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

Journal of Physics B Atomic Molecular and Optical Physics

Model of resonant high harmonic generation in multi-electron systems

Pavel V. Redkin, Rashid Ashirovich Ganeev

Published Aug 3, 2017• 6 citations
Publisher

Abstract

Abstract We extend the 4-step analytical model of resonant enhancement of high harmonic generation to the systems possessing resonant transitions of inner-shell electrons. Resonant enhancement is explained by lasing without inversion in a three-level system of ground, excited and shifted resonant states, which are coupled to the fundamental field and its high harmonics. The role of inelastic scattering is studied by simulation of an excited state’s population dynamics. It is shown that maximal gain is achieved when the energy shift between the excited state and resonant state is close to the energy of the fundamental photon. To prove the concept we demonstrate the enhancement of harmonics in the In plasma using different pumps.

DOI
10.1088/1361-6455/aa83d1

Related papers

Enhancing resonant four-wave mixing via dressed inversions

Christoph H. Keitel

Summary form only given.We provide additional insight into the process of resonant four-wave mixing via an analysis in the dressed states basis. As opposed to the common situation in lasing without inversion, both the excited and the ground state of the transition with enhanced coherent field generation are coupled to each other via external driving fields. For this reason we find more similarities to the well-understood process of light amplification in driven two-level systems. Initial gain does not need to arise from a spontaneous photon or a probe field but arises due to the coherence established directly by the strong external driving laser fields.

Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations

Population inversion by nonlinear excitation of atomic inner shells

Misha Ivanov, M. G. Malakhov

We present a detailed analysis of the creation of population inversion and coherent UV radiation with a new scheme, i.e., nonlinear excitation of an inner atomic electron in a strong laser field, accompanied by filling the resulting inner-shell vacancy with an external-shell electron. Our analysis is given for the experimental results obtained by Boyer et al. in 1984 [ J. Opt. Soc. Am. B1, 3 ( 1984)]. The principal new features of the scheme under consideration are the following: (1) the two-electron character of atomic excitation with subsequent emission of a high-energy photon, (2) the initial absence of multiphoton resonance between the ground state and the level to be excited, and (3) strong-field-induced level crossing and excitation of the upper working level by means of Landau–Zener-type transitions.

Journal of the Optical Society of America B•Apr 1, 1990•2 citations

Efficient generation of moderately high harmonics by multiphoton resonant excitation of atoms

H. K. Avetissian, B. R. Avchyan, G. F. Mkrtchian

The coherent scattering spectrum of a three-level atom driven by an intense laser field with multiphoton resonant excitation is considered. The spectrum corresponding to harmonic generation is investigated both analytically and numerically for different initial atomic states. The analytical calculations are based on the generalized rotating wave approximation, which allows one to explain obtained spectra containing in general both even and odd harmonics. The results applied to the hydrogen atom show that one can achieve efficient generation of moderately high harmonics using multiphoton resonant excitation by appropriate laser pulses.

Physical Review A•Feb 11, 2008•19 citations

Laser oscillations

E. Rosencher, B. Vinter

Introduction We were able to show in Chapter 3 that a medium in which we can obtain a population inversion (i.e. a situation in which the population density in the excited state is greater than that in the fundamental level) allows for optical gain of an electromagnetic wave having a frequency near to the resonant frequency of the system. By introducing feedback of the amplified signal into the medium, the system can be made to oscillate naturally, resulting in laser oscillations . To obtain this population inversion, we must introduce at least a third (and perhaps even a fourth) energy level into the system. (We saw how a two-level system under the influence of an intense pump beam will saturate with no resulting population inversion.) The aim then of this chapter is to introduce the concepts necessary to extend our two-level system into a working model capable of illustrating the phenomenon of laser oscillation. We will not spend too much time discussing atomic transition lasers as they do not figure readily in our treatment of quantum electronic properties of semiconductors. An exception will be made, however; we brush upon the particular topics of a diode pumped laser in Complement 4.E and a quantum cascade laser in Complement 13.H. Population inversion and optical amplification Population inversion We will show how population inversion can be achieved by carrier transfer from higher lying levels to the upper level of a two-level subsystem of interest.

