Dr. Maximilian Rinck

We consider the tunneling properties of a single fermionic impurity immersed in a Bose-Einstein condensate in a double-well potential. For strong boson-fermion interaction, we show the existence of a tunnel resonance where a large number of bosons and the fermion tunnel simultaneously. We give analytical expressions for the lineshape of the resonance using degenerate Brillouin-Wigner theory. We finally compute the time-dependent dynamics of the mixture. Using the fermionic tunnel resonances as beam splitter for wave-functions, we construct a Mach-Zehnder interferometer that allows complete population transfer from one well to the other by tilting the double-well potential and only taking into account the fermion's tunnel properties.

Rate equations are a common tool to describe the transport properties of weakly coupled single-molecule junctions. Here, we study the physics of the Anderson–Holstein model at a single vibronic resonance. We derive conditions on the Franck–Condon factors that the resonance increases or decreases the stationary current thus causing negative differential conductance. The role of backscattering of charge at vibronic resonances is also investigated. In strongly asymmetrically coupled devices backscattering causes the resonance to split into two. In symmetrically coupled devices, the Fano factor shows non-monotonicities, which are related to correlations of forward and backward scattering of charge.

We consider electronic transport through a weakly coupled single-molecule junction here the molecule has a degenerate electronic spectrum being linearly coupled to an internal vibrational mode. As for such molecules, a rate-equation description in the weak-coupling limit is not possible, we investigate the interplay of the coherent physics caused by the off-diagonal elements of the reduced density matrix with the molecular vibrations. We identify two distinct molecular models and provide an in-depth discussion of their properties on the Hamiltonian level, their transport characteristics for weak- and strong electron--phonon coupling and different parameter regimes. We finally extend our reasoning to the cases, when the orbital degeneracy is slightly broken and the leads have more than one electronic mode.

Geometric symmetries cause orbital degeneracies in a molecule's spectrum. In a single-molecule junction, these degeneracies are lifted by various symmetry-breaking effects. We study quantum transport through such nanostructures with an almost degenerate spectrum. We show that the master equation for the reduced density matrix must be derived within the singular-coupling limit as opposed to the conventional weak-coupling limit. This results in strong signatures of the density matrix's off-diagonal elements in the transport characteristics.

Understanding the influence of vibrational motion of the atoms on electronic transitions in molecules constitutes a cornerstone of quantum physics, as epitomized by the Franck– Condon principle of spectroscopy. Recent advances in building molecular-electronics devices and nanoelectromechanical systems open a new arena for studying the interaction between mechanical and electronic degrees of freedom in transport at the single-molecule level. The tunnelling of electrons through molecules or suspended quantum dots has been shown to excite vibrational modes, or vibrons. Beyond this effect, theory predicts that strong electron–vibron coupling strongly suppresses the current flow at low biases, a collective behaviour known as Franck–Condon blockade. Here, we show measurements on quantum dots formed in suspended single-wall carbon nanotubes revealing a remarkably large electron–vibron coupling that, owing to the high quality and unprecedented tunability of our samples, allow a quantitative analysis of vibron-mediated electronic transport in the regime of strong electron–vibron coupling. This enables us to unambiguously demonstrate the Franck–Condon blockade in a suspended nanostructure. The large observed electron;ndash&vibron coupling could ultimately be a key ingredient for the detection of quantized mechanical motion. It also emphasizes the unique potential for nanoelectromechanical device applications based on suspended graphene sheets and carbon nanotubes.

The vibrational modes of Jahn-Teller molecules are affected by a Berry phase that is associated with a conical intersection of the adiabatic potentials. We investigate theoretically the effect of this Berry phase on the electronic transport properties of a single Exe Jahn-Teller molecule when the tunneling electrons continually switch the molecule between a symmetric and a Jahn-Teller distorted charge state. We find that the Berry phase, in conjunction with a spectral trapping mechanism, leads to a current-blockade even in regions outside the Coulomb blockade. The blockade is strongly asymmetric in the gate voltage and induces pronounced negative differential conductance.

Constitutive equations for the long-wavelength behaviour of the orientational dynamics of a super-cooled liquid are derived using a projection-operator technique and resulting expressions for light-scattering spectra are formulated. We thus extend recent studies for axially symmetric molecules to the general case of arbitrarily shaped rigid molecules. The second part of the discussion considers hydrodynamic energy-fluctuations and thus arrives at expressions for light-scattering spectra which also include a Rayleigh-line. The role of the memory-kernels in the theory is treated in detail. In particular, the derivation of a theory that formally resembles earlier approaches to the problem is presented using a mathematically rigorous description of the Laplace-transforms of correlation-functions.