Topical Review: Extracting Molecular Frame Photoionization Dynamics from Experimental Data

Methods for experimental reconstruction of molecular frame (MF) photoionization dynamics, and related properties - specifically MF photoelectron angular distributions (PADs) and continuum density matrices - are outlined and discussed. General concepts are introduced for the non-expert reader, and experimental and theoretical techniques are further outlined in some depth. Particular focus is placed on a detailed example of numerical reconstruction techniques for matrix-element retrieval from time-domain experimental measurements making use of rotational-wavepackets (i.e. aligned frame measurements) - the ``bootstrapping to the MF" methodology - and a matrix-inversion technique for direct MF-PAD recovery. Ongoing resources for interested researchers are also introduced, including sample data, reconstruction codes (the \textit{Photoelectron Metrology Toolkit}, written in python, and associated \textit{Quantum Metrology with Photoelectrons} platform/ecosystem), and literature via online repositories; it is hoped these resources will be of ongoing use to the community.Comment: 65 pages, 17 figures. HTML version with interactive figures on Authorea: https://www.authorea.com/users/71114/articles/447808-extracting-molecular-frame-photoionization-dynamics-from-experimental-data Code and data archive on Figshare: http://dx.doi.org/10.6084/m9.figshare.2029378

Laser-induced rotational dynamics as a route to molecular frame measurements

Doctor of PhilosophyDepartment of PhysicsVinod KumarappanIn general, molecules in the gas phase are free to rotate, and measurements made on such samples are averaged over a randomly oriented distribution of molecules. Any orientation dependent information is lost in such measurements. The goal of the work presented here is to a) mitigate or completely do away with orientational averaging, and b) make fully resolved orientation dependent measurements. In pursuance of similar goals, over the past 50 years chemists and physicists have developed techniques to align molecules, or to measure their orientation and tag other quantities of interest with the orientation. We focus on laser induced alignment of asymmetric top molecules. The first major contribution of our work is the development of an effective method to align all molecular axes under field-free conditions. The method employs a sequence of nonresonant, impulsive laser pulses with varied ellipticities. The efficacy of the method is first demonstrated by solution of the time dependent Schr\"{o}dinger equation for iodobenzene, and then experimentally implemented to three dimensionally align 3,5 difluoroiodobenzene. Measurement from molecules aligned in this manner greatly reduces orientational averaging. The technique was developed via a thorough understanding and extensive computations of the dynamics of rotationally excited asymmetric top molecules. The second, and perhaps more important, contribution of our work is the development of a new measurement technique to extract the complete orientation dependence of a variety of molecular processes initiated by ultrashort laser pulses. The technique involves pump-probe measurements of the process of interest from a rotational wavepacket generated by impulsive excitation of asymmetric top molecules. We apply it to make the first measurement of the single ionization probability of an asymmetric top molecule in a strong field as a function of all relevant alignment angles. The measurement and associated calculations help identify the orbital from which the electron is ionized. We expect that this technique will be widely applicable to ultrafast-laser driven processes in molecules and provide unique insight into molecular physics and chemistry

A Laboratory Frame Density Matrix for Ultrafast Quantum Molecular Dynamics

In most cases the ultrafast dynamics of resonantly excited molecules are considered, and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here we provide a formalism in terms of a lab frame density matrix which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences which are potentially experimentally accessible are rejected by the orientation-averaged reduced vibronic density matrix. Instead, Molecular Angular Distribution Moments (MADMs) are introduced as a more accurate representation of experimentally accessible information. Furthermore, the formalism provides a clear definition of a molecular frame quantum tomography, and specifies the requirements to perform such a measurement enabling the experimental imaging of molecular frame vibronic dynamics. Successful completion of such a measurement fully characterizes the molecular frame quantum dynamics for a molecule at any orientation in the laboratory frame

An Investigation into Neuromorphic ICs using Memristor-CMOS Hybrid Circuits

The memristance of a memristor depends on the amount of charge flowing through it and when current stops flowing through it, it remembers the state. Thus, memristors are extremely suited for implementation of memory units. Memristors find great application in neuromorphic circuits as it is possible to couple memory and processing, compared to traditional Von-Neumann digital architectures where memory and processing are separate. Neural networks have a layered structure where information passes from one layer to another and each of these layers have the possibility of a high degree of parallelism. CMOS-Memristor based neural network accelerators provide a method of speeding up neural networks by making use of this parallelism and analog computation. In this project we have conducted an initial investigation into the current state of the art implementation of memristor based programming circuits. Various memristor programming circuits and basic neuromorphic circuits have been simulated. The next phase of our project revolved around designing basic building blocks which can be used to design neural networks. A memristor bridge based synaptic weighting block, a operational transconductor based summing block were initially designed. We then designed activation function blocks which are used to introduce controlled non-linearity. Blocks for a basic rectified linear unit and a novel implementation for tan-hyperbolic function have been proposed. An artificial neural network has been designed using these blocks to validate and test their performance. We have also used these fundamental blocks to design basic layers of Convolutional Neural Networks. Convolutional Neural Networks are heavily used in image processing applications. The core convolutional block has been designed and it has been used as an image processing kernel to test its performance.Comment: Bachelor's thesi