Cambridge University Press eBooks•May 30, 2002•0 citations

Chaos and nonlinearities in high harmonic generation

Emilio Fiordilino

Abstract Linearity is a fundamental postulate of quantum mechanics which is occasionally the subject of debate. This paper investigates the possibility of checking this assumption by using a laser field. We study the corrections caused by the presence of a small nonlinearity in the Hamiltonian of a quantum system. As a model we use a simplified two-level quantum system whose states are coupled by a small off-diagonal term proportional to the population of the upper level. The nonlinearity causes spontaneous decay of the upper level, shift and broadening of the line and the sensitive dependence of the final state on the initial condition. The presence of a strong laser field, resonant with the atomic transition, enhances the population transfer among the levels and introduces quantitative and qualitative modifications of the spectra of high order harmonic generation (HHG); these are cumulative effects which can be subject to experimental checks. Experiments are needed in order to set an upper limit to the nonlinear term.

Laser Physics Letters•Oct 17, 2016•4 citations

Super-Dressed Two-Level Atom: Very High Harmonic Generation and Multi-Resonances

A. E. Kaplan, P. L. Shkolnikov

We show that a simple nonperturbative two-level model of an atom driven by a very strong periodic field, results in a rich picture of very high harmonic generation and related phenomena. It reproduces experimentally observed plateau, yields for the first time simple analytic formulas for the plateau cutoff frequency, critical driving intensity, and saturation, and predicts intensity-induced multi-resonances. One of the most fascinating phenomenon discovered recently in nonlinear interaction of light with atoms and ions, is very high-order (up to 135) odd harmonic generation (HHG) by intense (∼ 1013 W/cm2 and higher) optical laser radiation in rare gasses and some ions [1], The spectra of generated harmonics drasticly deviate from the perturbation theory predictions [2], In particular, intensity of harmonics, falling monotonically with their orders only up to a certain point, levels off forming a so-called “plateau", and falls monotonically again beyond it. Generally, harmonte generation depends on phase-matching conditions and nonlinear response of individual atoms. It has recently become clear however [3,4] that the major features of HHG, in particular the plateau, result mainly from general properties of atomic nonlinear response. The most direct and apparently successful way so far to approach the problem theoretically has been numerical simulation of the Schrödinger [2,5-7] (including an empiric rule [6]) for many-electron atoms using Hartry-Slater approximation. This approach requires, however, tremendous amount of calculations and involves many processes, making it difficult to gain simple insights. An interesting simplified model [8] based on 3-D delta-potential with a single (ground) level [9] produces results in integration form. The idea of retaining a single energy scale (ionization energy) brings one close to an even simpler system: a two-level model atom. A two-level model of HHG [10], however, due to various complications introduced into it, failed to generate simple results, whereas an analytic solution [11] holds for a virtually degenerate two-level model only (see below) which is unapplicable to the experimental conditions [1-4,7,9]; besides, no relaxation was considered in [10,11].

