Nonlinear up-conversion of a polarization Möbius strip with half-integer optical angular momentum.

Symmetries and conservation laws of energy, linear momentum, and angular momentum play a central role in nonlinear optics. Recently, paraxial light fields with nontrivial topology have been attracting a keen interest. Despite not being eigenstates of the orbital and spin angular momenta (OAM and SAM), they are eigenstates of the generalized angular momentum (GAM) operator-a mixture of the OAM and SAM operators with fractional eigenvalues. By driving high harmonic generation with a polarization Möbius strip carrying a half-integer GAM charge and implementing angular momentum characterization methods in the extreme ultraviolet range, we demonstrate the linear scaling of the GAM with the harmonic order, each harmonic carrying a precise half-integer GAM charge. Our work shows that beyond SAM and OAM, the GAM is, in some situations, an appropriate quantum number. It paves the way for finer manipulations and applications of light beams containing fractional-order polarization singularities.

Enantiosensitive steering of free-induction decay.

Chiral discrimination, a problem of vital importance, has recently become an emerging frontier in ultrafast physics, with remarkable progress achieved in multiphoton and strong-field regimes. Rydberg excitations, unavoidable in the strong-field regime and intentional for few-photon processes, arise in all these approaches. Here, we show how to harness this ubiquitous feature by introducing a new phenomenon, enantiosensitive free-induction decay, steered by a tricolor chiral field at a gentle intensity, structured in space and time. We demonstrate theoretically that an excited chiral molecule accumulates an enantiosensitive phase due to perturbative interactions with the tricolor chiral field, resulting in a spatial phase gradient steering the free-induction decay in opposite directions for opposite enantiomers. Our work introduces a general, extremely sensitive, all-optical enantiosensitive detection technique that avoids strong fields and takes full advantage of recent advances in structuring light.

High Photon Number Entangled States and Coherent State Superposition from the Extreme Ultraviolet to the Far Infrared.

We present a theoretical demonstration on the generation of entangled coherent states and of coherent state superpositions, with photon numbers and frequencies orders of magnitude higher than those provided by the current technology. This is achieved by utilizing a quantum mechanical multimode description of the single- and two-color intense laser field driven process of high harmonic generation in atoms. It is found that all field modes involved in the high harmonic generation process are entangled, and upon performing a quantum operation, lead to the generation of high photon number optical cat states spanning from the far infrared to the extreme ultraviolet spectral region. This provides direct insights into the quantum mechanical properties of the optical field in the intense laser matter interaction. Finally, these states can be considered as a new resource for fundamental tests of quantum theory, quantum information processing, or sensing with nonclassical states of light.

Conservation laws for electron vortices in strong-field ionisation.

ABSTRACT: We investigate twisted electrons with a well-defined orbital angular momentum, which have been ionised via a strong laser field. By formulating a new variant of the well-known strong field approximation, we are able to derive conservation laws for the angular momenta of twisted electrons in the cases of linear and circularly polarised fields. In the case of linear fields, we demonstrate that the orbital angular momentum of the twisted electron is determined by the magnetic quantum number of the initial bound state. The condition for the circular field can be related to the famous ATI peaks, and provides a new interpretation for this fundamental feature of photoelectron spectra. We find the length of the circular pulse to be a vital factor in this selection rule and, employing an effective frequency, we show that the photoelectron OAM emission spectra are sensitive to the parity of the number of laser cycles. This work provides the basic theoretical framework with which to understand the OAM of a photoelectron undergoing strong field ionisation.

Dialogue on analytical and ab initio methods in attoscience.

The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience-covering both analytical and numerical methods-and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation.

A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one- or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5 × 1013 W/cm2 to 5 × 1014 W/cm2. We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.

Generation of extreme-ultraviolet beams with time-varying orbital angular momentum.

Light fields carrying orbital angular momentum (OAM) provide powerful capabilities for applications in optical communications, microscopy, quantum optics, and microparticle manipulation. We introduce a property of light beams, manifested as a temporal OAM variation along a pulse: the self-torque of light. Although self-torque is found in diverse physical systems (i.e., electrodynamics and general relativity), it was not realized that light could possess such a property. We demonstrate that extreme-ultraviolet self-torqued beams arise in high-harmonic generation driven by time-delayed pulses with different OAM. We monitor the self-torque of extreme-ultraviolet beams through their azimuthal frequency chirp. This class of dynamic-OAM beams provides the ability for controlling magnetic, topological, and quantum excitations and for manipulating molecules and nanostructures on their natural time and length scales.

Symphony on strong field approximation.

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagiellonski, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

Conservation of Torus-knot Angular Momentum in High-order Harmonic Generation.

High-order harmonic generation stands as a unique nonlinear optical up-conversion process, mediated by a laser-driven electron recollision mechanism, which has been shown to conserve energy, linear momentum, and spin and orbital angular momentum. Here, we present theoretical simulations that demonstrate that this process also conserves a mixture of the latter, the torus-knot angular momentum J_{γ}, by producing high-order harmonics with driving pulses that are invariant under coordinated rotations. We demonstrate that the charge J_{γ} of the emitted harmonics scales linearly with the harmonic order, and that this conservation law is imprinted onto the polarization distribution of the emitted spiral of attosecond pulses. We also demonstrate how the nonperturbative physics of high-order harmonic generation affect the torus-knot angular momentum of the harmonics, and we show that this configuration harnesses the spin selection rules to channel the full yield of each harmonic into a single mode of controllable orbital angular momentum.

Lorentz drift compensation in high harmonic generation in the soft and hard X-ray regions of the spectrum.

We present a semi-classical study of the effects of the Lorentz force on electrons during high harmonic generation in the soft and hard X-ray regions driven by near- and mid-infrared lasers with wavelengths from 0.8 to 20 µm, and at intensities below 1015 W/cm2. The transverse extent of the longitudinal Lorentz drift is compared for both Gaussian focus and waveguide geometries. Both geometries exhibit a longitudinal electric field component that cancels the magnetic Lorentz drift in some regions of the focus, once each full optical cycle. We show that the Lorentz force contributes a super-Gaussian scaling which acts in addition to the dominant high harmonic flux scaling of λ-(5-6) due to quantum diffusion. We predict that the high harmonic yield will be reduced for driving wavelengths > 6 µm, and that the presence of dynamic spatial mode asymmetries results in the generation of both even and odd harmonic orders. Remarkably, we show that under realistic conditions, the recollision process can be controlled and does not shut off completely even for wavelengths >10 µm and recollision energies greater than 15 keV.