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

We have studied the ionization of Rydberg atoms by few-cycle radio-frequency pulses and used two-color fields to control the ionization dynamics. We show that the number of times that electrons are emitted during a pulse can be limited and that the duration of the electron emission can be shortened. These results, once they are transposed to the optical domain, may inspire new strategies for the production of single attosecond pulses.

Control of atomic ionization by two-color few-cycle pulses.

Laser-induced plasma formation and subsequent relaxation in dielectric solids is the precursor to structural modifications serving as the basis for direct laser writing of functional optical micro- and nanostructures. Based on an experimental arrangement combining a time-resolved transmission measurement with a cross-phase modulation measurement, we isolate the plasma formation and relaxation dynamics in the bulk of amorphous fused silica excited by femtosecond short-wavelength infrared ( λ = 2100 nm) laser pulses. Whereas the relaxation time of the generated subcritical electron-hole plasma was so far assumed to be constant, our findings indicate an intensity-dependent relaxation time. We attribute this intensity dependence to vibrational activation of the medium, leading to detrapping of trapped carriers and a reduced trapping probability.

Plasma formation and relaxation dynamics in fused silica driven by femtosecond short-wavelength infrared laser pulses

Multi-electron dynamics in atoms and molecules very often occur on sub- to few-femtosecond time scales. The available intensities of extreme-ultraviolet (XUV) attosecond pulses have previously allowed the time-resolved investigation of two-photon, two-electron interactions. Here we study double and triple ionization of argon atoms involving the absorption of up to five XUV photons using a pair of intense attosecond pulse trains (APTs). By varying the time delay between the two APTs with attosecond precision and the spatial overlap with nanometer precision, we obtain information on complex nonlinear multi-photon ionization pathways. Our experimental and numerical results show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">A</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">r</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> is predominantly formed by a sequential two-photon process, whereas the delay dependence of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">A</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">r</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> ion yield exhibits clear signatures of the involvement of a simultaneous two-photon absorption process. Our experiment suggests that it is possible to investigate multi-electron dynamics using attosecond pulses for both pumping and probing the dynamics. 

Attosecond control of extreme-ultraviolet multi-photon ionization

Calculations show that with new short pulse x-ray light sources, it should be possible to use photoelectron emission to make movies of changes in molecular structure.

https://physics.aps.org/articles/pdf/10.1103/Physics.2.72

Illuminating molecules from within

We report experiments on laser-assisted electron recollisions that result from strong-field ionization of photoexcited ${\mathrm{I}}_{2}$ molecules in the regime of low-energy electron scattering ($l25\text{ }\text{ }\mathrm{eV}$ impact energy). By comparing differential scattering cross sections extracted from the angle-resolved photoelectron spectra to differential scattering cross sections from quantum-scattering calculations, we demonstrate that the electron-scattering dynamics is dominated by a shape resonance. When the molecular bond stretches during the evolution of a vibrational wave packet this shape resonance shifts to lower energies, both in experiment and theory. We explain this behavior by the nature of the resonance wave function, which closely resembles an antibonding molecular orbital of ${\mathrm{I}}_{2}$.

https://link.aps.org/pdf/10.1103/PhysRevLett.125.123001

Marc J. J. Vrakking

Papers

Control of atomic ionization by two-color few-cycle pulses.

Plasma formation and relaxation dynamics in fused silica driven by femtosecond short-wavelength infrared laser pulses

Attosecond control of extreme-ultraviolet multi-photon ionization

Illuminating molecules from within

Evolution of a Molecular Shape Resonance along a Stretching Chemical Bond