In quantum optics the g (2) -function is a standard tool to investigate photon emission statistics. We define a g (2) -function for electronic transport and use it to investigate the bunching and antibunching of electron currents. Importantly, we show that super-Poissonian electron statistics do not necessarily imply electron bunching, and that sub-Poissonian statistics do not imply anti-bunching. We discuss the information contained in g (2) (τ ) for several typical examples of transport through nano-structures such as few-level quantum dots.PACS numbers: 73.63. Kv, 73.50.Td, 73.23.Hk Current noise has long-since been established as an important tool for studying the physics of transport through mesoscopic and nano-scale conductors 1-5 . The character of the noise is typically assessed by considering the Fano factor, the ratio of the zero-frequency noise to the current 3 , and comparing with a Poisson process for which the Fano factor is equal to one. Systems with F < 1 are described as sub-Poissonian (non-interacting systems fall in this class 2 ) and systems which have F > 1 are called super-Poissonian. A common interpretation of this comparison is that a super-Poissonian Fano factor indicates a bunching of the current's constituent electrons, whereas sub-Poissonian values indicates anti-bunching (Fig. 1 ).In this paper we directly investigate bunching and antibunching in electronic transport as a phenomenon in the time domain through the introduction of a second-order correlation function g (2) (τ ), analogous to that used in quantum optics [6][7][8] . Within a quantum master equation (QME) framework in the appropriate limit, the g (2) -function is seen to be proportional to the conditional probability that, given an electron is emitted into the collector at time t = 0, a further such jump is observed a time τ later. Following quantum optics, we identifysince bunching means that particles are more likely to be emitted together than apart, and conversely for antibunching. By relating our g (2) -function to the correlation function between the current at two different times, we clarify the relationship between the g (2) -function, (anti-) bunching and the Fano factor.We then investigate bunching and anti-bunching in several widely-discussed transport models in the Coulomb blockade (CB) regime (see Fig. 2). This analysis shows that the simple picture relating superPoissonian Fano factors to bunching and sub-Poissonian ones to anti-bunching is often an oversimplification, and can even be outright wrong. In particular we discuss a simple quantum-dot (QD) model which has a Fano factor less than one, and is thus sub-Poissonian, and yet has g (2) (0) > g (2) (τ ) for all τ > 0 such that, according to Eq. (1), the electron-flow is completely bunched. We also give a model for which the converse is true, i.e. we find a super-Poissonian Fano factor in conjunction with electron anti-bunching. These results mirror the work of Singh 9 and Zou and Mandel 10 , who have made similar points for quantum-optical systems.This ...

We have studied the waiting time distributions (WTDs) for subgap transport through a singlelevel quantum dot tunnel coupled to one normal and one superconducting lead. The WTDs reveal the internal dynamics of the system, in particular, the coherent transfer of Cooper pairs between the dot and the superconductor. The WTDs exhibit oscillations that can be directly associated to the coherent oscillation between the empty and doubly occupied dot. The oscillation frequency is equal to the energy splitting between the Andreev bound states. These effects are more pronounced when the empty state and double-occupied state are in resonance.

No abstract

We propose a feedback control scheme for generating and stabilizing pure states of transport devices, such as charge qubits, under non-equilibrium conditions. The purification of the device state is conditioned on single electron jumps and leaves a clear signal in the full counting statistics which can be used to optimize control parameters. As an example of our control scheme, we are presenting the stabilization pure transport states in a double quantum dot setup with the inclusion of phonon dephasing.Comment: 7 pages, 5 figure

An open resonator fabricated in a two-dimensional electron gas is used to explore the transition from strongly invasive scanning gate microscopy to the perturbative regime of weak tip-induced potentials. With the help of numerical simulations that faithfully reproduce the main experimental findings, we quantify the extent of the perturbative regime in which the tip-induced conductance change is unambiguously determined by properties of the unperturbed system. The correspondence between the experimental and numerical results is established by analyzing the characteristic length scale and the amplitude modulation of the conductance change. In the perturbative regime, the former is shown to assume a disorder-dependent maximum value, while the latter linearly increases with the strength of a weak tip potential. arXiv:1709.08559v1 [cond-mat.mes-hall]

