Fullerene graphs have exponentially many perfect matchings

A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces. We show that fullerene graphs have exponentially many perfect matchings.Comment: 7 pages, 3 figure

Analytic pulse design for selective population transfer in many-level quantum systems: maximizing amplitude of population oscillations

State selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules or quantum dots is a the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision metrology and quantum computing. Rabi oscillations are one of the simplest, yet potentially quite useful mechanisms for achieving such manipulation. Rabi theory establishes that in the two-level systems resonant drive leads to the periodic and complete population oscillations between the two system levels. In this paper an analytic optimization algorithm for producing Rabi-like oscillations in the general discrete many-level quantum systems is presented.Comment: Published in Phys.Rev.A. This is the final published versio

Ultrafast electronic response of Ag(111) and Cu(111) surfaces: From early excitonic transients to saturated image potential

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY).We investigate the evolution of attosecond to femtosecond screening and emergent potentials that govern the dynamics and energetics of electrons and holes excited in the various stages of multiphoton photoemission processes and control the photoelectron yield in recently reported experiments [X. Cui, C. Wang, A. Argondizzo, S. Garrett-Roe, B. Gumhalter, and H. Petek, Nat. Phys. 10, 505 (2014)1745-247310.1038/nphys2981]. The study is focused on the dynamical screening of holes created in preexistent quasi-two-dimensional Shockley state bands on Ag(111) and Cu(111) surfaces and of electrons excited to the intermediate and emerging screened states. Using the formalism of self-consistent electronic response, we analyze first the effects of screening on the dynamics of photoexcited electrons and holes and then of the Coulomb correlated photoexcited pair. Special attention is paid to the correlated primary electron-hole states, which commence as transient surface excitons and develop in the course of screening into uncorrelated electrons and holes propagating in the image potential and surface state bands, respectively. The obtained results enable to establish a consistent picture of transient electron dynamics at Ag(111) and Cu(111) surfaces that are becoming accessible by the time-, energy-, and momentum-resolved pump-probe multiphoton photoelectron spectroscopies.V.M.S. acknowledges partial support from the Basque Departamento de Educacion, UPV/EHU (Grant No. IT-756-13) and the Spanish Ministry od Economy and Competitiveness MINECO (Grant No. FIS2013-48286-C2-1-P). N.D. acknowledges the support of the Unity Through Knowledge Fund (UKF B1). H.P. was supported by the Division of Chemical Sciences, Geosciences and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy through Grant DE-FG02-09ER 16056.Peer Reviewe

Tailoring laser pulses with spectral and fluence constraints using optimal control theory

Within the framework of optimal control theory we develop a simple iterative scheme to determine optimal laser pulses with spectral and fluence constraints. The algorithm is applied to a one-dimensional asymmetric double well where the control target is to transfer a particle from the ground state, located in the left well, to the first excited state, located in the right well. Extremely high occupations of the first excited state are obtained for a variety of spectral and/or energetic constraints. Even for the extreme case where no resonance frequency is allowed in the pulse the algorithm achieves an occupation of almost 100%

Optimal use of time dependent probability density data to extract potential energy surfaces

A novel algorithm was recently presented to utilize emerging time dependent probability density data to extract molecular potential energy surfaces. This paper builds on the previous work and seeks to enhance the capabilities of the extraction algorithm: An improved method of removing the generally ill-posed nature of the inverse problem is introduced via an extended Tikhonov regularization and methods for choosing the optimal regularization parameters are discussed. Several ways to incorporate multiple data sets are investigated, including the means to optimally combine data from many experiments exploring different portions of the potential. Results are presented on the stability of the inversion procedure, including the optimal combination scheme, under the influence of data noise. The method is applied to the simulated inversion of a double well system.Comment: 34 pages, 5 figures, LaTeX with REVTeX and Graphicx-Package; submitted to PhysRevA; several descriptions and explanations extended in Sec. I

Acetylacetone photodynamics at a seeded freeelectron laser

The first steps in photochemical processes, such as photosynthesis or animal vision, involve changes in electronic and geometric structure on extremely short time scales. Time-resolved photoelectron spectroscopy is a natural way to measure such changes, but has been hindered hitherto by limitations of available pulsed light sources in the vacuum-ultraviolet and soft Xray spectral region, which have insufficient resolution in time and energy simultaneously. The unique combination of intensity, energy resolution, and femtosecond pulse duration of the FERMI-seeded free-electron laser can now provide exceptionally detailed information on photoexcitation–deexcitation and fragmentation in pump-probe experiments on the 50- femtosecond time scale. For the prototypical system acetylacetone we report here electron spectra measured as a function of time delay with enough spectral and time resolution to follow several photoexcited species through well-characterized individual steps, interpreted using state-of-the-art static and dynamics calculations. These results open the way for investigations of photochemical processes in unprecedented detail

Ultrafast electron dynamics in pump-probe spectroscopies of surfaces: from transient excitonic to quasi-stationary polaronic states

Resumen del trabajo presentado al 7th Symposium on Ultrafast Surface Dynamics (USD), celebrado en Brijuni Islands (Croatia) del 22 al 26 de agosto de 2010.Peer reviewe

Laser control in a bifurcating region

We present a complete analysis of the laser control of a model molecular system using both optimal control theory and adiabatic techniques. This molecule has a particular potential energy surface with a bifurcating region connecting three potential wells which allows a variety of processes such as isomerization, tunneling, or implementation of quantum gates on one or two qubits. The parameters of the model have been chosen so as to reproduce the main features of H3CO which is a molecule benchmark for such dynamics. We show the feasibility of different processes and we investigate their robustness against variations of laser field. We discuss the conditions under which each method of control gives the best results. We also point out the relation between optimal control theory and local control