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

Physical Review A

High-order harmonic generation by excited helium: The atomic polarization effect

Vitali Averbukh

Published Apr 20, 2004• 23 citations
Publisher

Abstract

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 $2\phantom{\rule{0.2em}{0ex}}^{1}P$ helium subject to infrared radiation. The strong coupling between the $2\phantom{\rule{0.2em}{0ex}}^{1}P$ and $2\phantom{\rule{0.2em}{0ex}}^{1}S$ 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.

DOI
10.1103/physreva.69.043406

Related papers

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

Quantum-optical analysis of high-order harmonic generation

Javier Rivera Deán

High-order harmonic generation is a highly nonlinear phenomenon in which ultraviolet photons are generated when an atom is subjected to a high-intensity infrared laser field. This process has been extensively studied, but most of the formulations employ a semiclassical approach in which the electron is treated quantum mechanically while the driving field is treated classically. Although some recent studies follow a quantum-optical approach, the existing descriptions do not offer much insight into the physical processes taking place, and are always limited to monochromatic driving fields. In this thesis, we construct a fully quantized framework for strong-field ionization and high-harmonic generation that allows for quantization of both the driving field and the ultraviolet emission. The presented formalism extends the Strong-Field Approximation theory to a quantum-optical framework, with which we can obtain an analytical expression for the electron and the driving field after the interaction.

•Sep 9, 2019•1 citation

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

E. Cormier, P. Lambropoulos

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.

Journal of Physics B Atomic Molecular and Optical Physics•Jul 28, 1997•15 citations

Nonclassical light generation and control from laser-driven semiconductor intraband excitations

Ivan Gonoskov, René Sondenheimer, Christian Hünecke +3 more

The generation of higher-order harmonic radiation originating from the interaction of intense laser pulses with matter is typically described semiclassically: While the electronic structure and dynamics of matter is described quantum mechanically, the intense light field is described classically---and accordingly the generated harmonic radiation. However, pioneering experiments on quantum optical properties of high-order harmonic generation (HHG) in atomic gases from the group of P. Tzallas [I. Gonoskov et al., Sci. Rep. 6, 32821 (2016) and N. Tsatrafyllis et al., Nat. Commun. 8, 15170 (2017)], and theoretical investigations from the group of M. Lewenstein [M. Lewenstein et al., Nat. Phys. 17, 1104 (2021) and P. Stammer et al., Phys. Rev. Lett. 128, 123603 (2022)] have impressively demonstrated that light's quantum properties are observable in the strong-field realm. In this paper, we develop a quantum optical description of HHG in a bulk semiconductor originating from the nonlinear Bloch current. This mechanism of HHG, known as the intraband current, constitutes the major contribution to the emission spectrum for harmonic with energies of quanta roughly below the bandgap. Under certain approximations, employing a quantum description of both light and matter, we obtain analytical solutions, which allow us to analyze the classical and quantum optical characteristics of the fundamental mode of light and the harmonic modes. We find intricate but sufficiently mild modifications of the photon statistics of the fundamental mode and coherent displacements depending on the parameters of the driving laser field. Similar to high-harmonic generation in atoms, the fundamental and emitted harmonic field modes are entangled. Moreover, our analytical model predicts parameter ranges where these quantum optical properties will be most pronounced, allowing protocols for quantum information processing with high photon numbers over a large range of frequencies.

Physical review. B./Physical review. B•Mar 7, 2024•23 citations

Two-Photon Resonant Third Order Harmonic Generation from Atoms and Ions Interacting with Intense Short Laser Pulses

Young Soon Kim, Jung Seock Choi, Baek Il Nam +4 more

We investigate the third order harmonic generation for model atoms interacting with intense short laser pulses. We focus on the cases where the ponderomotive energy is not big enough to generate high-order harmonics, and where resonant transitions between bound states are also as important as multi-photon ionization and low-order harmonic generation. We find that the third order harmonic intensity from a model hydrogen atom can decrease as the laser frequency draws near a resonance between bound states. We explain this result by looking into the ionization and Rabi oscillation from the numerical calculation of the time-dependent 1-D Schrödinger equation. In order to support our explanation we also investigate the populations of bound states that play an important role in this atomic process.

Key engineering materials•Jan 15, 2005•1 citation

High-harmonic generation from two weakly coupled molecules: a simple tight-binding model

