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The application of the theory of integrably models to the calculation of dynamical correlation functions of systems such as quantum spin chains and low-dimensional atomic gases has made much progress in recent years. The main part of this talk will review some recent results on Heisenberg spin chains and bosonic atomic gases, providing an introduction to the underlying theory but also highlighting a number of experimental applications. The second part of the talk will be concerned with the nonequilibrium dynamics of interacting quantum systems after a sudden change in one of the system's parameters (quench). A new method based on integrability will be presented, allowing the study of such classes of problems.

Central to the understanding of the physics of degenerate Bose gases are the concepts of Bose-Einstein condensation and superfluidity. Both phenomena admit clear quantitative definitions, allowing a Bose gas to be characterised by "condensate" and "superfluid" fractions. For ultra-cold atomic Bose gases, the condensate fraction is readily measured through the mapping of occupation numbers in momentum space to real space by expansion imaging. While characteristic signatures of superfluidity have been observed in atomic gases, a general method for the quantitative measurement of the superfluid fraction remains outstanding. In this talk, I will describe how the superfluid fraction of an atomic gas can be measured using a light-induced vector potential. The proposed method is closely analogous to the classic experimental method of Andronikashvili for measuring the superfluid fraction of liquid helium.

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Fluctuation relations connect time-reversed pairs of probability distribution functions for nonequilibrium systems. Starting from a general one-step master equation, we employ the Martin-Siggia-Rose approach to derive transient fluctuation relations for time-dependent nonequilibrium transport currents. This generalizes the Crooks relation and the Jarzynski equation to currents. As application, I will discuss a prototypical single-electron transistor with time-dependent voltage bias. Work done in collaboration with A. Altland, A. De Martino and B. Narozhny.

I consider the finite temperature dynamical structure factor (DSF) of gapped quantum spin chains such as the transverse field Ising model and integer spin Heisenberg chains. At T=0 these models support coherent single-particle excitations, visible as sharp delta-function lines in the DSF. Using a novel low-temperature expansion the temperature-induced damping of coherent modes is calculated. The emergence of finite temperature resonances at low energies is discussed.

Shot noise measurements have proven to be a sensitive and accurate tool to determine charge and correlations among carriers propagating in edge modes. I will review some of the important results of charge measurements and demonstrate that the measured charge is not necessarily unique but depends on the conditions of the measurement. I will also present new (unpublished) results proving for the first time, also via shot noise measurements, the existence of counter propagating 'neutral modes'.

We study the properties of three-flavors fermions in an optical lattice in the presence of large three-body repulsion which can be experimentally induced by strong three-body losses. Low temperature static and dynamical properties of this system are addressed by using dynamical mean-field theory and variational Monte Carlo techniques. The resulting phase diagram shows a strong interplay between magnetization and superfluidity. In the absence of three-body repulsion, the system undergoes a phase transition from color superfluid to trionic phase, which shows additional CDW modulation at half-filling. This transition is suppressed when including a large three-body repulsion. In this case the color superfluid tends to fully polarize in strong coupling in marked contrast with the unconstrained case where the unpolarized trionic phase emerges.

A double quantum dot and a quantum point contacts can be coupled capacitively. This coupled system is a paradigmatic example for a quantum measurement setup. The quantum point contact can be seen as a detector sensing the charge state of the double quantum dot. Conversely, the double quantum dot can be used as an energy selective sensor for shot noise originating from the quantum point contact. In this contribution an overview will be presented of recent experiments performed on this system. The double quantum dot is either realized in InAs nanowires or in lateral quantum dots formed in Ga[Al]As heterostructures. In both cases, the quantum point contact is formed in a Ga[Al]As heterostructure. It will be shown that using such arrangements it is possible to measure the tunneling coupling between the neighboring dots, investigate cotunneling, and investigate the noise-induced spectral shift in the double quantum dot spectrum.

I will review recent work on quantum quenches in the Hubbard model and in quantum impurity models. The interaction quench in the Hubbard model permits to explore the opposite limit of the adiabatic switching procedure in the Landau Fermi liquid paradigm. The real time evolution shows the phenomenon of prethermalization, which is related to a universal relation between nonequilibrium and equilibrium expectation values for weak interaction quenches. Based on the flow equation method we will also find universal relations for the work distribution function for quenches in quantum impurity systems.

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We have measured the third cumulant of voltage quantum fluctuations

Fermionic atoms in optical lattices are ideal model systems to explore the physics of strongly correlated quantum systems. Experiments of the Bloch group on the compressibility of atomar clouds in the Mott regime allow for a quantitative comparison of theory and experiments [1]. Qualitatively new effects arise out of equilibrium. We investigate theoretically the physics of atoms expanding within an optical lattice and show that it is governed by a surprisingly complex interplay of diffusive and ballistic behavior. In recent experiments this physics is tracked by observing the shape of the atomar cloud which remains spherical in the diffusive regime but becomes cubic in its ballistic tails.

[1] U. Schneider, L. Hackermuller, S. Will, Th. Best, I. Bloch, T. A. Costi, R. W. Helmes, D. Rasch, A. Rosch, Science 322, 1520 (2008).

I will discuss a Bethe ansatz calculation of the noise and higher cumulants of the current for a non equilibrium interacting quantum impurity problem. I will also discuss a time dependent DMRG calculation of the same quantities, as well as a recent proposal of Klich and Levitov relating the full counting statistics to the rate of entanglement in this set up.

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In this talk I will discuss a few complementary characterizations of quantum quenches in strongly correlated systems either using fidelities, or the statistics of the work done to change the system parameters, or the asymptotics of correlators. I will first explore various intriguing connections between quantum quenches, edge singularities in strongly correlated systems and boundary critical phenomena. Using these connections for quantum critical systems I will describe in detail the critical behavior of various quantities, such as the fidelity susceptibilities and the statistics of the work, for a few models, i.e. the quantum Ising chain, the Dicke model and quantum impurities. Finally, I will briefly discuss how the critical behavior is encoded in the asymptotics of non-equilibrium correlators.

Quantum quenches i.e. instantaneous changes in the parameters of the Hamiltonian of a quantum system, have recently become a popular topic for condensed matter physicists, promising to improve our understanding of out of equilibrium quantum behaviour and address fundamental questions about the nature of thermalization. However it is not at all a new subject as closely related problems have been studied earlier in different contexts (e.g. cosmology). In this talk a review of various analytical methods used and main results obtained is attempted. Particular emphasis is given to quenches in interacting field theories using a non-perturbative self-consistent approximation.

