Coulomb phase in high harmonic generation

Popruzhenko, S. V.

doi:10.1088/1361-6455/aac787

Cited by 21 publications

(14 citation statements)

References 42 publications

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“…In order to eliminate the divergency, a matching with the phase of a stationary atomic scattering wave function has to be performed, along a method similar to that applied for the matching at the saddle point t = t s [18,47]. For the case of high harmonic generation this procedure has been realized in [57] employing the Coulomb-free trajectories. Extension of this method to ATI and Coulomb-distorted trajectories remains a serious challenge.…”

Section: Discussionmentioning

confidence: 99%

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Treating branch cuts in quantum trajectory models for photoelectron holography

2018

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Most implementations of Coulomb-distorted strong-field approaches that contain features such as tunneling and quantum interference use real trajectories in continuum propagation, while a fully consistent approach must use complex trajectories throughout. A key difficulty in the latter case are branch cuts that appear due to the specific form of the Coulomb potential. We present a method for treating branch cuts in quantum-trajectory models, which is subsequently applied to photoelectron holography. Our method is not numerically intensive, as it does not require finding the location of all branching points and branch cuts prior to its implementation, and is applicable to Coulomb-free and Coulomb-distorted trajectories. We show that the presence of branch cuts leads to discontinuities and caustics in the holographic fringes in above-threshold ionization (ATI) photoelectron angular distributions (PAD). These artefacts are removed applying our method, provided they appear far enough from the polarization axis. A comparison with the full solution of the time-dependent Schrödinger equation is also performed, and a discussion of the applicability range of the present approach is provided.

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Section: Discussionmentioning

confidence: 99%

“…For p ⊥ = 0 the topology of the problem changes, with poles instead of branch cuts, and there will be divergencies. We will discuss this problem in the subsequent sections, see also [57]. For a schematic representation of this contour and how it is deformed to avoid branch cuts, see Fig.…”

Section: Treatment Of Branch Cutsmentioning

confidence: 99%

Treating branch cuts in quantum trajectory models for photoelectron holography

2018

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“…The simulation shows that the recollision orientations remain separated by 120 • approximately, so its contribution is negligible [see figure S.3(b) in the supplementary]. In the experiment, the emerging selection rules are found for a QWP angle of 38 • , which slightly deviates from the values found by the semi-classical simulations, possibly due to the effect of the screened Coulomb potential [48,49]. The nearly linear relationship between the QWP angle and the suppressed harmonic orders in the experimental spectrogram (figure 2(b)) suggests that for multiple harmonic orders, the tuning of the QWP induces approximately equal relative phases between the recollisions.…”

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confidence: 82%

A dynamical symmetry triad in high-harmonic generation revealed by attosecond recollision control

et al. 2020

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A key element of optical spectroscopy is the link between observable selection rules and the underlying symmetries of an investigated physical system. Typically, selection rules directly relate to the sample properties probed by light, yielding information on crystalline structure or chirality, for example. Considering light-matter coupling more broadly may extend the scope of detectable symmetries, to also include those directly arising from the interaction. In this letter, we experimentally demonstrate an emerging class of symmetries in the electromagnetic field emitted by a strongly driven atomic system. Specifically, generating high-harmonic radiation with attosecond-controlled two-color fields, we find different sets of allowed and forbidden harmonic orders. Generalizing symmetry considerations of circularly polarized high-harmonic generation, we interpret these selection rules as a complete triad of dynamical symmetries. We expect such emergent symmetries also for multi-atomic and condensed-matter systems, encoded in the spectral and spatial features of the radiation field. Notably, the observed phenomenon gives robust access to chiral processes with few-attosecond time precision.The concept of emergence describes the appearance of entirely new properties of a coupled system, which only arise from the interaction of its constituents. In light-matter interaction, emergent phenomena are particularly prominent in strongly driven states of matter, as evident in light-induced variants of superconductivity [1], the Hall effect [2], and topological insulators [3] in the condensed phase, as well as exceptional points in molecules [4,5], Kramers-Henneberger states in gases [6,7], and time-crystals in isolated many-body systems [8,9]. Such emergent states are often governed by novel symmetry properties and topologies, which may be probed by external or emitted radiation fields. However, while much attention is drawn to the light-induced creation of novel states of matter, a wider scope should also include possible emergent states of the radiation field.Here, we report on the experimental observation of an emergent class of symmetries in the electromagnetic field emitted by a strongly driven atomic system. Specifically, we analyze the sets of allowed and forbidden harmonic orders in high-harmonic generation from tailored bi-circular and bi-elliptical fields. Corroborated by theoretical modeling, the identified selection rules correspond to a complete triad of dynamical symmetries. We believe that the general principles underlying our observations will be equally relevant for other systems, including crystalline solids.Spectral and polarization selection rules serve as direct measures for the symmetries of the underlying Hamiltonian and interaction [10,11]. Canonical examples in linear and perturbative nonlinear probing are molecular analysis by Raman and infrared spectroscopy [12,13] or selection rules in wave mixing and

