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

Revealing the Interplay between Strong Field Selection Rules and Crystal Symmetries

Symmetries are ubiquitous in condensed matter physics, playing an important role in the appearance of different phases of matter. Nonlinear light matter interactions serve as a coherent probe for resolving symmetries and symmetry breaking via their link to selection rules of the interaction. In the extreme nonlinear regime, high harmonic generation (HHG) spectroscopy offers a unique spectroscopic approach to study this link, probing the crystal spatial properties with high sensitivity while opening new paths for selection rules in the XUV regime. In this Letter we establish an advanced HHG polarimetry scheme, driven by a multicolor strong laser field, to observe the structural symmetries of solids and their interplay with the HHG selection rules. By controlling the crystal symmetries, we resolve nontrivial polarization states associated with new spectral features in the HHG spectrum. Our scheme opens new opportunities in resolving the symmetries of quantum materials, as well as ultrafast light driven symmetries in condensed matter systems.

Time-resolved plasmon-assisted generation of optical-vortex pulses

The microscopic mechanism of the light-matter interactions that induce orbital angular momentum (OAM) in electromagnetic fields is not thoroughly understood. In this work, we employ Archimedean spiral vortex generators in time-resolved numerical simulations using the Octopus code to observe the behind-the-scenes of OAM generation. We send a perfect circularly-polarized plane-wave light onto plasmonic optical vortex generators and observe the resulting twisted light formation with complete spatio-temporal information. In agreement with previous works, we find that emission from the plasmonic spiral branches shapes the vortex-like structure and governs the OAM generation in the outgoing electromagnetic field. To characterize the generated beam further, we emulate the emission from vortex generators with current emitters preserving the spiral geometry. We subject a point-particle system to the generated field and record the orbital angular momentum transfer between the electromagnetic field and the point particle. Finally, we probe the OAM density locally by studying the induced classical trajectory of point particles, which provides further insight into the spatio-temporal features of the induced OAM.

Multiscale dynamical symmetries and selection rules in nonlinear optics

Symmetries and their associated selection rules are extremely useful in many fields of science. For systems of electromagnetic (EM) fields interacting with matter, the symmetries of matter and the EM fields' time-dependent polarization determine the properties of the nonlinear responses, and they can be facilitated for controlling light emission and enabling ultrafast symmetry breaking spectroscopy of various properties. Here, we formulate a general theory that describes the macroscopic and microscopic dynamical symmetries (including quasicrystal-like symmetries) of EM vector fields, revealing many previously unidentified symmetries and selection rules in light-matter interactions. We demonstrate an example of multiscale selection rules experimentally in the framework of high harmonic generation. This work paves the way for novel spectroscopic techniques in multiscale systems and for imprinting complex structures in extreme ultraviolet-x-ray beams, attosecond pulses, or the interacting medium itself.

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.

Observation of Magnetic Helicoidal Dichroism with Extreme Ultraviolet Light Vortices

We report on the experimental evidence of magnetic helicoidal dichroism, observed in the interaction of an extreme ultraviolet vortex beam carrying orbital angular momentum with a magnetic vortex. Numerical simulations based on classical electromagnetic theory show that this dichroism is based on the interference of light modes with different orbital angular momenta, which are populated after the interaction between light and the magnetic topology. This observation gives insight into the interplay between orbital angular momentum and magnetism and sets the framework for the development of new analytical tools to investigate ultrafast magnetization dynamics.

Enhancing circularly polarized XUV vortices from bicircular Laguerre-Gaussian fields

In this work, we theoretically study the generation of circularly polarized XUV vortices from high harmonic generation driven by bicircular Laguerre-Gaussian (LG) fields with different frequency ratios, by using the strong-field approximation theory. Our simulation shows that the amplitude of the generated vortices from the ω-3ω bicircular LG field is about one order of magnitude larger than that from the ω-2ω field, irrespective of the harmonic order and the orbital angular momentum of the bicircular driving fields. Our analysis shows that the great increase of the vortex amplitude for the ω-3ω field originates from the harmonic enhancement of a single atom. Furthermore, in terms of quantum-orbit theory, the underlying physics of the harmonic enhancement of the single atom for the ω-3ω field is revealed. Our work provides a simple and robust method to increase the amplitude of the circularly polarized XUV vortices.

