Full counting statistics of laser excited Rydberg aggregates in a one-dimensional geometry.

We experimentally study the full counting statistics of few-body Rydberg aggregates excited from a quasi-one-dimensional atomic gas. We measure asymmetric excitation spectra and increased second and third order statistical moments of the Rydberg number distribution, from which we determine the average aggregate size. Estimating rates for different excitation processes we conclude that the aggregates grow sequentially around an initial grain. Direct comparison with numerical simulations confirms this conclusion and reveals the presence of liquidlike spatial correlations. Our findings demonstrate the importance of dephasing in strongly correlated Rydberg gases and introduce a way to study spatial correlations in interacting many-body quantum systems without imaging.

Nanotransformation and current fluctuations in exciton condensate junctions.

We analyze the nonlinear transport properties of a bilayer exciton condensate that is contacted by four metallic leads by calculating the full counting statistics of electron transport for arbitrary system parameters. Despite its formal similarity to a superconductor the transport properties of the exciton condensate turn out to be completely different. We recover the generic features of exciton condensates such as counterpropagating currents driven by excitonic Andreev reflections and make predictions for nonlinear transconductance between the layers as well as for the current (cross)correlations and generalized Johnson-Nyquist relationships. Finally, we explore the possibility of connecting another mesoscopic system (in our case a quantum point contact) to the bottom layer of the exciton condensate and show how the excitonic Andreev reflections can be used for transforming voltage at the nanoscale.

Spin-orbital phase synchronization in the magnetic field-driven electron dynamics in a double-well potential.

We study the dynamics of an electron confined in a one-dimensional double-well potential in the presence of driving external magnetic fields. The orbital motion of the electron is coupled to the spin dynamics by spin-orbit interaction of the Dresselhaus type. We derive an effective time-dependent model Hamiltonian for the orbital motion of the electron and obtain a condition for synchronization of the orbital and the spin dynamics. We find an analytical expression for the Arnold 'tongue' and propose an experimental scheme for realizing the proposed synchronization.

Quantum fluctuation theorem in an interacting setup: point contacts in fractional quantum Hall edge state devices.

We verify the validity of the Cohen-Gallavotti fluctuation theorem for the strongly correlated problem of charge transfer through an impurity in a chiral Luttinger liquid, which is realizable experimentally as a quantum point contact in a fractional quantum Hall edge state device. This is accomplished via the development of an analytical method to calculate the full counting statistics of the problem in all the parameter regimes involving the temperature, the Hall voltage, and the gate voltage.

Interaction-induced beats of Friedel oscillations in quantum wires.

We analyze the spectrum of electron density oscillations in an interacting one-dimensional electron system with an impurity. The system's inhomogeneity is characterized by different values of Fermi wave vectors kF=k L/R on left or right side of the scatterer, leading to a Landauer dipole formation. We demonstrate, that while in the noninteracting system the Friedel oscillations possess only one periodicity related to the local kF, say kL on the left side, the interplay of the interactions and the Landauer dipole generates an additional peak in the spectrum of density oscillations at the counterpart kR. Being only present in correlated systems, the position and shape of this spectral feature, which in coordinate space is observable as a beating pattern in the Friedel oscillations, reveals many important details about the nature of interactions. Thus it has a potential to become an investigation tool in condensed matter physics.

Hanbury Brown-Twiss correlations and noise in the charge transfer statistics through a multiterminal Kondo dot.

We analyze the charge transfer statistics through a quantum dot in the Kondo regime, when coupled to an arbitrary number of terminals N. Special attention is paid to current cross correlations between concurring transport channels, which show distinct Hanbury Brown-Twiss antibunching for N>2 reflecting the fermionic nature of charge carriers. While this effect weakens as one moves away from the Kondo fixed point, a new type of correlations between nonconcurring channels emerges which are due entirely to the virtual polarization of the Kondo singlet. As these are not obscured by the background from fixed-point correlations they provide a promising means for extracting information on the parameters of the underlying Fermi-liquid model from the experimental data.

Full counting statistics for the Kondo dot in the unitary limit.

We calculate the charge transfer probability distribution function chi(lambda) for the Kondo dot in the strong-coupling limit within the framework of the Nozières-Fermi-liquid theory of the Kondo effect. At zero temperature, the ratio of the moments Cn of the charge distribution to the backscattering current Ibs follows a universal law Cn/2Ibs = (-1)n(1+2n)/6. The functional form of chi(lambda) is consistent with tunneling of electrons and, possibly, electron pairs. We then discuss the crossover behavior of chi(lambda) from weak to strong Coulomb repulsion in the underlying Anderson impurity model and relate this to the existing results. Finally, we extend our analysis to the case of finite temperatures.

