Causal vs. Noncausal Description of Nonlinear Wave Mixing; Resolving the Damping-Sign Controversy

Frequency-domain nonlinear wave mixing processes may be described either using response functions whereby the signal is generated after all interactions with the incoming fields, or in terms of scattering amplitudes where all fields are treated symetrically with no specific time ordering. Closed Green's function expressions derived for the two types of signals have different analytical properties. The recent controversy regarding the sign of radiative damping in the linear (Kramers Heisenberg) formula is put in a broader context

Zero-Range Processes with Multiple Condensates: Statics and Dynamics

The steady-state distributions and dynamical behaviour of Zero Range Processes with hopping rates which are non-monotonic functions of the site occupation are studied. We consider two classes of non-monotonic hopping rates. The first results in a condensed phase containing a large (but subextensive) number of mesocondensates each containing a subextensive number of particles. The second results in a condensed phase containing a finite number of extensive condensates. We study the scaling behaviour of the peak in the distribution function corresponding to the condensates in both cases. In studying the dynamics of the condensate we identify two timescales: one for creation, the other for evaporation of condensates at a given site. The scaling behaviour of these timescales is studied within the Arrhenius law approach and by numerical simulations.Comment: 25 pages, 18 figure

Photon Statistics for Single Molecule Non-Linear Spectroscopy

We consider the theory of the non-linear spectroscopy for a single molecule undergoing stochastic dynamics and interacting with a sequence of two laser pulses. General expressions for photon counting statistics are obtained, and an exact solution to the problem of the Kubo-Anderson process is found. In the limit of impulsive pulses the information on the photon statistics is contained in the molecule's dipole correlation function. The selective limit where temporal resolution is maintained, the semi-classical approximation and the fast modulation limit exhibit general behaviors of this new type of spectroscopy. We show how the design of the external field leads to rich insights on dynamics of individual molecules which are different than those found for an ensemble

Coarsening of a Class of Driven Striped Structures

The coarsening process in a class of driven systems exhibiting striped structures is studied. The dynamics is governed by the motion of the driven interfaces between the stripes. When two interfaces meet they coalesce thus giving rise to a coarsening process in which l(t), the average width of a stripe, grows with time. This is a generalization of the reaction-diffusion process A + A -> A to the case of extended coalescing objects, namely, the interfaces. Scaling arguments which relate the coarsening process to the evolution of a single driven interface are given, yielding growth laws for l(t), for both short and long time. We introduce a simple microscopic model for this process. Numerical simulations of the model confirm the scaling picture and growth laws. The results are compared to the case where the stripes are not driven and different growth laws arise

X-Ray sum frequency generation; direct imaging of ultrafast electron dynamics

X-ray diffraction from molecules in the ground state produces an image of their charge density, and time-resolved X-ray diffraction can thus monitor the motion of the nuclei. However, the density change of excited valence electrons upon optical excitation can barely be monitored with regular diffraction techniques due to the overwhelming background contribution of the core electrons. We present a nonlinear X-ray technique made possible by novel free electron laser sources, which provides a spatial electron density image of valence electron excitations. The technique, sum frequency generation carried out with a visible pump and a broadband X-ray diffraction pulse, yields snapshots of the transition charge densities, which represent the electron density variations upon optical excitation. The technique is illustrated by ab initio simulations of transition charge density imaging for the optically induced electronic dynamics in a donor/acceptor substituted stilbene

Multiple Core-Hole Coherence in X-Ray Four-Wave-Mixing Spectroscopies

Correlation-function expressions are derived for the coherent nonlinear response of molecules to three resonant ultrafast pulses in the x-ray regime. The ability to create two-core-hole states with controlled attosecond timing in four-wave-mixing and pump probe techniques should open up new windows into the response of valence electrons, which are not available from incoherent x-ray Raman and fluorescence techniques. Closed expressions for the necessary four-point correlation functions are derived for the electron-boson model by using the second order cumulant expansion to describe the fluctuating potentials. The information obtained from multidimensional nonlinear techniques could be used to test and refine this model, and establish an anharmonic oscillator picture for electronic excitations

Slow Coarsening in a Class of Driven Systems

The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher dimensions. In particular we study a system of three types of particles that diffuse under local conserving dynamics in two dimensions. Arguments and numerical studies are presented indicating that the coarsening process in any number of dimensions is logarithmically slow in time. A key feature of this behavior is that the interfaces separating the various growing domains are smooth (well approximated by a Fermi function). This implies that the coarsening mechanism in one dimension is readily extendible to higher dimensions.Comment: submitted to EPJB, 13 page

Monitoring Nonadiabatic Electron-Nuclear Dynamics in Molecules by Attosecond Streaking of Photoelectrons

Streaking of photoelectrons has long been used for the temporal characterization of attosecond extreme ultraviolet pulses. When the time-resolved photoelectrons originate from a coherent superposition of electronic states, they carry an additional phase information, which can be retrieved by the streaking technique. In this contribution we extend the streaking formalism to include coupled electron and nuclear dynamics in molecules as well as initial coherences and demonstrate how it offers a novel tool to monitor non-adiabatic dynamics as it occurs in the vicinity of conical intersections and avoided crossings. Streaking can enhance the time resolution and provide direct signatures of electronic coherences, which affect many primary photochemical and biological events

Many-body Green's function approach to attosecond nonlinear X-ray spectroscopy

Closed expressions are derived for resonant multidimensional X-ray spectroscopy using the quasiparticle nonlinear exciton representation of optical response. This formalism is applied to predict coherent four wave mixing signals which probe single and two core-hole states. Nonlinear X-ray signals are compactly expressed in terms of one- and two- particle Green's functions which can be obtained from the solution of Hedin-like equations at the $GW$ level.Comment: 10 pages and 3 figures (To appear in Physical Review B