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“…A similar picture of quantum orbits also naturally arises within the analytical R-matrix theory [46][47][48][49][50], which uses semiclassical perturbation theory in the action to include the effects of the Coulomb potential on strongfield-driven electron dynamics. Using the QOA and either quasiclassical perturbation theory or the analytical R-matrix theory, Coulomb corrections may be derived for the first two steps of the HHG process [50][51][52], including Coulomb corrections to the ionization and recombination times.…”

Section: Introductionmentioning

confidence: 99%

“…However, although Coulomb phases are introduced ad hoc, the analysis is mainly suitable for short-range potentials, as the boundary conditions for the wave function at large distances do not take into account the long-range Coulomb interaction. Thus, additional Coulomb corrections to the HHG amplitude (taking into account ionization and propagation in the Coulomb field) are required [51,52]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Analytic description of high-order harmonic generation in the adiabatic limit with application to an initial s state in an intense bicircular laser pulse

et al. 2019

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An analytic description of high-order harmonic generation (HHG) is proposed in the adiabatic (low-frequency) limit for an initial s state and a laser field having an arbitrary wave form. The approach is based on the two-state time-dependent effective range theory and is extended to the case of neutral atoms and positively charged ions by introducing ad hoc the Coulomb corrections for HHG. The resulting closed analytical form for the HHG amplitude is discussed in terms of real classical trajectories. The accuracy of the results of our analytic model is demonstrated by comparison with numerical solutions of the time-dependent Schrödinger equation for a strong bicircular field composed of two equally intense components with carrier frequencies ω and 2ω and opposite helicities. In particular, we demonstrate the effect of ionization gating on HHG in a bicircular field, both for the case that the two field components are quasimonochromatic and for the case that the field components are time-delayed short pulses. We show how ionization in a strong laser field not only smooths the usual peak structures in HHG spectra but also changes the positions and polarization properties of the generated harmonics, seemingly violating the standard dipole selection rules. These effects appear for both short and long incident laser pulses. In the case of time-delayed short laser pulses, ionization gating provides an effective tool for control of both the HHG yield and the harmonic polarizations [Frolov et al., Phys. Rev. Lett. 120, 263203 (2018)]. For the case of short laser pulses, we introduce a simple two-dipole model that captures the physics underlying the harmonic emission process, describing both the oscillation patterns in HHG spectra and also the dependence of the harmonic polarizations on the harmonic energy.

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Coulomb phase in high harmonic generation

Cited by 21 publications

References 42 publications

Treating branch cuts in quantum trajectory models for photoelectron holography

Treating branch cuts in quantum trajectory models for photoelectron holography

A dynamical symmetry triad in high-harmonic generation revealed by attosecond recollision control

Analytic description of high-order harmonic generation in the adiabatic limit with application to an initial s state in an intense bicircular laser pulse

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