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We present results on ultrafast gas electron diffraction (UGED) experiments with femtosecond resolution using the MeV electron gun at SLAC National Accelerator Laboratory. UGED is a promising method to investigate molecular dynamics in the gas phase because electron pulses can probe the structure with a high spatial resolution. Until recently, however, it was not possible for UGED to reach the relevant timescale for the motion of the nuclei during a molecular reaction. Using MeV electron pulses has allowed us to overcome the main challenges in reaching femtosecond resolution, namely delivering short electron pulses on a gas target, overcoming the effect of velocity mismatch between pump laser pulses and the probe electron pulses, and maintaining a low timing jitter. At electron kinetic energies above 3 MeV, the velocity mismatch between laser and electron pulses becomes negligible. The relativistic electrons are also less susceptible to temporal broadening due to the Coulomb force. One of the challenges of diffraction with relativistic electrons is that the small de Broglie wavelength results in very small diffraction angles. In this paper we describe the new setup and its characterization, including capturing static diffraction patterns of molecules in the gas phase, finding time-zero with sub-picosecond accuracy and first time-resolved diffraction experiments. The new device can achieve a temporal resolution of 100 fs root-mean-square, and sub-angstrom spatial resolution. The collimation of the beam is sufficient to measure the diffraction pattern, and the transverse coherence is on the order of 2 nm. Currently, the temporal resolution is limited both by the pulse duration of the electron pulse on target and by the timing jitter, while the spatial resolution is limited by the average electron beam current and the signal-to-noise ratio of the detection system. We also discuss plans for improving both the temporal resolution and the spatial resolution.
In the first part of my work I have investigated the ageing properties of the first passage time distributions in a one-dimensional subdiffusive continuous time random walk with power law distributed waiting times of the form $\psi(\tau) \sim \tau^{-1-\alpha}$ with $0<\alpha<1$ and $1<\alpha<2$. The age or ageing time $t_a$ is the time span from the start of the stochastic process to the start of the observation of this process (at $t=0$). I have calculated the results for a single target and two targets, also including the biased case, where the walker is driven towards the boundary by a constant force. I have furthermore refined the previously derived results for the non-ageing case and investigated the changes that occur when the walk is performed in a discrete quenched energy landscape, where the waiting times are fixed for every site. The results include the exact Laplace space densities and infinite (converging) series as exact results in the time space. The main results are the dominating long time power law behavior regimes, which depend on the ageing time. For the case of unbiased subdiffusion ($\alpha < 1$) in the presence of one target, I find three different dominant terms for ranges of $t$ separated by $t_a$ and another crossover time $t^{\star}$, which depends on $t_a$ as well as on the anomalous exponent $\alpha$ and the anomalous diffusion coefficient $K_{\alpha}$. In all three regimes ($t \ll t_a$, $t_a \ll t \ll t^{\star}$, $t \gg t^{\star}$) one finds power law decay with exponents depending on $\alpha$. The middle regime only exists for $t_a \ll t^{\star}$. The dominant terms in the first two regimes (ageing regimes) come from the probability distribution of the forward waiting time, the time one has to wait for the stochastic process to make the first step during the observation. When the observation time is larger than the second crossover time $t^{\star}$, the first passage time density does not show ageing and the non-ageing first passage time dominates. The power law exponents in the respective regimes are $-\alpha$ for strong ageing, $-1-\alpha$ in the intermediate regime, and $-1-\alpha/2$ in the final non-ageing regime. A similar split into three regimes can be found for $1<\alpha<2$, only with a different second crossover time $t^*$. In this regime the diffusion is normal but also age-dependent. For the diffusion in quenched energy landscapes one cannot detect ageing. The first passage time density shows a quenched power law $^\sim t^{-(1+2\alpha)/(1+\alpha)}$. For diffusion between two target sites and the biased diffusion towards a target only two scaling regimes emerge, separated by the ageing time. In the ageing case $t \ll t_a$ the forward waiting time is again dominant with power law exponent $-\alpha$, while the non-ageing power law $-1-\alpha$ is found for all times $t \gg t_a$. An intermediate regime does not exist. The bias and the confinement have similar effects on the first passage time density. For quenched diffusion, the biased case is interesting, as the bias reduces correlations due to revisiting of the same waiting time. As a result, CTRW like behavior is observed, including ageing. Extensive computer simulations support my findings.