Lina Bielke, Samuel Schöpa, Falk-Erik Wiechmann +2 more

The generation of high harmonics is a strongly nonlinear effect that allows to probe properties of the target and to study electron dynamics in matter. It has been investigated in many different kinds of targets, including molecular gases, liquids and solids. Recently, high-harmonic generation was studied in organic molecular crystals by Wiechmann et al. [Nat. Commun. 16, 9890 (2025)]. It was found that the laser-polarization-dependent harmonic yield is sensitive to the weak couplings between nearest- and next-nearest-neighbor molecules. In this paper, the impact of the laser polarization angle and the intermolecular interaction on the harmonic yield is examined in detail using a simple but insightful two-dimensional tight-binding system that models a molecular dimer, i.e. two weakly coupled molecules. We find that the intensities of lower harmonic orders tend to maximize for a laser polarization direction aligning with the molecular axes, whereas higher harmonic orders rather show the strongest yield for a polarization direction along the intermolecular axis. We further demonstrate that the harmonic order at which the maximum flips from the molecular to the intermolecular direction strongly depends on the intermolecular coupling strength. To gain a deeper insight into the origins of the findings, we include a detailed adiabatic analysis, showing that the flipping of the maximum yield towards the intermolecular direction is already contained qualitatively in the adiabatically following states.

quant-pharXiv:2512.02623•Dec 3, 2025
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 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)].
High-order harmonic generation is a highly nonlinear phenomenon in which ultraviolet photons are generated when an atom is subjected to a high-intensity infrared laser field. This process has been extensively studied, but most of the formulations employ a semiclassical approach in which the electron is treated quantum mechanically while the driving field is treated classically. Although some recent studies follow a quantum-optical approach, the existing descriptions do not offer much insight into the physical processes taking place, and are always limited to monochromatic driving fields. In this thesis, we construct a fully quantized framework for strong-field ionization and high-harmonic generation that allows for quantization of both the driving field and the ultraviolet emission. The presented formalism extends the Strong-Field Approximation theory to a quantum-optical framework, with which we can obtain an analytical expression for the electron and the driving field after the interaction.
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.
The generation of higher-order harmonic radiation originating from the interaction of intense laser pulses with matter is typically described semiclassically: While the electronic structure and dynamics of matter is described quantum mechanically, the intense light field is described classically---and accordingly the generated harmonic radiation. However, pioneering experiments on quantum optical properties of high-order harmonic generation (HHG) in atomic gases from the group of P. Tzallas [I. Gonoskov et al., Sci. Rep. 6, 32821 (2016) and N. Tsatrafyllis et al., Nat. Commun. 8, 15170 (2017)], and theoretical investigations from the group of M. Lewenstein [M. Lewenstein et al., Nat. Phys. 17, 1104 (2021) and P. Stammer et al., Phys. Rev. Lett. 128, 123603 (2022)] have impressively demonstrated that light's quantum properties are observable in the strong-field realm. In this paper, we develop a quantum optical description of HHG in a bulk semiconductor originating from the nonlinear Bloch current. This mechanism of HHG, known as the intraband current, constitutes the major contribution to the emission spectrum for harmonic with energies of quanta roughly below the bandgap. Under certain approximations, employing a quantum description of both light and matter, we obtain analytical solutions, which allow us to analyze the classical and quantum optical characteristics of the fundamental mode of light and the harmonic modes. We find intricate but sufficiently mild modifications of the photon statistics of the fundamental mode and coherent displacements depending on the parameters of the driving laser field. Similar to high-harmonic generation in atoms, the fundamental and emitted harmonic field modes are entangled. Moreover, our analytical model predicts parameter ranges where these quantum optical properties will be most pronounced, allowing protocols for quantum information processing with high photon numbers over a large range of frequencies.
We investigate the third order harmonic generation for model atoms interacting with intense short laser pulses. We focus on the cases where the ponderomotive energy is not big enough to generate high-order harmonics, and where resonant transitions between bound states are also as important as multi-photon ionization and low-order harmonic generation. We find that the third order harmonic intensity from a model hydrogen atom can decrease as the laser frequency draws near a resonance between bound states. We explain this result by looking into the ionization and Rabi oscillation from the numerical calculation of the time-dependent 1-D Schrödinger equation. In order to support our explanation we also investigate the populations of bound states that play an important role in this atomic process.
The generation of high harmonics is a strongly nonlinear effect that allows to probe properties of the target and to study electron dynamics in matter. It has been investigated in many different kinds of targets, including molecular gases, liquids and solids. Recently, high-harmonic generation was studied in organic molecular crystals by Wiechmann et al. [Nat. Commun. 16, 9890 (2025)]. It was found that the laser-polarization-dependent harmonic yield is sensitive to the weak couplings between nearest- and next-nearest-neighbor molecules. In this paper, the impact of the laser polarization angle and the intermolecular interaction on the harmonic yield is examined in detail using a simple but insightful two-dimensional tight-binding system that models a molecular dimer, i.e. two weakly coupled molecules. We find that the intensities of lower harmonic orders tend to maximize for a laser polarization direction aligning with the molecular axes, whereas higher harmonic orders rather show the strongest yield for a polarization direction along the intermolecular axis. We further demonstrate that the harmonic order at which the maximum flips from the molecular to the intermolecular direction strongly depends on the intermolecular coupling strength. To gain a deeper insight into the origins of the findings, we include a detailed adiabatic analysis, showing that the flipping of the maximum yield towards the intermolecular direction is already contained qualitatively in the adiabatically following states.