Strong interactions between electrons in a solid material lead to surprising effects such as the Mott insulator, where a suppression of conductivity occurs due to interactions rather than due to a filled Bloch band. Proximity to the Mott insulating phase is the origin of many intriguing phenomena in condensed matter physics, most notably high-temperature superconductivity. We experimentally implement the Fermi-Hubbard model, which encompasses the physics of the Mott insulator, by trapping a repulsively interacting two-component Fermi gas in an optical lattice. The system is characterized though accurate measurements of the equilibrium double occupancy. By comparing the experimental data with ab initio calculations we determine the temperature of the sample. The unique control over the creation of double occupancies and the high resolution in detecting them also allow us to study non-equilibrium properties. Starting with a repulsively interacting gas of fermions we perturb the sample by generating doubly occupied lattice sites and monitor the subsequent relaxation in a time-resolved manner. We measure the lifetime of doublons in the isolated many-body system. Over two orders of magnitude, the doublon lifetime shows an exponential dependence on the ratio of interaction energy to kinetic energy.

Systems of ultracold atoms in optical lattices offer unique possibilities to study many-body dynamics both close to and far from equilibrium. Here, we present an experimental realization of a generalized Landau-Zener problem with ultracold rubidium atoms in one-dimensional Bose-liquids. A bichromatic optical superlattice together with an orthogonal monochromatic lattice forms an array of pair-wise coupled potential tubes. Within these pairs, we are able to control the coupling strength as well as the energy bias (detuning) of both sides. The system is initialized with all atoms loaded to the left tube by choosing a large negative detuning. As the detuning is swept to a large positive value, we cross the tunnel resonance at zero bias, causing particle transfer between the tubes. We study the transfer efficiency as a function of the sweep rate, changing the inter-tube coupling, the interaction strength and the correlations along the tubes. We find that the transfer ef ficiency is enhanced as correlations and interactions are increased, in agreement with a qualitative mean-field calculation. In a second set of experiments, we study sweeps far away from the ground state, initializing all atoms in the right tube being initially higher in energy. This inverses the scenario and when sweeping across the resonance, we find a dramatic breakdown of adiabaticity. We deliver a comprehensive explanation of this breakdown by the inclusion of an internal thermal bath of gapless phononic excitations, allowing for energy relaxation in the system. We show experimentally, how this phononic decay channel is shut off when driving the coupled Bose-liquids across the Mott transition.

An important step towards the realization of solid state based quantum computer is the demonstration of entangled spatially separated electrons. During the last years extensive theoretical investigation has been done and different device configurations were suggested. The Cooper-pairs of superconductors are a natural source of spin entangled electrons, the separation of these electron pairs is the underlying concept of several theoretical proposals [2-4]. In this work we present the first experimental realization of such a tunable Cooper Pair Splitter. The device contains a superconducting electrode coupled to two quantum dots, which is fabricated based on InAs Nanowire. In a superconducting beam splitter configuration two basic processes can happen with a Cooper-pair: the two electrons either split up into the two arms of the beam splitter or they leave the device in the same arm. The charging energy strongly suppresses to put two electrons on the same quantum dot, therefore implementing quantum dots into the arms of the beam splitter serves as a filter for the desired splitting process. Performing non-local transport measurements on such devices, we have demonstrated the Cooper-pair splitting process. Furthermore, the separate tunability of the two dots allows studying the splitter efficiency for different settings of the quantum dots' levels. The observed results show unexpected behavior, which is beyond the existing theoretical predictions [1].

[1] L. Hofstetter, S. Csonka, J. Nygard & C. Schonenberger, Nature 461, 963 (2009). [2] P. Recher, E. V. Sukhorukov and D. Loss, Phys. Rev. B 63, 1165314 (2001). [3] G. B. Lesovik, T. Martin and G. Blatter, Eur. Phys. J. B 24, 287 (2001). [4] P. Samuelsson and M. Buttiker, Phys. Rev. Lett. 89, 466011 (2001).

We show that the motion of a laser-driven Bose-Einstein condensate in a high-finesse optical cavity realizes the spin-boson Dicke-model. The quantum phase transition of the Dicke-model from the normal to the superradiant phase corresponds to the self-organization of atoms from the homogeneous into a periodically patterned distribution above a critical driving strength. The fragility of the ground state due to photon measurement induced back action is calculated.

Results are presented for the non-equilibrium dynamics of a quantum XXZ-spin chain whose spins are initially arranged in a domain wall profile via the application of a spatially varying magnetic field in the z-direction. The system is driven out of equilibrium in two ways: a). by rapidly turning off the magnetic field while keeping the interactions the same, b). by rapidly quenching the interactions at the same time as the magnetic field is turned off. The time-evolution of the domain wall profile as well as various two-point spin correlation functions is studied by the exact solution of the fermionic problem for the XX chain, and via a bosonization approach for the XXZ chain. The domain wall dynamics is found to be qualitatively different in the gapless XX phase and the gapped Ising phase. At long times the magnetization is found to equilibrate, while the two-point correlation functions in general do not. In particular, the correlation functions reach a nonequilibrium steady state which is also spatially inhomogenous with a structure which depends on the initial domain wall profile. A generalized Gibb's ensemble cannot capture this spatially inhomogenous structure.

We discuss the capacitance and the resistance, usually called the charge relaxation resistance, of a quantum coherent RC circuit driven by a low-frequency AC voltage. This circuit is the quantum analogue of the classical RC circuit: it comprises a dot capacitively coupled to a nearby gate and connected to a single reservoir lead. As a result of phase coherence and electronic interactions, the quantum circuit behaves quite differently and Kirchhoff's law is violated. Here we show that the charge relaxation resistance is perfectly quantized, regardless of the single lead transmission and for an arbitrary strength of the interaction. Its low-frequency value is h/2 e2. When the driving frequency exceeds the dot level spacing, we predict a transition to a metallic regime with a doubled quantized resistance h/e2. The novel quantized resistance h/e2 is connected to the Korringa-Shiba relation of the Kondo model, thereby revealing the physics behind these universal charges.

We perform a detailed quantum dynamical study of nonequilibrium Josephson oscillations between Bose-Einstein condensates confined in a finite-size double-well trap. We find that the Josephson junction can sustain multiple undamped Josephson oscillations up to a certain time scale, without quasi-particles being excited in the system. This may explain recent experimental observation. Beyond this characteristic time-scale the dynamics of the junction is governed by fast, quasi-particle assisted Josephson tunneling as well as Rabi oscillations between discrete quasi-particle levels. We show, for example, that initially self-trapped state of the junction will be destroyed by these fast dynamics.

The description of a stationary state in quantum transport suffers from the problem that statistical operators are mathematically ill-defined for infinite systems, but a rigorous use of scattering theory seems to require them. Starting with a nonequilibrium statistical operator for a finite system it is shown for the case of full counting statistics for noninteracting fermions how the thermodynamic limit can be performed and the scattering matrix enters in the long-time limit without ad-hoc assumptions.

