularly, every h/eV. Using harmonic and bi-harmonic ac voltage bias, we then show that quasiparticles excitations can be transferred through the junction in a controlled way. By measuring the reduction of the excess shot noise, we are able to determine the number of electron–hole pairs surrounding the injected electrons and demonstrate that bi-harmonic voltage pulses realize an on-demand electron source with a very small admixture of electron–hole pairs. A time-dependent voltage drive V(t)=Vdc+Vac(t) applied to a contact with transmission T generates an incoming excitation giving rise to transmitted and reflected quasiparticles. The excess noise ΔSV=( 〉I(t)2 〉ac+dc−〈I(t)2 〉dc)/Δf given by the difference between the noise measured with and without the ac excitation is measured by an ammeter with a bandwidth Δf. It gives the number of electron–hole pairs surrounding the transmitted electrons: Ne−h=h2e2TΔSVhν where ν is the repetition frequency of Vac.

Electron thermal, quantum, shot, and photo-assisted noise: From spectroscopy to current-current correlator in time domain

We have measured the current fluctuations emitted by a tunnel junction with a very wide bandwidth, from 0.3 to 13 GHz, down to very low temperature T = 35 mK. This allowed us to perform the spectroscopy (i.e., measure the frequency dependence) of thermal noise, shot noise and photo-assisted noise. Thanks to the very wide bandwidth of our measurement, we can deduce the current-current correlator in time domain. We observe the thermal decay of this correlator as well as its oscillations with a period h/eV, a direct consequence of the effect of the Pauli and Heisenberg principles in quantum electron transport.