The second part of my research was done on the subject of ageing Scher-Montroll transport, which is in parts closely related to the first passage densities. It explains the electrical current in an amorphous material. I have investigated the effect of the width of a given initial distribution of charge carriers on the transport coefficients as well as the ageing effect on the emerging power law regimes and a constant initial regime. While a spread out initial distribution has only little impact on the Scher-Montroll current, ageing alters the behavior drastically. Instead of the two classical power laws one finds four current regimes, up to three of which can appear in a single experiment. The dominant power laws differ for $t \ll t_a, t_c$, $t_a \ll t \ll t_c$, $t_c \ll t \ll t_a$, and $t \gg t_a,t_c$. Here, $t_c$ is the crossover time of the non-aged Scher-Montroll current. For strongly aged systems one can observe a constant current in the first regime while the others are dominated by decaying power laws with exponents $\alpha -1$, $-\alpha$, and $-1-\alpha$. The ageing regimes are the 1st and 3rd one, while the classical regimes are the 2nd and the 4th. I have verified the theory using numerical integration of the exact integrals and applied the new results to experimental data.
In the third part I considered a single file of subdiffusing particles in an energy landscape. Every occupied site of the landscape acts as a boundary, from which a particle is immediately reflected to its previous site, if it tries to jump there. I have analysed the effects single-file diffusion a quenched landscape compared to an annealed landscape and I have related these results to the number of steps and related quantities. The diffusion changes from ultraslow logarithmic diffusion in the annealed or CTRW case to subdiffusion with an anomalous exponent $\alpha/(1+\alpha)$ in the quenched landscape. The behavior is caused by the forward waiting time, which changes drastically from the quenched to the annealed case. Single-file effects in the quenched landscape are even more complicated to consider in the ensemble average, since the diffusion in individual landscapes shows extremely diverse behavior. Extensive simulations support my theoretical arguments, which consider mainly the long time evolution of the mean square displacement of a bulk particle.
Interplay of coupling and common noise at the transition to synchrony in oscillator populations
(2016)
There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes.
In this thesis we use integral-field spectroscopy to detect and understand of Lyman α (Lyα) emission from high-redshift galaxies.
Intrinsically the Lyα emission at λ = 1216 Å is the strongest recombination line from galaxies. It arises from the 2p → 1s transition in hydrogen. In star-forming galaxies the line is powered by ionisation of the interstellar gas by hot O- and B- stars. Galaxies with star-formation rates of 1 - 10 Msol/year are expected to have Lyα luminosities of 42 dex - 43 dex (erg/s), corresponding to fluxes ~ -17 dex - -18 dex (erg/s/cm²) at redshifts z~3, where Lyα is easily accessible with ground-based telescopes. However, star-forming galaxies do not show these expected Lyα fluxes. Primarily this is a consequence of the high-absorption cross-section of neutral hydrogen for Lyα photons σ ~ -14 dex (cm²). Therefore, in typical interstellar environments Lyα photons have to undergo a complex radiative transfer. The exact conditions under which Lyα photons can escape a galaxy are poorly understood.
Here we present results from three observational projects. In Chapter 2, we show integral field spectroscopic observations of 14 nearby star-forming galaxies in Balmer α radiation (Hα, λ = 6562.8 Å). These observations were obtained with the Potsdam Multi Aperture Spectrophotometer at the Calar-Alto 3.5m Telescope}. Hα directly traces the intrinsic Lyα radiation field. We present Hα velocity fields and velocity dispersion maps spatially registered onto Hubble Space Telescope Lyα and Hα images. From our observations, we conjecture a causal connection between spatially resolved Hα kinematics and Lyα photometry for individual galaxies. Statistically, we find that dispersion-dominated galaxies are more likely to emit Lyα photons than galaxies where ordered gas-motions dominate. This result indicates that turbulence in actively star-forming systems favours an escape of Lyα radiation.
Not only massive stars can power Lyα radiation, but also non-thermal emission from an accreting super-massive black hole in the galaxy centre. If a galaxy harbours such an active galactic nucleus, the rate of hydrogen-ionising photons can be more than 1000 times higher than that of a typical star-forming galaxy. This radiation can potentially ionise large regions well outside the main stellar body of galaxies. Therefore, it is expected that the neutral hydrogen from these circum-galactic regions shines fluorescently in Lyα. Circum-galactic gas plays a crucial role in galaxy formation. It may act as a reservoir for fuelling star formation, and it is also subject to feedback processes that expel galactic material. If Lyα emission from this circum-galactic medium (CGM) was detected, these important processes could be studied in-situ around high-z galaxies. In Chapter 3, we show observations of five radio-quiet quasars with PMAS to search for possible extended CGM emission in the Lyα line. However, in four of the five objects, we find no significant traces of this emission. In the fifth object, there is evidence for a weak and spatially quite compact Lyα excess at several kpc outside the nucleus. The faintness of these structures is consistent with the idea that radio-quiet quasars typically reside in dark matter haloes of modest masses. While we were not able to detect Lyα CGM emission, our upper limits provide constraints for the new generation of IFS instruments at 8--10m class telescopes.