We study the Kondo model at finite bias voltage using a recently developed nonequilibrium real-time renormalization group method in frequency space. We present an analytic and well-controlled procedure to solve the RG equations in the weak-coupling regime. We focus on the longitudinal and transverse spin-spin correlation and response functions and the real-time evolution of spin and current. For the correlation functions we obtain analytic results for the line-shape, the small- and large-frequency limits and several other features like the height and width of the peak in the transverse susceptibility at the renormalized magnetic field. For the time evolution we find that all observables decay both with the spin relaxation and decoherence rates. Various voltage-dependent logarithmic, oscillatory, and power-law contributions are dervied. For short times we obtain universal dynamics for spin and current. In the second part we study a quantum dot dominated by charge fluctuations, which is modeled by the interacting resonant level model. We present analytical results for the steady-state properties and describe the time evolution into this state. We particularly focus on the case of asymmetric couplings to the leads and broken particle-hole symmetry. The relaxation dynamics shows characteristic oscillations as well as an interplay of exponential and power-law decay.

We develop an effective theory of pulse propagation in a nonlinear and disordered medium in two dimensions. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena which we refer to as "locked explosion" and "diffusive" collapse. The equation can be relevant for laser beams propagating in disordered photonic crystals or Bose-Einstein condensates expanding in a disordered environment.

We study the steady-state current in a minimal model for a quantum dot dominated by charge fluctuations and analytically describe the time evolution into this state. The current is driven by a finite bias voltage across the dot. The Coulomb interaction of the localized dot electron with the lead electrons is treated using two complementary renormalization group methods. We find interesting non-equilibrium effects which can in general not be explained by simply considering the bias voltage as an additional infrared cutoff. The relaxation dynamics shows characteristic oscillations as well as an interplay of exponential and power-law decay.

We solve the dynamics of an ensemble of interacting rotors coupled to two leads at different chemical potential letting a current flow through the system and driving it out of equilibrium. We show that a coarsening phase persists under the bias voltage up to a critical value. We uncover the coarsening regime finding, in particular, which features are essentially quantum mechanical and which are basically classical in nature. We demonstrate that the system evolves via the growth of a coherence length with the same time-dependence as in the classical limit, $R(t) \\simeq t^{1/2}$ -- the scalar curvature driven universality class. We derive the scaling functions at late epochs in the coarsening regimes and prove that they coincide with the classical ones.

We present exact solutions for interacting quantum many-body systems with time-dependent parameters. First we consider wave-functions solvable by a scaling ansatz [1]. This is applied to expanding Bose gases in one and two dimensions. Another approach consists in the extension of the Bethe ansatz to non-equilibrium systems [2]. Using time-dependent Bethe equations we can address the question of emergence of quantum chaos from a new point of view.

[1] V. Gritsev, P. Barmettler, E. Demler, arXiv:0912.2744v1. [2] P. Barmettler, V. Gritsev, in preparation.

Dynamics of neutral modes for fractional quantum Hall states is investigated for a quantum point contact geometry in the weak-backscattering regime[1]. In the contest of the edge states effective theories for the Jain sequence, we demonstrate that the crossover regime between tunneling of single-quasiparticles and of agglomerates of $p$-quasiparticles can explain the recent observation of backscattering current noise done at extremely low temperatures[2,3]. In particular we compare the theory with the experiments for different values of filling factors[4,5]. The presence of non-universal phenomena induced by interactions is appropriately taken in account. In conclusion we demonstrate that higher order cumulants are a unique resource to study quantitatively the competition between different carrier charges and shed light on controversial results.

[1] D. Ferraro, A. Braggio, N. Magnoli and M. Sassetti, New J. Phys 12, 013012 (2010). [2] D. Ferraro, A. Braggio, M. Merlo, N. Magnoli and M. Sassetti Phys. Rev. Lett. 101, 166805 (2008). [3] D. Ferraro, A. Braggio, N. Magnoli and M. Sassetti, Physica E 42, 580 (2010). [4] Y.C. Chung, M. Heiblum, and V. Umansky, Phys. Rev. Lett. 91, 216804 (2003). [5] Aveek Bid, N. Ofek, M. Heiblum, V. Umansky, and D. Mahalu Phys. Rev. Lett. 103, 236802 (2009). Comments: Recent publications in the field: Neutral modes edge state dynamics through quantum point contacts D. Ferraro, A. Braggio, N. Magnoli and M. Sassetti New J. Phys 12, 013012 (2010).

Diabatic rapid passage allows a non-equilibrium population of excitons to be created in an ensemble of quantum dots. We show theoretically that a system prepared in this manner can be dynamically unstable to the formation of a non-equilibrium condensate, similar to that predicted in a quenched Fermi gas. The continuum of microcavity photon modes results in instabilities at a range of wavevectors, with the possibility of the dominant instabilities occuring at finite wavectors. Thus we predict the formation of inhomogeneous condensates, similar to Fulde-Ferrel-Larkin-Ovchinnikov states. Experiments seeking these non-equilibrium solid-state condensates are now being developed.

Accurate all-electric devices for the generation and filtering of spin currents are of crucial importance for spintronics experiments and applications. Here, we show that, in the presence of spin-orbit coupling, resonances associated with avoided level crossings of a quantum dot can be exploited to produce and control spin currents purely by cycling electrical gates. Using Brouwer's scattering matrix approach, we first analyze the general conditions to have spin currents in an adiabatically driven two-terminal device. We then focus on a dot with two resonant orbitals, showing with specific examples that both spin filtering and pure spin current generation can be achieved. Finally, we discuss the effect of Coulomb interaction.

We present an analysis of Bose--Fermi mixtures in optical lattices for the case where a static force is applied to the fermions, and the bosons (in the superfluid phase) are described by Bogoliubov phonons. Accordingly, the static force lifts the degeneracy of the energy levels in the lattice potential and the fermionic states form a Wannier--Stark ladder. We show that the Bogoliubov phonons enable hopping transitions between different Wannier--Stark states; these transitions are accompanied by energy dissipation into the superfluid and result in a net fermionic current along the lattice. We determine the dependence of the fermionic current on the static force and find that the phonon density of states strongly affects the emergent current. In particular, if the energy splitting between the Wannier--Stark states exceeds the width of the phonon band, then the current is strongly suppressed. This effect should be observable in a realistic experimental set-up.

