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Journal of Modern Optics

Coherent control of high-order harmonic generation in a two-level atom driven by intense two-colour laser fields

Shangqing Gong, Zhongyang Wang, Si-de Du, Zhizhan Xu

Published Sep 1, 1999• 7 citations
Publisher

Abstract

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.

DOI
10.1080/09500349908231364

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Acta Physica Sinica•Jan 1, 1999•1 citation
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.
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.
We investigate the coherent and incoherent contributions of the scattering spectrum of strongly driven two-level atoms as a function of the initial preparation of the atomic system. The initial ``phasing'' of the coherent superposition of the excited and ground states is shown to influence strongly the generation of both harmonics and hyper-Raman lines. In particular, we point out conditions under which harmonic generation can be inhibited at the expense of the hyper-Raman lines. Our numerical findings are supported by approximate analytical evaluation in the dressed state picture.
Numerical results are presented on the spectrum of the light scattered into the vacuum modes by a two-level atom driven by a strong ramped field of frequency smaller than the natural atomic frequency. The attention is focused on the role of the hyper-Raman part of the spectrum, which is shown to decrease dramatically with increasing ramp time. It is suggested that this may explain lack of experimental observation of the hyper-Raman lines. For zero ramp time, the numerical intensity of both high-order harmonics and hyper-Raman peaks is shown to agree satisfactorily with previous analytical predictions except in the region of overlap of the two series of peaks. This lends support for the suggestion that the plateau in the spectrum is related to quantum-mechanical interference between high-order harmonics and hyper-Raman processes. There is also good agreement between the numerical amplitude of the plateau and previous analytical predictions. A physical mechanism for the cut-off frequency which terminates the plateau, based on approximate energy conservation in hyper-Raman transitions, is presented and is shown to be in agreement with present numerical and previous analytical results.