S-matrix treatments of multichannel ionization of atoms by high-intensity lasers

Burlon, R.; Leone, Cláudio; Trombetta, F.; Ferrante, G.

doi:10.1007/bf02464854

Cited by 25 publications

(11 citation statements)

References 18 publications

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“…[27] However, due to the fact that we have to use some approximations in the S-matrix theory calculations, the results calculated under the two gauges may be gauge dependent. [28,29] For instance, photoelectron energy spectra of negative ions in linearly or circularly polarized fields calculated by the L gauge S-matrix theory are consistent with the results of TDSE [30] or experiment. [31] However, for molecules with large internuclear separation, L gauge only works well when effect of the excited state is taken into account.…”

Section: Introductionsupporting

confidence: 76%

Comparative study on atomic ionization in bicircular laser fields by length and velocity gauges S-matrix theory*

Xia¹,

Jia²,

Hao³

et al. 2020

Chinese Phys. B

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Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges. We show that for both the bicircular fields, ionization rates are enhanced when the two circularly polarized lights have comparable intensities. In addition, the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5 × 1014 W/cm2, which agrees with the experimental observation. Moreover, the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity. With the help of the ADK theory, the above characteristics of the ionization rate curves can be well interpreted, which is related to the transition from the tunneling to multiphoton ionization mechanism.

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Section: Introductionsupporting

confidence: 76%

Comparative study on atomic ionization in bicircular laser fields by length and velocity gauges S-matrix theory*

Xia¹,

Jia²,

Hao³

et al. 2020

Chinese Phys. B

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“…However, as we have noted above, Û( r, t) = 1 is not satisfied in strong laser fields. Burlon et al [45] and Leone et al [46] long ago considered in fact the same problem (nonresonant multiphoton ionization) in the S-matrix theory. With the help of some approximations done in the Green function representation of the S-matrix element they arrived at the same conclusion.…”

Section: Appendix Amentioning

confidence: 97%

Comparison of two forms of theS-matrix element of strong-field photoionization

Bauer¹

2008

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

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We numerically compare ionization rates and photoelectron energy spectra resulting from the so-called length gauge (LG) and velocity gauge (VG) forms of the Keldysh–Faisal–Reiss (KFR) theory for a circularly polarized laser field. To this end, we use the well-known analytical formulae for the ground state of a hydrogen atom and we derive analogous formulae for its first excited (degenerate) state. It appears that both forms of the KFR theories show qualitatively different behaviour of ionization rate as a function of frequency and intensity of the laser field. In the LG KFR theory, one obtains much smaller stabilization of the hydrogen atom than in the VG KFR theory. Unlike the latter one, the LG KFR theory shows that for sufficiently strong laser field (in the non-relativistic and dipole approximations) ionization rate from a given initial state is only a function of intensity, but not of frequency of the laser field. We also find substantial differences in the shape of photoelectron energy spectra for both theories. In contrast to the VG KFR theory, the LG one shows a minimum in photoelectron energy spectra for some initial states of the hydrogen atom. We discuss our results by comparing them, where possible, to other theoretical calculations.

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“…[4]. Comparisons that have been carried out indeed have exhibited significant disagreements between the results obtained from L gauge and V gauge [5]. Different authors have preferred different gauges.…”

mentioning

confidence: 99%

Strong-field approximation for intense-laser–atom processes: The choice of gauge

2005

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The strong-field approximation can be and has been applied in both length gauge and velocity gauge with quantitatively conflicting answers. For ionization of negative ions with a ground state of odd parity, the predictions of the two gauges differ qualitatively: in the envelope of the angularresolved energy spectrum, dips in one gauge correspond to humps in the other. We show that the length-gauge SFA matches the exact numerical solution of the time-dependent Schrödinger equation.PACS numbers: 42.50. Hz, 32.80.Rm, 32.80.Gc Quantum mechanics is gauge invariant: it is easily proven that a given physical quantity can be evaluated in any gauge with the same result [1]. In nonrelativistic quantum mechanics, when the dipole approximation is adopted, the interaction of an atom with a timedependent field such as a laser field is usually described in either one of two gauges: the length gauge (L gauge) or the velocity gauge (V gauge). In numerical solutions of the time-dependent Schrödinger equation (TDSE), gauge invariance has been confirmed many times. In analytical work, however, some approximations almost always have to be adopted. There is no formal reason of why after such approximations the resulting theory should still be gauge invariant. Indeed, the lack of gauge invariance after what seems like very well justified approximations has driven many a researcher to despair [2].In this paper, we will address one of the most glaring manifestations of this "gauge problem": the lack of gauge invariance of the strong-field approximation (SFA) in intense-laser-atom physics [3]. The SFA underlies almost any analytical approach to total ionization rates, above-threshold ionization, high-order harmonic generation, and nonsequential double ionization, both of atoms and of molecules. Briefly, it assumes that the initial bound state of the atom or molecule is unaffected by the laser field while the final state, which is in the continuum, does not feel the presence of the binding potential. The lack of gauge invariance of the SFA has been noted many times; see, e.g., Ref. [4]. Comparisons that have been carried out indeed have exhibited significant disagreements between the results obtained from L gauge and V gauge [5]. Different authors have preferred different gauges. The question of which gauge is superior for which problem has often been raised, but never led to any consensus about its answer. Below, we will give an answer for the case of a short-range binding potential, where the SFA is expected to be most accurate [6], by comparing the SFA in L gauge and V gauge with the numerical solution of the TDSE.For a fixed nucleus and in the single-active-electron approximation, where the effects of all electrons but one are absorbed into an effective binding potential, the complete Hamiltonian in the presence of an external electromagnetic field can be decomposed aswhere the subscript x specifies the gauge (x = L, V) andThis operator contains the binding potential V (r) and is independent of the gauge. With the dipole approximat...

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S-matrix treatments of multichannel ionization of atoms by high-intensity lasers

Cited by 25 publications

References 18 publications

Comparative study on atomic ionization in bicircular laser fields by length and velocity gauges S-matrix theory*

Comparative study on atomic ionization in bicircular laser fields by length and velocity gauges S-matrix theory*

Comparison of two forms of theS-matrix element of strong-field photoionization

Strong-field approximation for intense-laser–atom processes: The choice of gauge

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