We study the dynamics following a quantum quench of two onedimensional systems under the effect of disorder: the random Ising model and the XXZ model with random magnetic fields. The first system is always integrable, while in the second case disorder breaks integrability. We investigate the possibility of thermalization, comparing the thermal behavior of observables with the one following the quench. In the random XXZ model we also study the energy level statics in order to characterize quantitatively the loss of integrability, both as a function of the strength of the random fields and as a function of the different regions of the energy spectrum.

A Haldane conjecture is revealed for spin-singlet charge modes in 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of a low-energy approach and DMRG calculations, we show the emergence of gapless and gapped phases depending on the parity of N for attractive interactions at half-filling. The analogue of the Haldane phase of the spin-1 Heisenberg chain is stabilized for N=2 with non-local string charge correlation, and pseudo-spin 1/2 edge states. At the heart of this even-odd behavior is the existence of a spin-singlet pseudo-spin $N/2$ operator which governs the low-energy properties of the model for attractive interactions and gives rise to the Haldane physics.

We study the response of a Bose-Einstein condensate to an unbiased periodic driving potential. By controlling the space and time symmetries of the driving we show how a directed current can be induced, producing a coherent quantum ratchet. The ratchet current can be induced by two different mechanisms. Weak driving induces a regular behavior that is strongly suppressed by the interparticle interaction, which eventually induces a self-trapping transition. For strong driving the behavior becomes chaotic, producing a quasiperiodic current with a stable, non-zero time average.

We analyze an interacting Bose-Fermi mixture in a 1D disordered potential using a combination of renormalization group and variational methods. We obtain the complete phase diagram of this system for parameters of experimental relevance as a function of bosonic and inter-species interaction strengths, in the weak disorder limit. Superfluid correlations are enhanced by the Bose-Fermi interaction and compete with backscattering on disorder. The system is thus characterized by several phase transitions between superfluid and various glassy insulating states, including a new Bose-Fermi glass phase, where both species are coupled and localized. The dynamical response of the system depends on whether one or both species are pinned by disorder. The dynamical structure factor, as measured through Bragg scattering experiments, can distinguish between the various localized phases and probe their dynamics.

A unified approach to decoherence and relaxation of single electron excitations in Integer Quantum Hall edge channels is presented. Within the bosonization framework, relaxation and decoherence induced by interactions and capacitive coupling to an external linear circuit are computed. An explicit connexion with high frequency transport properties is established. This work provides a non perturbative solution to the quasi particle relaxation problem originally considered by Landau and provides an efficient framework to discuss the feasability of "electron quantum optics".

An asymmetric variant of the fermionic Hubbard model, with different hopping coefficients for the two species, was originally introduced to model certain metal-insulator transitions in solid-state physics and has recently gathered a renewed interest in the context of optical lattices. Here we discuss a series of numerical results for the one-dimensional case with equally populated species, obtained by means of the density-matrix renormalisation group. We consider both the repulsive case, where phase separation may occur, and the attractive case to study the robustness of pairing correlations with increasing asymmetry. We also inspect the nature of the excitations related to population imbalance (the 'spin gap'). These results are compared to bosonisation predictions and to perturbative calculations in the strong and weak coupling regimes.

We apply continuous-time Quantum Monte Carlo algorithms to the imaginary-time formalism introduced by Han and Heary [1]. The analytic structure of the two-variable Green’s functions is discussed, and an algorithm for the numerical analytic continuation is proposed. In principle, results compatible with those from other methods are obtained. [2]

[1] J. E. Han, and R. J. Heary, Phys. Rev. Lett. 99, 236808 (2007) [2] A. Dirks, Ph. Werner, M. Jarrell, Th. Pruschke; to be published; http://arxiv.org/abs/1002.4081

We present a unified view of electric transport in undoped graphene for finite electric field. The weak field results agree with the Kubo approach. For strong electric field, the current increases non-linearly with the electric field as E^{3/2}. As the Dirac point is moved around in reciprocal space by the field, excited states are generated, in a way analogous to the generation of defects in a quench through a quantum critical point. These results are also analyzed in terms of Schwinger's pair production and Landau-Zener tunneling. An experiment for cold atoms in optical lattices is proposed to test these ideas.

We use non-equilibrium dynamical mean-field theory in combination with a recently developed Quantum Monte Carlo impurity solver to study the real-time dynamics of the Hubbard model after an interaction quench. We find that the relaxation behavior undergoes a qualitative change at an intermediate value of U [1], showing collapse and revival oscillations after quenches to the strongly interacting regime, and prethermalization after quenches to the weakly interacting regime. This transition, which coincides with a pronounced minimum in the thermalization time, occurs similarly for rather general initial states, although the location of transition depends on the initial state.

[1] M. Eckstein, M. Kollar, and P. Werner, Phys. Rev. Lett. 103, 056403 (2009); arXiv:0910.5674.

The Dynamical Casimir effect (DCE) is the particle production induced on the quantum vacuum by moving boundaries (mirrors)[1]. For practical mirror velocities, much slower than light, the emitted flux is too weak to be detected. Therefore this effect, though considered a corner-stone of quantum field theory, has never been observed experimentally. We propose a new framework for observing and investigating DCE using a Bose Einstein condensate flowing in a Y-junction, or 'atom beam splitter' [2]. In this scheme the relative phase between the two arms of the split condensate behaves as a free massless scalar field, while the splitting point imposes a boundary condition of vanishing relative phase. It therefore plays the role of the moving mirror (in the condensate frame), which excites the relative phase vacuum and leads to quasi-particle production. Contrary to the QED version of the effect, the relevant velocity here is of course the sound velocity of the condensate, which is easily attainable. We predict clear signatures of the effect in the statistics of interference fringes, which directly measure the relative phase correlations[3]. Finally we note that for a specific, accelerated splitting trajectory, the emitted radiation can be linked following [4] to the Hawking radiation emitted in formation of gravitational black holes.

[1] G.T. Moore, J. Math. Phys. 11, 2679 (1970) [2] S. Fagnocchi, E. Altman, E. Demler, in preparation [3] A. Polkovnikov, E. Altman and E. Demler , PNAS 103, 6125 (2006) [4] R.D. Carlitz, and R.S. Willey, Phys. Rev. D 36, 2327 (1987)

The aim of this talk is to present how one can, through the Algebraic Bethe Ansatz (ABA), use integrability in order to study numerically the dynamics of specific strongly interacting models. Not only does ABA give access to the exact eigenstates and eigenenergies of the Hamiltoninan, it can also provide numerically tractable expressions for various form factors. The latter then allow one to compute various static and dynamical correlation functions in equilibrium, and even treat time evolution in certain non-equilibrium situations. Moreover working in the eigenbasis of the system can usually allow to drastically truncate the effective Hilbert space needed for a given calculation. In the end, this grants access to system sizes which would be untreatable with matrix diagonalization while keeping the numerical error under perfect control. In that spirit, numerical results related to the Richardson model (and a wide class of similar models related to Gaudin magnets) will be discussed.

