The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

https://arxiv.org/pdf/cond-mat/9806038.pdf

Theory of Bose-Einstein condensation in trapped gases

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

To date, copper is the only heterogeneous catalyst that has shown a propensity to produce valuable hydrocarbons and alcohols, such as ethylene and ethanol, from electrochemical CO2 reduction (CO2R). There are variety of factors that impact CO2R activity and selectivity, including the catalyst surface structure, morphology, composition, the choice of electrolyte ions and pH, and the electrochemical cell design. Many of these factors are often intertwined, which can complicate catalyst discovery and design efforts. Here we take a broad and historical view of these different aspects and their complex interplay in CO2R catalysis on Cu, with the purpose of providing new insights, critical evaluations, and guidance to the field with regard to research directions and best practices. First, we describe the various experimental probes and complementary theoretical methods that have been used to discern the mechanisms by which products are formed, and next we present our current understanding of the complex reaction networks for CO2R on Cu. We then analyze two key methods that have been used in attempts to alter the activity and selectivity of Cu: nanostructuring and the formation of bimetallic electrodes. Finally, we offer some perspectives on the future outlook for electrochemical CO2R.

/pdf/progress-and-perspectives-of-electrochemical-co2-reduction-hut0der0e7.pdf

Progress and Perspectives of Electrochemical CO2 Reduction on Copper in Aqueous Electrolyte

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

The application of velocity map imaging for the detection of photoelectrons resulting from atomic or molecular ionization allows the observation of interferometric, and in some cases holographic structures that contain detailed information on the target from which the photoelecrons are extracted. In this contribution we present three recent examples of the use of photoelectron velocity map imaging in experiments where atoms are exposed to strong optical and dc electric fields. We discuss (i) observations of the nodal structure of Stark states of hydrogen measured in a dc electric field, (ii) mid-infrared strong-field ionization of metastable Xe atoms and (iii) the reconstruction of helium electronic wavepackets in an attosecond pump-probe experiment. In each case, the interference between direct and indirect electron pathways, reminiscent of the reference and signal waves in holography, is seen to play an important role.

https://iopscience.iop.org/article/10.1088/1742-6596/488/1/012007/pdf

Photoelectron holography in strong optical and dc electric fields

A high power optical parametric amplifier operating at 100 kHz repetition rate has been integrated into an attosecond pump-probe beamline. Attosecond pulses with high photon flux are generated and characterized in pump-probe experiments.

High repetition rate OPCPA driving an attosecond pump-probe beamline

The photoionization of CF3I molecules in the photon energy range between 10 eV and 40 eV is investigated using angle-resolved photoelectron spectroscopy in the molecular frame. Using a femtosecond laser pulse, the molecules are impulsively aligned prior to their ionization by a series of extreme ultra-violet photon energies obtained by high-harmonic generation. The manifestation of molecular alignment in the photoelectron angular distributions (PADs) is well reproduced by non-relativistic quantum-mechanical photoionization calculations carried out with the ePolyScat software package, taking into account all open ionization channels. Our analysis points to two prominent shape resonances that dominate the photoelectron scattering dynamics and that therefore largely explain the observed changes in the PADs as a function of molecular alignment.

https://iopscience.iop.org/article/10.1088/1361-6455/acbad0/pdf

Shape resonances in angle-resolved photoionization of aligned CF3I molecules

The efficiency of energy transfer in ultrafast electronic relaxation of molecules depends strongly on the complex interplay between electronic and nuclear motion. In this study we use wavelength-selected XUV pulses to induce relaxation dynamics of highly excited cationic states of naphthalene. Surprisingly, the observed relaxation lifetimes increase with the cationic excitation energy. We propose that this is a manifestation of a quantum mechanical population trapping that leads to delayed relaxation of molecules in the regions with a high density of excited states.

Delayed relaxation of highly excited naphthalene cations

Non-perturbative low-order harmonics can be dominated by the nonlinearity of strong-field-ionization. We demonstrate the reconstruction of strong-field-driven carrier generation dynamics from ionization-related harmonics in fused silica using a phase-retrieval algorithm.

Marc J. J. Vrakking

Papers

Photoelectron holography in strong optical and dc electric fields

High repetition rate OPCPA driving an attosecond pump-probe beamline

Shape resonances in angle-resolved photoionization of aligned CF3I molecules

Delayed relaxation of highly excited naphthalene cations

Reconstruction of Strong-Field-Driven Carrier Generation Dynamics from Injection Harmonics in Solid Dielectrics