Full counting statistics of chiral Luttinger liquids with impurities.

We study the statistics of charge transfer through an impurity in a chiral Luttinger liquid (realized experimentally as a quantum point contact in a fractional quantum Hall edge state device). Taking advantage of the integrability we present a procedure for obtaining the cumulant generating function of the probability distribution to transfer a fixed amount of charge through the constriction. Using this approach we analyze in detail the behavior of the third cumulant C3 as a function of applied voltage, temperature, and barrier height. We predict that C3 can be used to measure the fractional charge at temperatures, which are several orders of magnitude higher than those needed to extract the fractional charge from the measurement of the second cumulant. Moreover, we identify the component of C3, which carries the information about the fractional charge.

Nonequilibrium dynamics of correlated electron transfer in molecular chains.

The relaxation dynamics of correlated electron transport along molecular chains is studied based on a substantially improved numerically exact path integral Monte Carlo approach. As an archetypical model, we consider a Hubbard chain containing two interacting electrons coupled to a bosonic bath. For this generalization of the ubiquitous spin-boson model, non-Boltzmann equilibrium distributions are found for many-body states. By mapping the multiparticle dynamics onto an isomorphic single particle motion, this phenomenon is shown to be sensitive to particle statistics and, due to its robustness, allows for new control schemes in designed quantum aggregates.

Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas.

The four-body problem for an interacting two-species Fermi gas is solved analytically in a confined quasi-one-dimensional geometry, where the two-body atom-atom scattering length a(aa) displays a confinement-induced resonance. We compute the dimer-dimer scattering length a(dd) and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.

Full counting statistics for the Kondo dot.

The generating function for the cumulants of charge current distribution is calculated for two generalized Majorana resonant level models: the Kondo dot at the Toulouse point and the resonant level embedded in a Luttinger liquid with the interaction parameter g=1/2. We find that the low-temperature nonequilibrium transport in the Kondo case occurs via tunneling of physical electrons as well as by coherent transmission of electron pairs. We calculate the third cumulant ("skewness") explicitly and analyze it for different couplings, temperatures, and magnetic fields. For the g=1/2 setup the statistics simplifies and is given by a modified version of the Levitov-Lesovik formula.

Atom-dimer scattering for confined ultracold fermion gases.

We solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a (perpendicular) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a (perpendicular)/a approximately 1.46, and a dimer state for arbitrary a (perpendicular)/a. The three-body problem is shown to be universal, and described by the atom-dimer scattering length a(ad) and a range parameter b(ad). In the dimer limit a (perpendicular)/a>>1, we find a repulsive zero-range atom-dimer interaction. For a (perpendicular)/a<<-1, however, the potential has long range, with a(ad)>0 and b(ad)>>a(ad). There is no trimer state, and despite a(ad)=0 at a( perpendicular)/a approximately 2.6, there is no resonance enhancement of the interaction.

Evidence for Luttinger-liquid behavior in crossed metallic single-wall nanotubes.

Transport measurements through crossed metallic single-wall nanotubes are presented. We observe a zero-bias anomaly in one tube which is suppressed by a current flowing through the other nanotube. These results are compared with a Luttinger-liquid model which takes into account electrostatic tube-tube coupling together with crossing-induced backscattering processes. Explicit solution of a simplified model is able to describe qualitatively the observed experimental data with only one adjustable parameter.

Resonant tunneling between Luttinger liquids: a solvable case.

We discuss the conductance of a Luttinger liquid interrupted by a quantum dot containing a single resonant level. Using bosonization and refermionization methods, we find a mapping to a Kondo-type problem which possesses a nontrivial Toulouse-type solvable point. At this point, we obtain an analytic expression for the nonlinear current-voltage characteristics and analyze the differential conductance and the width of the resonance peak as functions of bias and gate voltages, temperature, and barrier asymmetry. We also determine the exact scaling function for the linear conductance.

Field emission from Luttinger liquids and single-wall carbon nanotubes.

We develop a theory for the field emission effect in Luttinger liquids and single-wall carbon nanotubes at the level of the energy resolved current distribution. We generalize Fowler-Nordheim relations. Just below the Fermi edge, we find a power-law vanishing current distribution with the density of states exponent. The current distribution above the Fermi edge owes its existence to a peculiar interplay of interactions and correlated tunneling. It displays a nontrivial power-law divergence just above the Fermi energy.