Ultrafast Field-Resolved Nonlinear Optical Spectroscopy in the Molecular Frame

We resolve the real-time electric field of a femtosecond third-order nonlinear optical signal in the molecular frame. The electric field emitted by the induced third-order polarization from impulsively pre-aligned gas-phase molecules at room temperature, in a degenerate four-wave mixing (DFWM) scheme, is measured using a spectral interferometry technique. We show that by measuring both the amplitude and phase of the emitted femtosecond pulse, information related to electronic symmetries can be accessed. The nonlinear signal is measured around a rotational revival to extract its molecular-frame angle dependence from pump-probe time delay scans. By comparing these measurements for two linear molecules, carbon dioxide (CO2) and Nitrogen (N2), we show that the measured second-order phase parameter (temporal chirp) of the signal is sensitive to the valence electronic symmetry of the molecules, whereas the amplitude of the signal does not show such sensitivity. We compare these measurements to theoretical calculations of the chirp observable in the molecular frame. This work is an important step towards using field-resolved nonlinear optical measurements to study ultrafast dynamics in electronically excited molecules.Comment: 10 pages, 3 figures and 1 supplemental documen

N2 HOMO-1 orbital cross section revealed through high-order-harmonic generation

Citation: Troß, J., Ren, X., Makhija, V., Mondal, S., Kumarappan, V., & Trallero-Herrero, C. A. (2017). N2 HOMO-1 orbital cross section revealed through high-order-harmonic generation. Physical Review A - Atomic, Molecular, and Optical Physics, 95(3). doi:10.1103/PhysRevA.95.033419We measure multi-orbital contributions to high harmonic generation from aligned nitrogen. We show that the change in revival structure in the cutoff harmonics has a counterpart in the angular distribution when a lower-lying orbital contributes to the harmonic yield. This angular distribution is directly observed in the laboratory without any further deconvolution. Because of the high degree of alignment we are able to distinguish angular contributions of the highest occupied molecular orbital 1 (HOMO-1) orbital from angle-dependent spectroscopic features of the HOMO. In particular, we are able to make a direct comparison with the cross section of the HOMO-1 orbital in the extreme ultraviolet region. © 2017 American Physical Society

Time-resolved multi-mass ion imaging: femtosecond UV-VUV pump-probe spectroscopy with the PImMS camera

The Pixel-Imaging Mass Spectrometry (PImMS) camera allows for 3D charged particle imaging measurements, in which the particle time-of-flight is recorded along with $(x,y)$ position. Coupling the PImMS camera to an ultrafast pump-probe velocity-map imaging spectroscopy apparatus therefore provides a route to time-resolved multi-mass ion imaging, with both high count rates and large dynamic range, thus allowing for rapid measurements of complex photofragmentation dynamics. Furthermore, the use of vacuum ultraviolet wavelengths for the probe pulse allows for an enhanced observation window for the study of excited state molecular dynamics in small polyatomic molecules having relatively high ionization potentials. Herein, preliminary time-resolved multi-mass imaging results from C$_2$F$_3$I photolysis are presented. The experiments utilized femtosecond UV and VUV (160.8~nm and 267~nm) pump and probe laser pulses in order to demonstrate and explore this new time-resolved experimental ion imaging configuration. The data indicates the depth and power of this measurement modality, with a range of photofragments readily observed, and many indications of complex underlying wavepacket dynamics on the excited state(s) prepared

Measuring the Angle-Dependent Photoionization Cross Section of Nitrogen using High-Harmonic Generation

We exploit the relationship between high harmonic generation (HHG) and the molecular photorecombination dipole to extract the molecular-frame differential photoionization cross section (PICS) in the extreme ultraviolet (XUV) for molecular nitrogen. A shape resonance and a Cooper-type minimum are reflected in the pump-probe time delay measurements of different harmonic orders, where high-order rotational revivals are observed in N₂. We observe the energy- and angle-dependent Cooper minimum and shape resonance directly in the laboratory-frame HHG yield by achieving a high degree of alignment, [SEE FORMULA IN ABSTRACT cos2 θ] 0.8. The interplay between PICS and rotational revivals is confirmed by simulations using the quantitative rescattering theory. Our method of extracting molecular-frame structural information points the way to similar measurements in more complex molecules

Bayesian inferencing and deterministic anisotropy for the retrieval of the molecular geometry ∣Ψ(r)∣2|\Psi(\mathbf{r})|^2 in gas-phase diffraction experiments

Currently, our general approach to retrieve the molecular geometry from ultrafast gas-phase diffraction heavily relies on complex geometric simulations to make conclusive interpretations. In this manuscript, we develop a broadly applicable ultrafast gas-phase diffraction method that approximates the molecular frame geometry $|\Psi(\mathbf{r}, t)|^2$ distribution using Bayesian Inferencing. This method does not require complex molecular dynamics simulation and can identify the unique molecular structure. We demonstrate this method's viability by retrieving the ground state geometry distribution $|\Psi(\mathbf{r})|^2$ for both simulated stretched NO$_2$ and measured ground state N$_2$O. Due to our statistical interpretation, we retrieve a coordinate-space resolution on the order of 100~fm, depending on signal quality, an improvement of order 100 compared to commonly used Fourier transform based methods. By directly measuring the width of $|\Psi(\mathbf{r})|^2$, this is generally only accessible through simulation, we open ultrafast gas-phase diffraction capabilities to measurements beyond current analysis approaches. Our method also leverages deterministic ensemble anisotropy; this provides an explicit dependence on the molecular frame angles. This method's ability to retrieve the unique molecular structure with high resolution, and without complex simulations, provides the potential to effectively turn gas-phase ultrafast diffraction into a discovery oriented technique, one that probes systems that are prohibitively difficult to simulate.Comment: 16 pages, 8 figures, 2 tables. Please find the analysis code and templates for new molecules at https://github.com/khegazy/BIG