Control of recollision wave packets for molecular orbital tomography using short laser pulses

The tomographic imaging of arbitrary molecular orbitals via high-order harmonic generation requires that electrons recollide from one direction only. Within a semi-classical model, we show that extremely short phase-stabilized laser pulses offer control over the momentum distribution of the returning electrons. By adjusting the carrier-envelope phase, recollisions can be forced to occur from mainly one side, while retaining a broad energy spectrum. The signatures of the semi-classical distributions are observed in harmonic spectra obtained by numerical solution of the time-dependent Schr\"{o}dinger equation.Comment: 8 pages, 4 figures; v2: Added some extra clarifications; v3: minor grammatical change

Semiclassical two-step model for ionization of hydrogen molecule by strong laser field

We extend the semiclassical two-step model for strong-field ionization that describes quantum interference and accounts for the Coulomb potential beyond the semiclassical perturbation theory to the hydrogen molecule. In the simplest case of the molecule oriented along the polarization direction of a linearly polarized laser field, we predict significant deviations of the two-dimensional photoelectron momentum distributions and the energy spectra from the case of atomic hydrogen. Specifically, for the hydrogen molecule the electron energy spectrum falls off slower with increasing energy, and the holographic interference fringes are more pronounced than for the hydrogen atom at the same parameters of the laser pulse.Comment: 9 pages, 6 figure

Strong-field approximation for harmonic generation in diatomic molecules

The generation of high-order harmonics in diatomic molecules is investigated within the framework of the strong-field approximation. We show that the conventional saddle-point approximation is not suitable for large internuclear distances. An adapted saddle-point method that takes into account the molecular structure is presented. We analyze the predictions for the harmonic-generation spectra in both the velocity and the length gauge. At large internuclear separations, we compare the resulting cutoffs with the predictions of the simple-man's model. Good agreement is obtained only by using the adapted saddle-point method combined with the velocity gauge.Comment: 24 pages, 7 figure

Ultrahigh harmonics from laser-assisted ion-atom collisions

We present a theoretical analysis of high-order harmonic generation from ion-atom collisions in the presence of linearly polarized intense laser pulses. Photons with frequencies significantly higher than in standard atomic high-harmonic generation are emitted. These harmonics are due to two different mechanisms: (i) collisional electron capture and subsequent laser-driven transfer of an electron between projectile and target atom; (ii) reflection of a laser-driven electron from the projectile leading to recombination at the parent atom.Comment: 5 pages, 4 figure

Positive Quantization in the Presence of a Variable Magnetic Field

Starting with a previously constructed family of coherent states, we introduce the Berezin quantization for a particle in a variable magnetic field and we show that it constitutes a strict quantization of a natural Poisson algebra. The phase-space reinterpretation involves a magnetic version of the Bargmann space and leads naturally to Berezin-Toeplitz operators.Comment: 15 page

How large is the Financial Accelerator? Some Evidence from Firm-level Data

This paper analyzes how the size and composition of the balance sheet affects firms financing cost within a large panel of Swiss firms in the non-financial sector from 1998 to 2011. The data includes a large number of small firms, which makes the data representative. We use an instrumental variables approach to identify the investment finance supply curve. Our finding that financing cost increase with exogenous changes in leverage supports the financial accelerator mechanism a la Bernanke, Gertler and Gilchrist. We quantitatively evaluate the implications of our findings for the aggregate business cycle and find that the amplification mechanism of the financial accelerator is economically significant: the volatility of the business cycle is amplified by a factor of 2.25 due to the presence of the financial accelerator channel

Accurate retrieval of structural information from laser-induced photoelectron and high-harmonic spectra by few-cycle laser pulses

By analyzing ``exact'' theoretical results from solving the time-dependent Schr\"odinger equation of atoms in few-cycle laser pulses, we established the general conclusion that differential elastic scattering and photo-recombination cross sections of the target ion with {\em free} electrons can be extracted accurately from laser-generated high-energy electron momentum spectra and high-order harmonic spectra, respectively. Since both electron scattering and photoionization (the inverse of photo-recombination) are the conventional means for interrogating the structure of atoms and molecules, this result shows that existing few-cycle infrared lasers can be implemented for ultrafast imaging of transient molecules with temporal resolution of a few femtoseconds.Comment: 4 pages, 4 figure

A calculus for magnetic pseudodifferential super operators

This work develops a magnetic pseudodifferential calculus for super operatorsOpA(F); these map operators onto operators (as opposed to Lp functions onto Lqfunctions). Here, F could be a tempered distribution or a H\"ormander symbol.An important example is Liouville super operators defined in terms of amagnetic pseudodifferential operator. Our work combines ideas from magneticWeyl calculus developed in [MP04, IMP07, Lei11] and the pseudodifferentialcalculus on the non-commutative torus from [HLP18a, HLP18b]. Thus, our calculusis inherently gauge-covariant, which means all essential properties of OpA(F)are determined by properties of the magnetic field B = dA rather than thevector potential A. There are conceptual differences to ordinary pseudodifferential theory. Forexample, in addition to an analog of the (magnetic) Weyl product that emulatesthe composition of two magnetic pseudodifferential super operators on the levelof functions, the so-called semi-super product describes the action of apseudodifferential super operator on a pseudodifferential operator.<br

Convolutional neural network for retrieval of the time-dependent bond length in a molecule from photoelectron momentum distributions

We apply deep learning for retrieval of the time-dependent bond length in the dissociating two-dimensional H+2 molecule using photoelectron momentum distributions. We consider a pump-probe scheme and calculate electron momentum distributions from strong-field ionization by treating the motion of the nuclei classically, semiclassically or quantum mechanically. A convolutional neural network trained on momentum distributions obtained at fixed internuclear distances retrieves the time-varying bond length with an absolute error of 0.2–0.3 a.u