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.

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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