Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Acta Physica Sinica

HIGH-ORDER HARMONICS FROM TWO-LEVEL ATOMS IN LASER FIELD WITH LOW-FREQUENCY

Weixing Qu, Yu Wei, HU SU-XING, XU ZHI-ZHAN, 上海 201800 中国科学院上海光学精密机械研究所强光光学开放研究实验室

Published Jan 1, 1998• 0 citations
Publisher

Abstract

This paper derives the equation of motion followed by the induced polarization of the two-level atoms subject to the laser field with frequency much lower than that of the transition between the levels.With the approximate solution to the equation of motion under the conditions of the weak external field and of the ultra-intense one,we obtain the characteristics of the corresponding high-order harmonics from the two-level atoms.

DOI
10.7498/aps.47.1458

Related papers

THEORETICAL DESCRIPTION OF HARMONICS GENERATION FOR TWO-LEVEL ATOMS

Weixing Qu, HU SU-XING, XU ZHI-ZHAN +1 more

The process of harmonic generation for a two-level atom is investigated theoretically.The model of oscillator driven by a nonlinear external force is used to simulate an induced porlarization of the atom,and the characteristics in harmonic spectrum of the atom are analyzed for a weak and a super-intense laser pulses.

Acta Physica Sinica•Jan 1, 1998•0 citations

THEORETICAL DESCRIPTION OF HARMONICS GENERATION FOR TWO LEVEL ATOMS

Ei X

Abstract The process of harmonic generation for a two level atom is investigated theoretically.The model of oscillator driven by a nonlinear external force is used to simulate an induced porlarization of the atom,and the characteristics in harmonic spectrum of the atom are analyzed for a weak and a super intense laser pulses.

Acta Physica Sinica•Jan 1, 1998•0 citations

High-order harmonic generation and parametric oscillations

Emilio Fiordilino

The differential equation of the mean electric-dipole moment induced by a laser field in a two-level atom is that of a driven parametric oscillator with time-dependent frequency. In the case of a laser field with constant intensity, a connection with the Mathieu equation is stated and it is shown from the known theory that the spectrum emitted must present only odd harmonics of the pumping field.

Physical Review A•Jan 1, 1999•15 citations

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 +1 more

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.

Journal of Modern Optics•Sep 1, 1999•7 citations

Interference spectra in a two-level atom

Constantine Mavroyannis

We have considered the interference spectra arising from the competition between a spontaneous process and one induced by a laser field in a two-level atom. Expressions for the spectral functions have been derived describing the spectra of the excited and ground states of the atom in the low- and high-intensity limit of the laser field. For the excited-state spectra in the low-intensity limit, the frequency profiles of the two peaks, which arise from the spontaneous and the induced processes, cancel each other out completely near the center of the line, while for the ground state the induced process dominates. For finite values of the detuning, the spectra of the excited state consist of two peaks, which have positive and negative frequency profiles, respectively. The computed spectra have been graphically presented and discussed. In the high-intensity limit, the dynamic Stark effect dominates the spectra of the excited and ground states of the atom. Expressions for the correlation functions have been derived that describe the emission or the absorption of a laser photon at two different times. The derived expressions for the corresponding delay functions in the low- and high-intensity limits have been found to be identical to those recently proposed in the literature. The laser field has been treated as a classical as well as a quantized entity.

Canadian Journal of Physics•Dec 1, 1990•6 citations

Generation of ultrashort pulses of harmonics

Ph Antoine, B. Piraux, Dejan B. Milošević +1 more

We study harmonic generation by a single atom exposed to two short perpendicularly polarized laser pulses. The two perpendicular electric fields oscillate at two different frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$. Hence, the resultant field has a polarization which depends on time. Since harmonics are emitted when the resultant oscillating field is linearly polarized, it is expected that a short pulse of harmonics may be emitted if the external field is linearly polarized during a short period of time. We show that, indeed, the atom may emit an ultrashort pulse of a given harmonic. This result has been obtained by time-frequency analyzing the acceleration of the induced dipole moment with a filter whose frequency bandwidth is smaller than twice the frequency of the external field. Our calculation of the dipole acceleration is based on the numerical solution of the time-dependent Schr\"odinger equation. We then address the question of how far it is possible to reduce the duration of the emitted pulse of one given harmonic by adjusting both ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ and keeping the amplitude of this pulse significant. In order to answer to this question, we used the quantum version of the two-step model [M. Lewenstein et al., Phys. Rev. A 49, 2117 (1994)].

Physical Review A•Sep 1, 1996•39 citations
This paper derives the equation of motion followed by the induced polarization of the two-level atoms subject to the laser field with frequency much lower than that of the transition between the levels.With the approximate solution to the equation of motion under the conditions of the weak external field and of the ultra-intense one,we obtain the characteristics of the corresponding high-order harmonics from the two-level atoms.
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 have considered the interference spectra arising from the competition between a spontaneous process and one induced by a laser field in a two-level atom. Expressions for the spectral functions have been derived describing the spectra of the excited and ground states of the atom in the low- and high-intensity limit of the laser field. For the excited-state spectra in the low-intensity limit, the frequency profiles of the two peaks, which arise from the spontaneous and the induced processes, cancel each other out completely near the center of the line, while for the ground state the induced process dominates. For finite values of the detuning, the spectra of the excited state consist of two peaks, which have positive and negative frequency profiles, respectively. The computed spectra have been graphically presented and discussed. In the high-intensity limit, the dynamic Stark effect dominates the spectra of the excited and ground states of the atom. Expressions for the correlation functions have been derived that describe the emission or the absorption of a laser photon at two different times. The derived expressions for the corresponding delay functions in the low- and high-intensity limits have been found to be identical to those recently proposed in the literature. The laser field has been treated as a classical as well as a quantized entity.
We study harmonic generation by a single atom exposed to two short perpendicularly polarized laser pulses. The two perpendicular electric fields oscillate at two different frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$. Hence, the resultant field has a polarization which depends on time. Since harmonics are emitted when the resultant oscillating field is linearly polarized, it is expected that a short pulse of harmonics may be emitted if the external field is linearly polarized during a short period of time. We show that, indeed, the atom may emit an ultrashort pulse of a given harmonic. This result has been obtained by time-frequency analyzing the acceleration of the induced dipole moment with a filter whose frequency bandwidth is smaller than twice the frequency of the external field. Our calculation of the dipole acceleration is based on the numerical solution of the time-dependent Schr\"odinger equation. We then address the question of how far it is possible to reduce the duration of the emitted pulse of one given harmonic by adjusting both ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ and keeping the amplitude of this pulse significant. In order to answer to this question, we used the quantum version of the two-step model [M. Lewenstein et al., Phys. Rev. A 49, 2117 (1994)].