Invalidity of the Ehrenfest theorem in the computation of high-order-harmonic generation within the strong-field approximation

Granados, C.; Plaja, Luis

doi:10.1103/physreva.85.053403

Cited by 9 publications

(6 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other attempts to improve the SFA include using different forms of dipole such as dipole acceleration and dipole velocity [88,89,95]. We also mention here other modifications of the SFA by including the effect of field dressing on the bound state [96][97][98].…”

Section: Other Modifications To the Sfamentioning

confidence: 99%

Strong-field approximation and its extension for high-order harmonic generation with mid-infrared lasers

Wei

Jin

et al. 2016

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

In recent years intense mid-infrared lasers with wavelength of a few microns have become the standard tools for research in strong field physics laboratories worldwide. These lasers offer the opportunities to extend the traditional study of high-order harmonics generation and attosecond sciences from the extreme ultraviolet to soft x-rays. In this tutorial we revisit the familiar strong field approximation and its simplification-the quantum orbits theory. We draw special emphasis on the factorization of laser induced dipole moment as the product of a returning electron wave packet with the photo-recombination dipole transition matrix element. The former depends on the laser properties only (up to a normalization constant) while the latter is related to laser-free photoionization transition dipole. The factorization leads to the suggested modification beyond the strong field approximation-the quantitative rescattering theory. In applying these theories to mid-infrared lasers, we analyze the behavior of the returning electron wave packet and its scaling properties vs the wavelength of the laser. A few examples are given to demonstrate how the quantitative rescattering theory is capable of reproducing experimental harmonic spectra under various conditions. Future opportunities in employing harmonics generated by optimized mid-infrared lasers for probing molecular structure and for serving as useful table-top coherent light sources up to the x-ray region are also discussed.

show abstract

Section: Other Modifications To the Sfamentioning

confidence: 99%

Strong-field approximation and its extension for high-order harmonic generation with mid-infrared lasers

Wei

Jin

et al. 2016

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

show abstract

“…Although these laser-electromagnetic gauges should provide the same results for a physical observable, for instance, the HHG spectra, previous studies have found that, unfortunately, it is not the case in several systems [29][30][31]. This breaking of the gauge-symmetry occurs when an approximation is carried out to solve the Time-Dependent Schrödinger Equation (TDSE).…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…This supports the observation that any approximation of the TDSE can break the laserelectromagnetic gauge-symmetry. For instance, in the Strong Field Approximation (SFA) applied to a gas, this laser-electromagnetic gauge-symmetry is broken [34]; producing different HHG spectra, particularly for the emitted intensity yield [30,31]. Nevertheless, the main qualitative features of the high harmonics are reproduced by the LG and VG in the SFA formalism.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Theory for all-optical responses in topological materials: the velocity gauge picture

Kim,

Shin,

Landsman

et al. 2021

Preprint

View full text Add to dashboard Cite

High Harmonic Generation (HHG), which has been widely used in atomic gas, has recently expanded to solids as a means to study highly nonlinear electronic response in condensed matter and produce coherent high frequency radiation with new properties. Most recently, attention has turned to Topological Materials (TMs) and the use of HHG to characterize topological bands and invariants. Theoretical interpretation of nonlinear electronic response in TMs, however, presents many challenges. In particular, the Bloch wavefunction phase of TMs has undefined points in the Brillouin Zone. This leads to singularities in calculating the inter-band and intra-band transition dipole matrix elements of Semiconductor Bloch Equations (SBEs). Here, we use the laser-electromagnetic velocity gauge p ⋅ A(t) to numerically integrate the SBEs and treat the singularity in the production of the electrical currents and HHG spectra. We use a prototype of Chern Insulators (CIs), the Haldane model, to demonstrate our approach. We find good qualitative agreement of the velocity gauge compared to the length gauge and the Time-Dependent Density Functional theory in the case of topologically trivial materials such as MoS2. For velocity gauge and length gauge, our two-band Haldane model reproduces key HHG spectra features: (i) The selection rules for linear and circular light drivers, (ii) The linear cut-off law scaling and (iii) The anomalous circular dichroism. We conclude that the velocity-gauge approach captures experimental observations and provides theoretical tools to investigate topological materials.

show abstract

“…The SFA, however, has serious limitations. Apart from the gauge dependence and its influence on the structural interference [28,29,35], different forms of recombination dipole matrix element affect this condition [31,36,37]. The most appropriate form to be used has raised considerable debate in the context of the tomographical reconstruction of molecular orbitals [38][39][40] If the field however is orthogonally polarized, the electron's angle of return is effectively incorporated in the two-center interference condition.…”

Section: Introductionmentioning

confidence: 99%

Shifting nodal-plane suppressions in high-order-harmonic spectra from diatomic molecules in orthogonally polarized driving fields

Das¹,

Faria²

2016

Phys. Rev. A

View full text Add to dashboard Cite

We analyze the imprint of nodal planes in high-order harmonic spectra from aligned diatomic molecules in intense laser fields whose components exhibit orthogonal polarizations. We show that the typical suppression in the spectra associated to nodal planes is distorted, and that this distortion can be employed to map the electron's angle of return to its parent ion. This investigation is performed semi-analytically at the single-molecule response and single-active orbital level, using the strong-field approximation and the steepest descent method. We show that the velocity form of the dipole operator is superior to the length form in providing information about this distortion. However, both forms introduce artifacts that are absent in the actual momentum-space wavefunction. Furthermore, elliptically polarized fields lead to larger distortions in comparison to two-color orthogonally polarized fields. These features are investigated in detail for O2, whose highest occupied molecular orbital provides two orthogonal nodal planes.

show abstract

Invalidity of the Ehrenfest theorem in the computation of high-order-harmonic generation within the strong-field approximation

Cited by 9 publications

References 15 publications

Strong-field approximation and its extension for high-order harmonic generation with mid-infrared lasers

Strong-field approximation and its extension for high-order harmonic generation with mid-infrared lasers

Theory for all-optical responses in topological materials: the velocity gauge picture

Shifting nodal-plane suppressions in high-order-harmonic spectra from diatomic molecules in orthogonally polarized driving fields

Contact Info

Product

Resources

About