Inverse mean field theories.

In this work we discuss the extraction of mean field single particle Hamiltonians from a many body wave function of a fermionic system. While we primarily discuss lattice models we also look at neon in an augccpvdz basis set as an example. Our approach allows us to discuss the result of a many particle wave function in terms of a non-interacting description. In contrast to density functional theory approaches on the lattice this approach allows the extraction of appropriate kinetic terms. In result the extracted mean field theories are closer to the physics of the problem under investigation. Therefore, the extracted mean field Hamiltonians may provide an improved starting point for perturbative approaches. In addition, the technique can be used to decide whether a density matrix renormalization group calculation for interacting fermions has converged to the true ground state.

Signature of the Dirac cone in the properties of linear oligoacenes.

Organic electronics offers prospects of functionality for science, industry and medicine that are new as compared with silicon technology and available at a very low material cost. Among the plethora of organic molecules available for materials design, polymers and oligomers are very promising, for example, because of their mechanical flexibility. They consist of repeated basic units, such as benzene rings, and the number of these units N determines their excitation gap, a property that is often used in proposals of organic photovoltaics. Here, we show that contrary to a widely held belief the magnitudes of excitation gaps do not always decay monotonously with N, but can oscillate due to the presence of a 'Dirac cone' in the band structure. With an eye on the more fundamental question how a molecular wire becomes metallic with increasing length, our research suggests that the process can exhibit incommensurate oscillations.

Correlated photons in one-dimensional waveguides.

We study two-photon transport in a one-dimensional waveguide with a side-coupled two-level system. Depending on the momentum of the incoming photons, we find that the nature of the scattering process changes considerably. We further show that bunching behavior can be found in the scattered light. As a result, we find that the waveguide dispersion has a strong influence on the photon correlations. By modifying the momentum of the pulse, the nature of the correlations can therefore be altered or optimized.

The dark side of DFT based transport calculations.

We compare the conductance of an interacting ring with six lattice sites threaded by flux π in a two terminal setup with the conductance of the corresponding Kohn-Sham particles. Based on symmetry considerations we can show that even within (lattice) Density Functional Theory employing the exact Kohn-Sham exchange-correlation functional the conductance of the Kohn-Sham particles is exactly zero, while the conductance of the physical system is close to the unitary limit. We provide a clear demonstration that the linear conductance is not given by the conductance of the Kohn-Sham particles. We show that this fundamental problem might be solved by extending the standard DFT scheme.

Strongly coupled slow-light polaritons in one-dimensional disordered localized states.

Cavity quantum electrodynamics advances the coherent control of a single quantum emitter with a quantized radiation field mode, typically piecewise engineered for the highest finesse and confinement in the cavity field. This enables the possibility of strong coupling for chip-scale quantum processing, but till now is limited to few research groups that can achieve the precision and deterministic requirements for these polariton states. Here we observe for the first time coherent polariton states of strong coupled single quantum dot excitons in inherently disordered one-dimensional localized modes in slow-light photonic crystals. Large vacuum Rabi splittings up to 311 µeV are observed, one of the largest avoided crossings in the solid-state. Our tight-binding models with quantum impurities detail these strong localized polaritons, spanning different disorder strengths, complementary to model-extracted pure dephasing and incoherent pumping rates. Such disorder-induced slow-light polaritons provide a platform towards coherent control, collective interactions, and quantum information processing.

Exact time-dependent density functional theory for impurity models.

We employ the density matrix renormalization group to construct the exact time-dependent exchange-correlation potential for an impurity model with an applied transport voltage. Even for short-ranged interaction we find an infinitely long-ranged exchange-correlation potential which is built up instantly after switching on the voltage. Our result demonstrates the fundamental difficulties of transport calculations based on time-dependent density functional theory. While formally the approach works, important information can be missing in the ground-state functionals and may be hidden in the usually unknown non-equilibrium functionals.

Full counting statistics in the self-dual interacting resonant level model.

We present a general technique to obtain the zero temperature cumulant generating function of the full counting statistics of charge transfer in interacting impurity models out of equilibrium from time-dependent simulations on a lattice. We demonstrate the technique with application to the self-dual interacting resonant level model, where very good agreement between numerical simulations using the density matrix renormalization group and those obtained analytically from the thermodynamic Bethe ansatz is found. We show from the exact form of counting statistics that the quasiparticles involved in transport carry charge 2e in the low bias regime and e/2 in the high bias regime.

Few-photon transport in low-dimensional systems: interaction-induced radiation trapping.

We present a detailed analysis of the dynamics of photon transport in waveguiding systems in the presence of a two-level system. In these systems, quantum interference effects generate a strong effective optical nonlinearity on the few-photon level. We clarify the relevant physical mechanisms through an appropriate quantum many-body approach. Based on this, we demonstrate that a single-particle photon-atom bound state with an energy outside the band can be excited via multiparticle scattering processes. We further show that these trapping effects are robust and, therefore, will be useful for the control of photon entanglement in solid-state based quantum-optical systems.

Persistent currents in one dimension: the counterpart of Leggett's theorem.

We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external potentials. Those bounds are the counterparts of upper bounds derived by Leggett. Rings with odd (even) numbers of polarized electrons are always diamagnetic (paramagnetic). We show that unpolarized electrons with N being a multiple of four exhibit either paramagnetic behavior or a superconductorlike current-phase relation.

Exact ground state density-functional theory for impurity models coupled to external reservoirs and transport calculations.

A method is presented employing the density matrix renormalization group to construct exact ground state (GS) exchange correlation functionals for models of correlated electrons coupled to leads. We apply it to show that conductance calculations with Kohn-Sham GS density-functional theory can yield quantitative results in the Coulomb blockade regime. Our study is relevant for "molecular electronics" since it strongly suggests that the well documented discrepancies between theoretical and experimental transport coefficients originate (mainly) from approximations in GS functionals.

Commensurability effects for fermionic atoms trapped in 1D optical lattices.

Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control the amplitude of the atomic density waves in the central region of the trap.