The interaction of heavy atoms in a Mott state and light spin-1/2 fermionic atoms is studied in a double well potential. Inelastic scattering processes between both atomic species excite the heavy atoms and renormalize the tunneling rate as well as the interaction of the light atoms. An effective Hamiltonian for the latter is derived, which describes tunneling of single fermions, tunneling of fermionic pairs and an exchange of fermionic spins. We study the dynamics of quantum states in a double well potential. This shows a signature of the first order phase transition between N'eel and dimer states occuring in the extended system, as well as the polaronic effect.

An optical Quantum Dot, where the electron and hole levels are coupled to superconducting leads can produce photons at discrete energy levels as well as in a continuous spectrum. Energies in the vicinity of the applied bias voltage will induce pairwise emission of polarization correlated photons. Further, at energies near twice the bias voltage also photons are emitted, which is associated to the transfer of Cooper pairs. This is reminiscent of Josephson radiation. By designing a cavity around the quantum dot it may be possible to realize lasing.

The dynamics and decoherence of solid state qubits are often determined by a few non-Gaussian fluctuators. Paradigmatic models often used to represent the qubit environment system like the spin-boson model cannot be applied here because they describe Gaussian distributed fluctuations. The simplest model for non-Gaussian quantum noise is the so-called ”quantum telegraph noise” model. It involves a qubit subject to the charge fluctuations of a single electron level that is tunnel coupled to a reservoir. We use the adaptive time-dependent density-matrix renormalization group method (tDMRG) to study the dynamics of this model with arbitrary time-dependence. In particular, we present tDMRG results on spectroscopy of the qubit under periodic driving.

Break junction techniques have been proved to be a suitable method for the creation of high stability single-atom or single-molecule junctions. However, as the detailed configuration of the nano-scale junction cannot be traced by direct microscopic imaging, all the information must be collected from current and voltage measurements. Several techniques applying the toolbox of mesoscopic physics were developed for the study of atomic and molecular junctions [1], including the identification of stable atomic configurations by conductance histogram technique, the study of the transmission eigenchannels by conductance fluctuation [2], shot noise [3], or superconducting subgap structure measurements [4,5], as well as the detection of the vibrational modes by point-contact spectroscopy [2]. We present a novel characterization method based on the statistical correlation analysis of conductance traces. For the creation of a conductance histogram thousands of conductance versus electrode separation traces are recorded, from which the histogram only grabs partial information. Significantly more knowledge can be tracked by also studying the cross-correlations between the different atomic and molecular configurations. This analysis can show, whether two configurations are always occurring together, one configuration is excluding the other, or their occurrences are independent events. Furthermore, the correlation analysis can resolve fine structures related to different atomic configurations, which are smeared out in the conductance histogram. We show that the correlation analysis may also demonstrate the gradual change of the number of atoms in the minimal cross-section up to high conductance values, where no features are detectected in the traditional conductance histogram.

[1] N. Agrait, A. Levy Yeyati, J. M. van Ruitenbeek, Quantum properties of atomic-sized conductors, Physics Reports 377, 81 (2003). [2] R. H. M. Smit, Y. Noat, C. Untiedt, N. D. Lang, M. C. van Hemert, J. M. van Ruitenbeek, Measurement of the conductance of a hydrogen molecule, Nature 419, 906 (2002). [3] D. Djukic and J.M. van Ruitenbeek, Shot noise measurement on a single molecule, Nano Letters, 6 (2006) [4] E. Scheer, N. Agrait, J. C. Cuevas, A. Levy Yeyati et al., The signature of chemical valence in the electrical conduction through a single atom contact, Nature 394, 154 (1998). [5] P. Makk, Sz. Csonka, A. Halbritter, Effect of hydrogen molecules on the electronic transport through atomic-sized metallic junctions in the superconducting state, PRB 78, 045414 (2008).

We study the double occupancy in a fermionic Mott insulator at half-filling generated via a dynamical periodic modulation of the hopping amplitude. Tuning the modulation amplitude, we describe a crossover in the nature of doublon-holon excitations from a Fermi Golden Rule regime to damped Rabi oscillations. The decay time of excited states diverges at a critical modulation strength, signaling the transition to a dynamically bound non-equilibrium state of doublon-holon pairs. A setup using a fermionic quantum gas should allow to study the critical exponents.

We show that the Crooks relation can be measured in optical spectra for a wide class of condensed matter systems where the absorption or emission of a photon corresponds to the sudden switch on or off of a local perturbation. In those systems, the Crooks relation establishes a general connection between the absorption and emission spectra at a given frequency of the incident radiation. For the particular case of a weak local perturbation, the Crooks relation manifests itself in the absorption and emission spectra separately allowing to test it in a single experiment. As two concrete examples we treat the X-ray edge problem and the Kondo exciton.

The problem of dephasing at zero temperature is studied by a prototype system of a charged particle on a ring that is coupled to a dissipative environment, such as a Caldeira Leggett type or a dirty metal. We find that large dissipation follows an RG scaling into a smaller one, with an apparent finite fixed point. The position correlation functions decay then with time as 1/t2. A spin 1/2 particle with spin orbit coupling is also studied. We show that for a spin texture with finite S_z perpendicular to the ring plane S_z is conserved. Dephasing between Kramer\'s degenerate states is also considered.

We prove that experimental detection of quantum phase slips is achievable for small phase slip amplitudes, contrary to what is usually assumed, by making use of a driven oscillator. Such oscillator can be realized on the basis of a thin superconducting wire or a chain of Josephson junctions. The first order correction to the amplitude of a damped-driven exhibits a cosine dependence on the charge induced by a gate electrode and very unusual oscillatory dependence on the drive/frequency.

We investigate nonequilibrium properties of the single impurity Anderson model by means of the functional renormalization group (fRG) within Keldysh formalism. We present how the level broadening Gamma/2 can be used as flow parameter for the fRG. This choice preserves important aspects of the Fermi liquid behaviour that the model exhibits in case of particle-hole symmetry. An approximation scheme for the Keldysh fRG is developed which accounts for the frequency dependence of the two-particle vertex in a way similar but not equivalent to a recently published approximation to the equilibrium Matsubara fRG. Our method turns out to be a rather flexible tool for the study of weak to intermediate on-site interactions U <= 3 Gamma. In equilibrium we find excellent agreement with NRG results for the linear conductance at finite gate voltage, magnetic field, and temperature. In nonequilibrium, our results for the current agree well with TD-DMRG. For the nonlinear conductance as function of the bias voltage, we propose reliable results at finite magnetic field and finite temperature. Furthermore, we demonstrate the exponentially small scale of the Kondo temperature to appear in the second order derivative of the self-energy.