Controlling Photon Transverse Orbital Angular Momentum in High Harmonic Generation

High harmonic generation (HHG) with longitudinal optical orbital angular momentum has attracted much attention over the past decade. Here, we present the first study on the HHG with transverse orbital angular momentum driven by the spatiotemporal optical vortex (STOV) pulses. We show that the produced spatial-resolved harmonic spectra reveal unique structures, such as the spatially spectral tilt and the fine interference patterns. We show these spatiospectral structures originate from both the macroscopic and microscopic effect of spatiotemporal optical singularity in HHG. Employing two-color counterspin and countervorticity STOV pulses, we further discuss a robust method to control the spatiotemporal topological charge and spectral structure of high-order harmonics. The conservation rule of photon transverse orbital angular momentum in HHG process is also discussed when mixing with photon spin angular momenta.

Study on spin angular momentum balance in harmonics generated from counter-rotating two-color laser fields

High-order harmonics generated from Xe driven by counter-rotating two-color driving fields are studied in the frame of a quantum-field scattering theory, and the spin angular momentum transfer is discussed. The driving field is composed by a circularly polarized (CP) mode and an elliptically polarized (EP) mode. We treat the EP mode as a compostition of counter-rotating CP fields of unequal intensity. We use a pair of phased generalized Bessel functions to describe the harmonic generation amplitude, and the conservation of the spin angular momentum during harmonic generation in the two-color field is derived in a solid base and in a straightforward way. The experimentally observed V-type and Λ-type distributions of the harmonic spectra with ellipticity are recovered theoretically. Balance pattern of the spin angular momentum is disclosed substantially.

Topological complex-energy braiding of non-Hermitian bands

Effects connected with the mathematical theory of knots¹ emerge in many areas of science, from physics^2,3 to biology⁴. Recent theoretical work discovered that the braid group characterizes the topology of non-Hermitian periodic systems⁵, where the complex band energies can braid in momentum space. However, such braids of complex-energy bands have not been realized or controlled experimentally. Here, we introduce a tight-binding lattice model that can achieve arbitrary elements in the braid group of two strands 𝔹₂. We experimentally demonstrate such topological complex-energy braiding of non-Hermitian bands in a synthetic dimension^6,7. Our experiments utilize frequency modes in two coupled ring resonators, one of which undergoes simultaneous phase and amplitude modulation. We observe a wide variety of two-band braiding structures that constitute representative instances of links and knots, including the unlink, the unknot, the Hopf link and the trefoil. We also show that the handedness of braids can be changed. Our results provide a direct demonstration of the braid-group characterization of non-Hermitian topology and open a pathway for designing and realizing topologically robust phases in open classical and quantum systems.

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.

Shortcut to study angular momentum transfer of harmonic generation in intense laser fields

High-order harmonics generated from atoms driven by counter-rotating two-color circularly (CRTC) polarized laser fields are studied in the frame of a quantum-field scattering theory. We use a pair of generalized phased Bessel (GPB) functions to describe the harmonic generation amplitude. The use of GPB functions allows us to define the phase of a harmonic channel accurately, by which we obtain the spin angular momentum conservation relation in a straightforward way. The known selection rule of harmonic order in the CRTC field is obtained concisely. Main features of the harmonic spectra are recovered. Our treatment provides a shortcut to study the angular momentum transfer in intense laser fields.

Generation of necklace-shaped high harmonics in a two-color vortex field

We numerically studied gas high-harmonic generation in a two-color vortex laser field using the non-adiabatic Lewenstein model. Macroscopic responses were calculated by numerically solving the three-dimensional propagation equation in cylindrical coordinates. It was confirmed that unique high-harmonic signals with necklace-like shapes exhibit orbital angular momentum (OAM). The azimuthally distributed necklace harmonics exhibit periodic modulation as a function of laser frequency and topological charges of the driving field. Phase investigation showed that the OAM of the necklace harmonics is attributable to the tuning of the relative intensity of the two driving pulses. These findings provide a new dimension for high-harmonic manipulation in the vortex field. The two-color vortex field is the first scheme proposed for manipulating the intensity profile of high harmonics.

Solvable Model of a Generic Driven Mixture of Trapped Bose-Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

A solvable model of a periodically driven trapped mixture of Bose-Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose-Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose-Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.

Symphony on strong field approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, 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.

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.