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Physical Review A

Why hyper-Raman lines are absent in high-order harmonic generation

ANTONINO DI PIAZZA, Emilio Fiordilino

Published May 29, 2001• 30 citations
Publisher

Abstract

The absence of hyper-Raman lines in the observed spectrum emitted by an atom in the presence of a strong laser field is explained by evaluating the spectrum emitted by a unidimensional atom. It is found that the lines are emitted during a short time interval by the atom and that they therefore are small when compared with harmonical lines that are instead emitted during the laser pulse.

DOI
10.1103/physreva.64.013802

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The absence of hyper-Raman lines in the observed spectrum emitted by an atom in the presence of a strong laser field is explained by evaluating the spectrum emitted by a unidimensional atom. It is found that the lines are emitted during a short time interval by the atom and that they therefore are small when compared with harmonical lines that are instead emitted during the laser pulse.
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We present the most prominent features in two-colour coherent control of high-order harmonic generation using a strongly driven two-level atom model, which are known to generate high harmonics as well as hyper-Raman lines with a plateau and a cut-off. Furthermore, for one laser field case, we find, when the hyper-Raman lines are located at the position of the high harmonics, that the high harmonics are strongly enhanced due to the interference effect between the high harmonics and the hyper-Raman lines. Within these conditions, by combining the laser field with another much weaker laser field, we show plentiful and strong high harmonics in the light spectrum of the driven atomic system.
High-order harmonic generations from a one-dimensional Coulomb potential atom are calculated with the initial state prepared as a coherent superposition between its ground and first excited states. When the energy difference of the two states is small, we can choose proper laser pulse such that the first excited state can be excited only to other bound states instead of being ionized. We show that only the hyper-Raman lines are observable instead of the harmonics. The energy difference of the ground and the first excited state can be deduced from the highest peak of the hyper-Raman lines. We further show that the similar results can be obtained by using a combination of two laser pulses with different frequencies interacting with the atom initially at the ground state.
Abstract Hyper-Raman lines (HRL) resulting from strong-field light–matter interaction have been predicted theoretically in the 1990s but never identified in high-order harmonic generation experiments. Here, we use a combination of 800 and 400 nm laser pulses to control independently the two processes required for the hyper-Raman emission: creation of a coherence between two electronic states and laser-dressing of these states. As a result we observe simultaneously high-order harmonics, XUV free induction decay and HRL. We investigate experimentally and numerically the properties of this novel emission source. It can be of high interest, amongst others, for high-resolution spatio-temporal spectroscopy of excited electronic states in the same fashion high-order harmonics generation provides it for ground state.
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.