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Journal of Physics B Atomic Molecular and Optical Physics

Effect of a strong dressing field on the polarizability of atomic helium at harmonic frequencies

E. Cormier, P. Lambropoulos

Published Jul 28, 1997• 15 citations
Publisher

Abstract

We investigate the effect of a strong dressing field on the polarizability of atomic helium at harmonic frequencies. This study is carried out in a time-dependent non-perturbative calculation by looking at the harmonic spectrum resulting from the interaction with the combination of two fields: a strong pump field at the fundamental frequency and a weak probe field at some odd harmonic frequency. We present results for harmonic frequencies extending over the characteristic spectrum of high-order harmonic generation.

DOI
10.1088/0953-4075/30/14/006

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We investigate the effect of a strong dressing field on the polarizability of atomic helium at harmonic frequencies. This study is carried out in a time-dependent non-perturbative calculation by looking at the harmonic spectrum resulting from the interaction with the combination of two fields: a strong pump field at the fundamental frequency and a weak probe field at some odd harmonic frequency. We present results for harmonic frequencies extending over the characteristic spectrum of high-order harmonic generation.
Atomic polarization can have a profound effect on the generation of the high-order harmonics during the interaction of the polarized atom with intense field. In this work, the atomic polarization effect is investigated for the specific case of the 21P2\phantom{\rule{0.2em}{0ex}}^{1}P21P helium subject to infrared radiation. The strong coupling between the 21P2\phantom{\rule{0.2em}{0ex}}^{1}P21P and 21S2\phantom{\rule{0.2em}{0ex}}^{1}S21S states of helium is taken into account using a multichannel version of the strong-field approximation of Lewenstein and co-workers [Lewenstein et al., Phys. Rev. A 49, 2117 (1994); Antoine et al., Phys. Rev. A 53, 1725 (1996)]. The analysis reveals a strong dependence of the high-order harmonic generation efficiency on the atomic polarization. While the occurrence of the predicted effect can be explained in terms of the recollision model, its magnitude is deeply affected by the fast population oscillations between the excited bound states. Moreover, the induced bound-bound transitions bring about the interesting double-maximum structure in the ellipticity dependences of the emitted harmonics, both maxima occurring for nonzero field ellipticities. This unusual structure shows up even for the high-energy harmonics generated solely by the bound-continuum mechanism.
We present the first measurement of the vectorial response of strongly dressed helium atoms probed by an attosecond pulse train (APT) polarised either parallel or perpendicular to the dressing field polarisation. The transient absorption is probed as a function of delay between the APT and the linearly polarised 800 nm field of peak intensity . The APT spans the photon energy range 16–42 eV, covering the first ionisation energy of helium (24.59 eV). With parallel polarised dressing and probing fields, we observe modulations with periods of one half and one quarter of the dressing field period. When the polarisation of the dressing field is altered from parallel to perpendicular with respect to the APT polarisation we observe a large suppression in the modulation depth of the above ionisation threshold absorption. In addition to this we present the intensity dependence of the harmonic modulation depth as a function of delay between the dressing and probe fields, with dressing field peak intensities ranging from 2 × 10 12 to 2 × 10 14 . We compare our experimental results with a full-dimensional solution of the single-atom time-dependent (TD) Schrödinger equation obtained using the recently developed abinitio TD B-spline ADC method and find good qualitative agreement for the above threshold harmonics.
We present a theory of harmonic generation by a strongly driven atom within the framework of non-relativistic QED. The atom is assumed to possess a finite number N of levels and ionization is neglected. This atom is dressed by the driving field using a unitary time-dependent transformation. Within the quasistatic approximation this transformation is shown to lead from the bare to the Floquet atom. The interaction of the Floquet atom with the vacuum modes is derived and it is shown to give rise both to the high-order harmonic and to the hyper-Raman spectrum. In the case N=2 the spectrum of the light scattered into the vacuum modes can be evaluated analytically and it is shown to consist of two parts. Neglecting interference between these two parts, the first of them is the high-order harmonic spectrum displaying peaks at the odd harmonics of the driving field. The second part is the hyper-Raman spectrum which has finite bandwidth and which displays peaks at the even harmonics of the laser frequency, centred at the Stark-shifted natural atomic frequency. These two spectra partially overlap and they are discussed in various ranges of intensity of the driving field, both in the minimal coupling and in the multipolar scheme. The results support recent suggestions that the presence of the plateau is related to interference between the two spectra. The dependence of the high-order harmonic spectrum from the driving field intensity is found to be related to that of the hyper-Raman spectrum in such a way that when the former increases the latter decreases and vice versa. It is argued that this might help to explain the non-visibility of the hyper-Raman lines when the high-order harmonics are visible.
Two-electron processes can generate high harmonics beyond the conventional single-active-electron cutoff. Motivated by recent experimental evidence of an extended secondary plateau in the helium high-harmonic spectrum [S. Wang et al, Optica, (2023); S. Wang et al, In Print in Nature Photon., (2026)], we present a two-electron generalisation of the strong-field approximation. We analyse the resulting expressions using the saddle-point method and determine the extended cutoff. We find good agreement with classical predictions of cutoff scalings of 4.74.74.7 and 5.55.55.5 times the ponderomotive energy, which significantly exceed the established single-electron scaling of 3.17. We calculate high-harmonic spectra generated via a two-electron process in helium atoms driven by an intense few-cycle infrared laser pulse. Our results demonstrate that the harmonic spectrum extends far beyond the water window, reaching photon energies up to ≈1.2 keV\approx 1.2\,\mathrm{keV}≈1.2keV in the soft x-ray region. The large spectral bandwidth can support the generation of sub-attosecond soft x-ray pulses, which are of particular interest for probing ultrafast dynamics across matter, including applications in core-level spectroscopy and biological imaging.
We study the generation of high-order harmonics during the ionization process for atoms described by relativistic classical mechanics with a special focus on retardation and Doppler shifts. We will then extend the discussion to a regime for which the atom-laser interaction takes place in a static homogeneous magnetic field. We demonstrate theoretically the possibility to tune the strength of the magnetic field to relativistic resonances to enhance the frequency components in the scattered light harmonic signal.