We study the interplay between superfluid and magnetic order in an unbalanced three-component ultracold fermionic gas with SU(3) symmetrical attractive interaction, as realized by Li6 mixtures. In this system, interesting "color-superconducting" phases appear, with two components forming a superfluid, and the third component remaining gapless. Furthermore, superfluidity leads to the appearance of spontaneous ferromagnetism. We use an equation of motion-based mean field approach to analyze the phase diagram as a function of the chemical potential of the three components for temperatures around the superconducting phase transition temperature, T_c, and investigate how the chemical potential imbalance destroys superconductivity. We find first order transitions between different ordered phases, while second order transitions appear between normal and ordered phases. We do not find, however, an imbalance-induced superfluid phase, as predicted by Chenrg et al. [Phys. Rev. Lett. 99, 130406 (2007)]. The free energy functional of the system is also determined at lower temperatures using a variational approach, which is used to analyze the phase diagram at lower temperatures, where the normal-superfluid transition is expected to become of first order.

Recent experiments[1] on Bose-Einstein condensates in optical cavities have reported a quantum phase transition to a coherent state of the matter-light system - superradiance. The time dependent nature of these experiments demands consideration of collective dynamics. After a brief introduction to the superradiance phase transition, and its recent experimental realisation, I will discuss how by varying experimentally controllable parameters, one finds a much richer phase diagram than for the simple Dicke model[2]. The richness of this phase diagram arises from including the effects of cavity leakage, backreaction of the light field on the atomic states, and the combination of co- and counter-rotating wave coupling terms. Distinct regimes of different dynamical behaviour exist, separated by non-equilibrium phase transitions, and this range of dynamical behaviour can be experimentally accessed by quench experiments. As well as superradiant and normal phases, there are also a variety of multi-phase co-existence regions, and regions of persistent optomechanical oscillations described by a damped driven pendulum. Proximity to some of the phase boundaries results in critical slowing down of the decay of many-body oscillations. Notably, this slow decay can be assisted by large cavity losses. These findings open new directions to study collective dynamics and non-equilibrium phase transitions in matter-light systems.

[1] K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, arXiv:0912.3261. [2] J. Keeling, M. J. Bhaseen, and B. D. Simons arXiv:1002.3108.

We investigate the linear ac-conductance for tunneling through an arbitrary interacting quantum dot in the presence of a finite dc-bias. In analogy to the well-known Meir-Wingreen formula for the dc case, we are able to derive a general formula for the ac-conductance. It can be expressed entirely in terms of local correlations on the quantum dot, in the form of a Keldysh block diagram with four external legs. We illustrate the use of this formula as a starting point for diagrammatic calculations by considering the ac-conductance of the noninteracting resonant level model and deriving the result for the lowest order of electron-phonon coupling. We show how known results are recovered in the appropriate limits.

Recently, Aharonov-Bohm (AB) effect in electronic Mach-Zehnder (MZ) interferometers has attracted much attention among experimental and theoretical physicists. These interferometers, for the first time experimentally realized in the group of Heiblum [1], utilize quantum Hall edge states in place of optical beams, and quantum point contacts (QPC) as beam splitters, to partition edge channels. Theoretical attempts to explain experimentally observed puzzling lobe-type behavior of the visibility of AB oscillations as a function of voltage bias [2-5], have led to a number of publications [6-9]. They have focused on the filling factor ν=1 state, and suggested different mechanisms of dephasing, including the resonant interaction with a counter-propagating edge state [6], the dispersion of the Coulomb interaction potential [7], and non-Gaussian noise effects [8,9]. To date, however, all the experiments, reporting multiple side lobes in the visibility function of voltage bias, have been done at filling factor ν=2. We will argue that, in fact, there are two main mechanisms of dephasing in MZ interferometers. One mechanism [10], due to spontaneous emission of edge magneto-plasmons, leads to a size effect, which explains the lobes and many other details of experiments [2-5]. According to the second mechanism [11], dephasing in electronic MZ interferometers is due to an external non-equilibrium noise source. Experimentally [2], such a noise is created with the help of an additional QPC with the transparency T that partitions incident edge channels. We predict that a phase transition occurs at T=1/2, where the visibility function of voltage bias sharply changes its behavior. An important role in this phenomenon is played by a non-Gaussianity of noise, which is typically negligible because of a weak coupling. It turns out that MZ interferometers are strongly coupled to noise. They, therefore, can be considered efficient detectors of full counting statistics [12].

[1] Y. Ji et al., Nature (London) 422, 415 (2003). [2] I. Neder et al., Phys. Rev. Lett. 96, 016804 (2006). [3] E. Bieri et al., Phys. Rev. B 79, 245324 (2009). [4] P. Roulleau et al., Phys. Rev. B 76, 161309(R) (2007). [5] L.V. Litvin et al., Phys. Rev. B 75, 033315 (2007). [6] E.V. Sukhorukov, and V.V. Cheianov, Phys. Rev. Lett. 99, 156801 (2007). [7] J.T. Chalker, Y. Gefen, and M.Y. Veillette, Phys. Rev. B 76, 085320 (2007). [8] S.-C. Youn, H.-W. Lee, and H.-S. Sim, Phys. Rev. Lett. 100, 196807 (2008). [9] I. Neder and E. Ginossar, Phys. Rev. Lett. 100, 196806 (2008). [10] I.P. Levkivskyi, and E.V. Sukhorukov, Phys. Rev. B 78, 045322 (2008). [11] I.P. Levkivskyi, E.V. Sukhorukov, Phys. Rev. Lett. 103, 036801 (2009). [12] L.S. Levitov, H. Lee, and G.B. Lesovik, J. Math. Phys. 37, 4845 (1996).

The future aim of building functional single-molecule devices necessitates the development of reliable characterization techniques of molecular nanojunctions. In many cases the direct microscopic imaging of the junction is not possible, thus all the information about the molecular device must be extracted from its electronic properties. The conduction properties of the device can be characterized by the so-called mesoscopic PIN-code [1], the set of the transmission eigenvalues of the junction. From simple conductance measurements the transmission eigenvalues cannot be determined, but further quantities, like conductance fluctuations [2,3] and shot noise [4] can provide additional information of the mesoscopic PIN code. However, for a junction with arbitrary conductance and a larger number of conductance channels the conductance fluctuation and shot noise measurements are not efficient. By placing the junction between superconducting electrodes, and measuring the nonlinear subgap features in the current voltage characteristic, principally all the transmission eigenvalues can be determined, which was demonstrated for single-atom contacts [5]. We have studied the behavior of superconducting atomic-sized nanojunctions and their interactions with simple molecules [6]. The conductance of favorable atomic configurations was determined by conductance histogram measurement, whereas the transmission eigenvalues were determined by subgap method. We show that the channel decomposition of individual configurations may vary for junctions with similar conductance, however for a statistical ensemble of a large amount of independent configurations the evolution of the channel transmissions as a function of the total conductance is specific for the studied material. Therefore, the statistical analysis of subgap curves is a powerful spectroscopic tool for studying material specific features of atomic and molecular nanostructures.