The Multi Unit Spectroscopic Explorer (MUSE) at ESOs Very Large Telescopeis such an unique instrument. One of the main motivating drivers in its construction was the use as a survey instrument for Lyα emitting galaxies at high-z. Currently, we are conducting such a survey that will cover a total area of ~100 square arcminutes with 1 hour exposures for each 1 square arcminute MUSE pointing. As a first result from this survey we present in Chapter 5 a catalogue of 831 emission-line selected galaxies from a 22.2 square arcminute region in the Chandra Deep Field South. In order to construct the catalogue, we developed and implemented a novel source detection algorithm -- LSDCat -- based on matched filtering for line emission in 3D spectroscopic datasets (Chapter 4). Our catalogue contains 237 Lyα emitting galaxies in the redshift range 3 ≲ z ≲ 6. Only four of those previously had spectroscopic redshifts in the literature. We conclude this thesis with an outlook on the construction of a Lyα luminosity function based on this unique sample (Chapter 6).
Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus–Levich–Dogonadze(MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer, a profound breaking of ergodicity occurs. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings.
We introduce azobenzene-functionalized polyelectrolyte multilayers as efficient, inexpensive optoacoustic transducers for hyper-sound strain waves in the GHz range. By picosecond transient reflectivity measurements we study the creation of nanoscale strain waves, their reflection from interfaces, damping by scattering from nanoparticles and propagation in soft and hard adjacent materials like polymer layers, quartz and mica. The amplitude of the generated strain ε ∼ 5 × 10−4 is calibrated by ultrafast X-ray diffraction.
The goal of the presented work is to explore the interaction between gold nanorods (GNRs) and hyper-sound waves. For the generation of the hyper-sound I have used Azobenzene-containing polymer transducers. Multilayer polymer structures with well-defined thicknesses and smooth interfaces were built via layer-by-layer deposition. Anionic polyelectrolytes with Azobenzene side groups (PAzo) were alternated with cationic polymer PAH, for the creation of transducer films. PSS/PAH multilayer were built for spacer layers, which do not absorb in the visible light range. The properties of the PAzo/PAH film as a transducer are carefully characterized by static and transient optical spectroscopy. The optical and mechanical properties of the transducer are studied on the picosecond time scale. In particular the relative change of the refractive index of the photo-excited and expanded PAH/PAzo is Δn/n = - 2.6*10‐4. Calibration of the generated strain is performed by ultrafast X-ray diffraction calibrated the strain in a Mica substrate, into which the hyper-sound is transduced. By simulating the X-ray data with a linear-chain-model the strain in the transducer under the excitation is derived to be Δd/d ~ 5*10‐4.
Additional to the investigation of the properties of the transducer itself, I have performed a series of experiments to study the penetration of the generated strain into various adjacent materials. By depositing the PAzo/PAH film onto a PAH/PSS structure with gold nanorods incorporated in it, I have shown that nanoscale impurities can be detected via the scattering of hyper-sound.
Prior to the investigation of complex structures containing GNRs and the transducer, I have performed several sets of experiments on GNRs deposited on a small buffer of PSS/PAH. The static and transient response of GNRs is investigated for different fluence of the pump beam and for different dielectric environments (GNRs covered by PSS/PAH).
A systematic analysis of sample architectures is performed in order to construct a sample with the desired effect of GNRs responding to the hyper-sound strain wave. The observed shift of a feature related to the longitudinal plasmon resonance in the transient reflection spectra is interpreted as the event of GNRs sensing the strain wave. We argue that the shift of the longitudinal plasmon resonance is caused by the viscoelastic deformation of the polymer around the nanoparticle. The deformation is induced by the out of plane difference in strain in the area directly under a particle and next to it. Simulations based on the linear chain model support this assumption. Experimentally this assumption is proven by investigating the same structure, with GNRs embedded in a PSS/PAH polymer layer.
The response of GNRs to the hyper-sound wave is also observed for the sample structure with GNRs embedded in PAzo/PAH films. The response of GNRs in this case is explained to be driven by the change of the refractive index of PAzo during the strain propagation.