Counting statistics of tunneling through a single molecule: effect of distortion and displacement of vibrational potential surface

We analyze the effects of a distortion of the nuclear potential of a molecular quantum dot (QD), as well as a shift of its equilibrium position, on nonequilibrium-vibration-assisted tunneling through the QD with a single level ($\epsilon_d$) coupled to the vibrational mode. For this purpose, we derive an explicit analytical expression for the Franck-Condon (FC) factor for a displaced-distorted oscillator surface of the molecule and establish rate equations in the joint electron-phonon representation to examine the current-voltage characteristics and zero-frequency shot noise, and skewness as well. Our numerical analyses shows that the distortion has two important effects. The first one is that it breaks the symmetry between the excitation spectra of the charge states, leading to asymmetric tunneling properties with respect to $\epsilon_d>0$ and $\epsilon_d<0$. Secondly, distortion (frequency change of the oscillator) significantly changes the voltage-activated cascaded transition mechanism, and consequently gives rise to a different nonequilibrium vibrational distribution from that of the case without distortion. Taken in conjunction with strongly modified FC factors due to distortion, this results in some new transport features: the appearance of strong NDC even for a single-level QD with symmetric tunnel couplings; a giant Fano factor even for a molecule with an extremely weak electron-phonon interaction; and enhanced skewness that can have a large negative value under certain conditions.Comment: 29 pages, 11 figures, published versio

Excited-state Forces within a First-principles Green's Function Formalism

We present a new first-principles formalism for calculating forces for optically excited electronic states using the interacting Green's function approach with the GW-Bethe Salpeter Equation method. This advance allows for efficient computation of gradients of the excited-state Born-Oppenheimer energy, allowing for the study of relaxation, molecular dynamics, and photoluminescence of excited states. The approach is tested on photoexcited carbon dioxide and ammonia molecules, and the calculations accurately describe the excitation energies and photoinduced structural deformations.Comment: 2 figures and 2 table

Quantum resonance, Anderson localisation and selective manipulations in molecular mixtures by ultrashort laser pulses

We demonstrate that the current laser technology used for field-free molecular alignment via a cascade of Raman rotational transitions allows for observing long-discussed non-linear quantum phenomena in the dynamics of the periodically kicked rotor. This includes the scaling of the absorbed energy near the conditions of quantum resonance and Anderson-like localisation in the angular momentum. Based on these findings, we suggest a novel approach to tunable selective rotational excitation and alignment in a molecular mixture, using trains of short laser pulses. We demonstrate the efficiency of this approach by applying it to a mixture of two nitrogen isotopologues (14N2 and 15N2), and show that strong selectivity is possible even at room temperature

Non-adiabatic Effects in the Dissociation of Oxygen Molecules at the Al(111) Surface

The measured low initial sticking probability of oxygen molecules at the Al(111) surface that had puzzled the field for many years was recently explained in a non-adiabatic picture invoking spin-selection rules [J. Behler et al., Phys. Rev. Lett. 94, 036104 (2005)]. These selection rules tend to conserve the initial spin-triplet character of the free O2 molecule during the molecule's approach to the surface. A new locally-constrained density-functional theory approach gave access to the corresponding potential-energy surface (PES) seen by such an impinging spin-triplet molecule and indicated barriers to dissociation which reduce the sticking probability. Here, we further substantiate this non-adiabatic picture by providing a detailed account of the employed approach. Building on the previous work, we focus in particular on inaccuracies in present-day exchange-correlation functionals. Our analysis shows that small quantitative differences in the spin-triplet constrained PES obtained with different gradient-corrected functionals have a noticeable effect on the lowest kinetic energy part of the resulting sticking curve.Comment: 17 pages including 11 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Optimal Topological Test for Degeneracies of Real Hamiltonians

We consider adiabatic transport of eigenstates of real Hamiltonians around loops in parameter space. It is demonstrated that loops that map to nontrivial loops in the space of eigenbases must encircle degeneracies. Examples from Jahn-Teller theory are presented to illustrate the test. We show furthermore that the proposed test is optimal.Comment: Minor corrections, accepted in Phys. Rev. Let

Predicting and verifying transition strengths from weakly bound molecules

We investigated transition strengths from ultracold weakly bound 41K87Rb molecules produced via the photoassociation of laser-cooled atoms. An accurate potential energy curve of the excited state (3)1Sigma+ was constructed by carrying out direct potential fit analysis of rotational spectra obtained via depletion spectroscopy. Vibrational energies and rotational constants extracted from the depletion spectra of v'=41-50 levels were combined with the results of the previous spectroscopic study, and they were used for modifying an ab initio potential. An accuracy of 0.14% in vibrational level spacing and 0.3% in rotational constants was sufficient to predict the large observed variation in transition strengths among the vibrational levels. Our results show that transition strengths from weakly bound molecules are a good measure of the accuracy of an excited state potential.Comment: 7 pages, 7 figure

Exact Coupling Coefficient Distribution in the Doorway Mechanism

In many--body and other systems, the physics situation often allows one to interpret certain, distinct states by means of a simple picture. In this interpretation, the distinct states are not eigenstates of the full Hamiltonian. Hence, there is an interaction which makes the distinct states act as doorways into background states which are modeled statistically. The crucial quantities are the overlaps between the eigenstates of the full Hamiltonian and the doorway states, that is, the coupling coefficients occuring in the expansion of true eigenstates in the simple model basis. Recently, the distribution of the maximum coupling coefficients was introduced as a new, highly sensitive statistical observable. In the particularly important regime of weak interactions, this distribution is very well approximated by the fidelity distribution, defined as the distribution of the overlap between the doorway states with interaction and without interaction. Using a random matrix model, we calculate the latter distribution exactly for regular and chaotic background states in the cases of preserved and fully broken time--reversal invariance. We also perform numerical simulations and find excellent agreement with our analytical results.Comment: 22 pages, 4 figure

A geometrical approach to the dynamics of spinor condensates I: Hydrodynamics

In this work, we derive the equations of motion governing the hydrodynamics of spin-F spinor condensates. We pursue a description based on standard physical variables (total density and superfluid velocity), alongside 2F `spin-nodes': unit vectors that describe the spin F state, and also exhibit the point-group symmetry of a spinor condensate's mean-field ground state. The hydrodynamic equations of motion consist of a mass continuity equation, 2F Landau-Lifshitz equations for the spin-nodes, and a modified Euler equation. In particular, we provide a generalization of the Mermin-Ho relation to spin one, and find an analytic solution for the skyrmion texture in the incompressible regime of a spin-half condensate. These results exhibit a beautiful geometrical structure that underlies the dynamics of spinor condensates.Comment: 12 pages. First paper in two-part serie