[1] N. Agrait, A.L. Yeyati, J.M. van Ruitenbeek, Physics Reports 377, 81-279 (2003). [2] B. Ludoph, M. H. Devoret, D. Esteve, C. Urbina and J. M. van Ruitenbeek, Phys. Rev. Lett. 82, 1530 (1999) [3] A. Halbritter, S. Csonka, G. Mihály, O.I. Shklyarevskii, S. Speller, H. van Kempen, PRB 69, 121411 (2004) [4] H. E. van den Brom and J. M. van Ruitenbeek, Phys. Rev. Lett., 82, 1526 (1999) [5] E. Scheer, N. Agrait, J. C. Cuevas, A. Levy Yeyati, B. Ludoph, A. Martin-Rodero, G. Rubio Bollinger, J. M. van Ruitenbeek, C. Urbina, Nature 394, 154 (1998) [6] P. Makk, Sz. Csonka, A. Halbritter, Phys. Rev. B 78, 045414(2008)

We study the expansion of a cloud of strongly correlated fermionic atoms in an optical lattice. Initially, the cloud has a narrow Gaussian density profile but it spreads apart after being released from an additional confining potential. In experiment, it is observed that the particles at the edge of the cloud move ballistically. This ballistic motion is governed by the cubic symmetry of the lattice which is reflected in the characteristic shape of the expanding cloud. In contrast, the atoms at the center of the cloud are dominated by interparticle collisions and behave diffusively. Modelling the system in the framework of the Boltzmann equation in combination with memory-matrix theory, we describe the spatial crossover from ballistic to diffusive dynamics and recover the experimental observations made by the group of Immanuel Bloch.

Using the adaptive time-dependent density matrix renormalization group, we study the time evolution of density correlations of interacting spinless fermions on a one-dimensional lattice after a sudden change in the interaction strength. Over a broad range of model parameters, the correlation function exhibits a characteristic light-cone-like time evolution representative of a ballistic transport of information. Such behavior is observed both when quenching an insulator into the metallic region and also when quenching within the insulating region. However, when a metallic state beyond the quantum critical point is quenched deep into the insulating regime, no indication for ballistic transport is observed. Instead, stable domain walls in the density correlations emerge during the time evolution, consistent with the predictions of the Kibble-Zurek mechanism.

Web-Schrödinger is a program for the interactive solution of the time dependent two dimensional (2D) Schrödinger equation. The program itself runs on our server and can be used through the Internet with a simple Web browser (Internet Explorer, Mozilla, Opera was tested). Nothing is installed on the user's computer. The user can load, run, and modify ready-made example files, or prepare her/his own configuration(s), which can be saved on her/his own computer for later use. The program is available at: http://www.nanotechnology.hu/online/web-schroedinger/index.html

We study a three-mode Hamiltonian modelling a heteronuclear molecular Bose–Einstein condensate. Two modes are associated with two distinguishable atomic constituents, which can combine to form a molecule represented by the third mode. Beginning with a semi-classic alanalogue of the model, we conduct an analysis to determine the phase space fixed points of the system. Bifurcations of the fixed points naturally separate the coupling parameter space into different regions. Two distinct scenarios are found, dependent on whether the imbalance between the number operators for the atomic modes is zero or non-zero. This result suggests the ground-state properties of the model exhibit an unusual sensitivity on the atomic imbalance. We then test this finding for the quantum mechanical model. Specifically we use Bethe ansatz methods, ground-state expectation values, the character of the quantum dynamics, and ground-state wave function overlaps to clarify the nature of the groundstate phases. The character of the transition is smoothed due to quantum fluctuations, but we may nonetheless identify the emergence of a quantum phase boundary in the limit of zero atomic imbalance. DOI:10.1016/j.nuclphysb.2006.12.015

We investigate the non-equlibrium frequency dependent charge noise and the out of equilibrium ac-conductance of a quantum dot in the Kondo regime in the limit of large voltages as compared to the Kondo temperature. Using the real time, functional renormalization group (FRG) method, generalized to stationary situations we first calculate the renormalized, frequency dependent couplings and the current vertices by solving the renormalized group equations. Special care is put on the analysis of the two-frequency current vertex such that the current operator remains a conserved quantity along the renormalized group flow. In the high frequency limit, which is captured correctly by the second order perturbation theory, the non-equilibrium noise scales linearly with the frequency. For frequencies comparable to the voltage drop the second order perturbation theory fails, and the symmetric noise acquires a logarithmic singularity, while the ac-conductance develops a hump. To connect our calculations with experimental measurements, special emphasis is put on the emission/absorption noise spectrum.

We study the dynamics of a quench-prepared domain wall state released into a system whose unitary time evolution is dictated by the Hamiltonian of the Heisenberg spin-1/2 gapped antiferromagnetic chain. Using exact wavefunctions and their overlaps with the domain wall state allows us to describe the release dynamics to high accuracy, up to the long-time limit, for finite as well as infinite systems. The results for the infinite system allow us to rigorously prove that the system in the gapped regime ($\\Delta >1$) cannot thermalize in the strict sense.

In this talk we will introduce a new concept: the geometric quantum quench. As opposed to the usual quenches where a microscopic parameter of the Hamiltonian is varied abruptly, a geometric quench describes a situation where the size of the system is varied instantaneously (e.g. expansion of a quantum gas). For solvable models, the overlaps between states in the initial geometry and the eigenstates of the final larger system can be computed exactly using the Algebraic Bethe Ansatz. Taking as a playground both the 1d Bose gas and the XXZ spin chain, we will show how to use these overlaps to fully reconstruct the time-evolved wave function after the quench. In particular the long-time average of physical observables can be reached with great accuracy compared to ab-initio numerical techniques. We shall conclude on issues related to relaxation and thermalization in those particular quantum low-dimensional models.