We consider theoretically the transport through the double quantum dot structure of the recent experiment of C. Payette et al. [Phys. Rev. Lett. 102, 026808 (2009)] and calculate stationary current and shotnoise. Three-level mixing gives rise to a pronounced current suppression effect, the character of which charges markedly with bias direction. We discuss these results in connexion with the dark states of coherent population trapping in quantum dots.PACS numbers: 73.63. Kv, 73.50.Td, 73.23.Hk In a recent experiment [1], Payette and co-workers studied the transport through a double quantum dot (DQD) in which the source-side QD (QD1) had a single electronic level within the transport window, whilst the drain-side dot (QD2) possessed three (see Fig. 1). Gate voltages enabled the position of the former "s-level" to be adjusted and thus used as a probe of the second QD. Due to non-ellipticity, the levels of QD2 were found not to be the familiar Fock-Darwin (FD) levels [2], but rather mixtures of them. This gave rise to a distinctive feature in the tunneling magnetospectrum consisting of an avoided crossing with a central line running through it. Strikingly, this central current line was not continuous as a function of magnetic field, as one might expect, but rather showed a strong suppression near the centre of the avoided crossing. The authors of Ref.[1] suggested a connection between this phenomenon and that of the all-electronic coherent population trapping (CPT) of Refs. [3,4,5,6]. It is the aim of this paper to explore this connexion further.We use a master equation treatment and calculate stationary current and shotnoise. We consider a sourcedrain bias direction both as in Ref.[1] (forward bias), as well in the opposite direction (reverse bias). Both bias directions yield a current suppression, but as our calculations here reveal, the character is rather different in each case. In forward bias, the current suppression valley is wide (proportional to the mixing energy between the levels) as observed in the experiment of Ref.[1] and the shotnoise is subPoissonian. In the reverse bias configuration, the current suppression valley is narrow (proportional to the coupling rate with the leads) and the current statistics are strongly superPoissonian. We argue that only in the latter case does the current blocking mechanism bear strong resemblance to coherent population trapping. I. MODELWe assume strong Coulomb blockade such that at most one excess electron can occupy the DQD at any one time and write the Hamiltonian of the complete system as1: Double quantum dot with a bias window that includes the single probe s-level in QD1 and three levels of QD2. The depicted bias configuration is as in Ref.[1], which we describe here as forward bias. In the sequential tunneling regime, electron tunneling is described by the rates ΓL from left lead to QD1, ΓR from QD2 to the right lead, and by γα; α = 0, ± between the dots.The Hamiltonian of the first dot reads H 1 = ǫ s |s s| with |s denoting the single QD1 s-type orbital. De...

We investigate the electronic transport through two parallel double quantum dots coupled both capacitively and via a perpendicularly aligned charge qubit. The presence of the qubit leads to a modification of the coherent tunnel amplitudes of each double quantum dot. We study the influence of the qubit on the electronic steady state currents through the system, the entanglement between the transport double quantum dots, and the back action on the charge qubit. We use a Born-Markov-Secular quantum master equation for the system. The obtained currents show signatures of the qubit. The stationary qubit state may be tuned and even rendered pure by applying suitable voltages. In the Coulomb diamonds it is also possible to stabilize pure entangled states of the transport double quantum dots

Scanning gate microscopy measurements in a circular ballistic cavity with a tip placed near its center yield a non-monotonic dependence of the conductance on the tip voltage. Detailed numerical quantum calculations reproduce these conductance oscillations, and a classical scheme leads to its physical understanding. The large-amplitude conductance oscillations are shown to be of classical origin, and well described by the effect of a particular class of short trajectories.Comment: 12 pages, 8 figures, final versio