We address the problem of how a quantum local interacting dissipative system evolves towards nonequilibrium stationary state. Applying the recently established method of real-time renormalization group (RTRG) we study the real-time evolution of observables after a sudden switching of a coupling to reservoirs with chemical potentials +V/2 and -V/2 in two basic models. In particular, we consider the anisotropic Kondo model (both antiferromagnetic and ferromagnetic) and asymmetric interacting resonant-level model (IRLM) which are the minimal models for the study of spin and charge fluctuations, respectively. We derive analytic expressions for all time scales and find that: 1) all observables (spin, current, dot population) decay with both relaxation and decoherence rates; 2) bias voltage V appears as a important energy scale for the dynamics setting the frequency of an oscillatory behavior; 3) the decay is not purely exponential but is rather accompanied by the power-law decay. The last result is of particular importance for applications in error correction schemes of quantum information processing.

We analyze the heat exchange between two many-particle quantum systems -- cold gases with a finite number of bosonic atoms trapped in separated optical lattices. The systems are initially prepared in Gibbs states, at different temperatures. Then they are brought into a thermal contact (no particle exchange between the systems is possible). We numerically analyze the statistics of heat exchange between the gases by the exact diagonalization of composite system Hamiltonian. In the limit of weak thermal coupling, we derive a general analytical prediction for the statistics of heat exchange between two subsystems represented by identical Hamiltonians.

We address the issue of the stability of thermal equilibrium of large quantum systems with respect to variations of the thermal contact between them. We study the Schrodinger time evolution of a free bosonic field in two coupled one dimensional cavities after a sudden change of the contact between the cavities. Though the coupling we consider is thermodynamically small, modifying it has a considerable impact on the two-point correlation functions of the system.

Supersolidity - the simultaneous appearance of Bose condensation and crystalline order in a degenerate system of bosons - is a long-sought and elusive phenomenon in condensed matter. Cold-atom realizations of a supersolid can be envisioned in optical lattices, in which spontaneous crystallization of atoms occurs in presence of finite-range or long-range interactions, or in the case of interactions mediated by a secondary atomic species. In this talk I will theoretically discuss how (quasi-)condensation can emerge dynamically in a mixture of two hardcore boson species with mass and number imbalance in a one-dimensional optical lattice. Starting from a "molecular crystal" of trimers (made of two heavy and one light particle) and suddenly changing the Hamiltonian of the system, we observe that (quasi-)condensation appears in both atomic species without disrupting the crystalline order imprinted in the system. An extensive study of the ground state phase diagram of this model shows that this supersolid state has no equilibrium counterpart. This suggests the intriguing possibility of engineering novel many-body states via a controlled collective quantum evolution in cold-atom systems.

Recent experiments with ultracold atomic gases have triggered a great deal of theoretical interest in some fundamental aspects of the non-equilibrium dynamics of strongly correlated quantum systems. In particular, they raised an intense discussion on the general relation between system integrability and thermalization in the long-time dynamics of such systems. We provide evidence that the presence or absence of thermal behavior after a quantum quench does not exclusively depend on the integrability of the model, but also on the considered observable. In particular, we investigate the dynamics of the one-dimensional quantum Ising model at zero temperature, as the transverse field strength is suddenly quenched. Even if this is a completely integrable system, the asymptotics of observables which are non-local with respect to the quasi-particle fermions diagonalizing the model in the continuum limit, such as the two-point correlation functions of the order parameter, display perfectly thermal behavior. On the other hand, this is definitely not the case for local ones, such as correlation functions of the transverse magnetization or the density of kinks.

We study the problem of an interaction quantum quench in the Hubbard model using both numerical and analytical techniques. Within Non Equilibrium Dynamical Mean Field Theory we compute the real-time dynamics starting from an interacting equilibrium density matrix and discuss the dependence of the relaxation on the nature of the initial state and on the strength of the quench.

We investigate the transport properties of cold bosonic atoms in a triple-well potential that consists of two large outer wells, which act as microscopic source and drain reservoirs, and a small inner well, which represents a quantum-dot-like scattering region. Such configurations can be realized by optical triple-well lattices generalizing the setup realized in the interaction blockade experiment by Cheinet et al. [Phys. Rev. Lett. 101, 090404 (2008)]. Bias and gate "voltages" are introduced in order, respectively, to tilt the triple-well configuration and to shift the energetic level of the inner well with respect to the outer ones. By means of exact diagonalization considering a total number of 6 atoms in the triple-well potential, we find diamond-like structures for the occurrence of single-atom transport in the parameter space spanned by the bias and gate voltages, in close analogy with the Coulomb blockade in electronic quantum dots. We demonstrate how one can infer the interaction energy in the central well from the distance between the diamonds, and discuss the possibility of realizing single-atom pumping across the quantum dot.

We investigate the collective modes of strongly correlated ultracold atoms in an optical lattice subjected to an additional harmonic confinement potential. In particular, we study whether the collective modes can be used as experimental probes for the characterization of (quantum) phase transitions.

We present an analytic theory of quantum interference and Anderson localization in the quantum kicked rotor (QKR). The behavior of the system is known to depend sensitively on the value of its effective Planck's constant $\\he$. We here show that for rational values of $\\he/(4\\pi)=p/q$, it bears similarity to a disordered metallic ring of circumference $q$ and threaded by an Aharonov-Bohm flux. Building on that correspondence, we obtain quantitative results for the time--dependent behavior of the QKR kinetic energy, $E(\\tilde t)$ (this is an observable which sensitively probes the system\'s localization properties). For values of $q$ smaller than the localization length $\\xi$, we obtain scaling $E(\\tilde t) \\sim \\Delta \\tilde t2$, where $\\Delta=2\\pi/q$ is the quasi--energy level spacing on the ring. This scaling is indicative of a long time dynamics that is neither localized nor diffusive. For larger values $q\\gg \\xi$, the functions $E(\\tilde t)\\to \\xi2$ saturates (up to exponentially small corrections $\\sim\\exp(-q/\\xi)$), thus reflecting essentially localized behavior.

Recent experiments of Calvo and coworkers (Nature 458, p.1150, 2009) have demonstrated Fano-like lineshapes in the I-V characteristics of single atom contacts in magnetic metals, cobalt, iron and nickel. These zero bias anomalies were attributed to Kondo effect due to the significantly modified magnetism of the low-coordinated atomic-scale junctions. We present a detailed statistical analysis of current-voltage characteristics of atomic-sized ferromagnetic contacts addressing the question to what extent the observed features can be described by Kondo effect or as an alternative by the decoherence of conductance fluctuations.

We analyze the equilibrium and nonequilibrium frequency-dependent spin noise and spin conductance of a quantum dot in the Kondo regime. The equilibrium spin noise is characterized by two universal functions that we determine perturbatively for large frequencies, and compute numerically for T=0 temperature. A dynamical spin accumulation is found for asymmetrical quantum dots in the Kondo regime. For temperatures well above the Kondo scale, a low-frequency anomaly appears in the spin current correlations below the Korringa relaxation rate.