Shortwavelength: Physics with Intense Laser Pulses•Jan 1, 1993•1 citation
Abstract We extend the 4-step analytical model of resonant enhancement of high harmonic generation to the systems possessing resonant transitions of inner-shell electrons. Resonant enhancement is explained by lasing without inversion in a three-level system of ground, excited and shifted resonant states, which are coupled to the fundamental field and its high harmonics. The role of inelastic scattering is studied by simulation of an excited state’s population dynamics. It is shown that maximal gain is achieved when the energy shift between the excited state and resonant state is close to the energy of the fundamental photon. To prove the concept we demonstrate the enhancement of harmonics in the In plasma using different pumps.
Summary form only given.We provide additional insight into the process of resonant four-wave mixing via an analysis in the dressed states basis. As opposed to the common situation in lasing without inversion, both the excited and the ground state of the transition with enhanced coherent field generation are coupled to each other via external driving fields. For this reason we find more similarities to the well-understood process of light amplification in driven two-level systems. Initial gain does not need to arise from a spontaneous photon or a probe field but arises due to the coherence established directly by the strong external driving laser fields.
We present a detailed analysis of the creation of population inversion and coherent UV radiation with a new scheme, i.e., nonlinear excitation of an inner atomic electron in a strong laser field, accompanied by filling the resulting inner-shell vacancy with an external-shell electron. Our analysis is given for the experimental results obtained by Boyer et al. in 1984 [ J. Opt. Soc. Am. B1, 3 ( 1984)]. The principal new features of the scheme under consideration are the following: (1) the two-electron character of atomic excitation with subsequent emission of a high-energy photon, (2) the initial absence of multiphoton resonance between the ground state and the level to be excited, and (3) strong-field-induced level crossing and excitation of the upper working level by means of Landau–Zener-type transitions.
The coherent scattering spectrum of a three-level atom driven by an intense laser field with multiphoton resonant excitation is considered. The spectrum corresponding to harmonic generation is investigated both analytically and numerically for different initial atomic states. The analytical calculations are based on the generalized rotating wave approximation, which allows one to explain obtained spectra containing in general both even and odd harmonics. The results applied to the hydrogen atom show that one can achieve efficient generation of moderately high harmonics using multiphoton resonant excitation by appropriate laser pulses.
Introduction We were able to show in Chapter 3 that a medium in which we can obtain a population inversion (i.e. a situation in which the population density in the excited state is greater than that in the fundamental level) allows for optical gain of an electromagnetic wave having a frequency near to the resonant frequency of the system. By introducing feedback of the amplified signal into the medium, the system can be made to oscillate naturally, resulting in laser oscillations . To obtain this population inversion, we must introduce at least a third (and perhaps even a fourth) energy level into the system. (We saw how a two-level system under the influence of an intense pump beam will saturate with no resulting population inversion.) The aim then of this chapter is to introduce the concepts necessary to extend our two-level system into a working model capable of illustrating the phenomenon of laser oscillation. We will not spend too much time discussing atomic transition lasers as they do not figure readily in our treatment of quantum electronic properties of semiconductors. An exception will be made, however; we brush upon the particular topics of a diode pumped laser in Complement 4.E and a quantum cascade laser in Complement 13.H. Population inversion and optical amplification Population inversion We will show how population inversion can be achieved by carrier transfer from higher lying levels to the upper level of a two-level subsystem of interest.
Abstract Linearity is a fundamental postulate of quantum mechanics which is occasionally the subject of debate. This paper investigates the possibility of checking this assumption by using a laser field. We study the corrections caused by the presence of a small nonlinearity in the Hamiltonian of a quantum system. As a model we use a simplified two-level quantum system whose states are coupled by a small off-diagonal term proportional to the population of the upper level. The nonlinearity causes spontaneous decay of the upper level, shift and broadening of the line and the sensitive dependence of the final state on the initial condition. The presence of a strong laser field, resonant with the atomic transition, enhances the population transfer among the levels and introduces quantitative and qualitative modifications of the spectra of high order harmonic generation (HHG); these are cumulative effects which can be subject to experimental checks. Experiments are needed in order to set an upper limit to the nonlinear term.
We show that a simple nonperturbative two-level model of an atom driven by a very strong periodic field, results in a rich picture of very high harmonic generation and related phenomena. It reproduces experimentally observed plateau, yields for the first time simple analytic formulas for the plateau cutoff frequency, critical driving intensity, and saturation, and predicts intensity-induced multi-resonances. One of the most fascinating phenomenon discovered recently in nonlinear interaction of light with atoms and ions, is very high-order (up to 135) odd harmonic generation (HHG) by intense (∼ 1013 W/cm2 and higher) optical laser radiation in rare gasses and some ions [1], The spectra of generated harmonics drasticly deviate from the perturbation theory predictions [2], In particular, intensity of harmonics, falling monotonically with their orders only up to a certain point, levels off forming a so-called “plateau", and falls monotonically again beyond it. Generally, harmonte generation depends on phase-matching conditions and nonlinear response of individual atoms. It has recently become clear however [3,4] that the major features of HHG, in particular the plateau, result mainly from general properties of atomic nonlinear response. The most direct and apparently successful way so far to approach the problem theoretically has been numerical simulation of the Schrödinger [2,5-7] (including an empiric rule [6]) for many-electron atoms using Hartry-Slater approximation. This approach requires, however, tremendous amount of calculations and involves many processes, making it difficult to gain simple insights. An interesting simplified model [8] based on 3-D delta-potential with a single (ground) level [9] produces results in integration form. The idea of retaining a single energy scale (ionization energy) brings one close to an even simpler system: a two-level model atom. A two-level model of HHG [10], however, due to various complications introduced into it, failed to generate simple results, whereas an analytic solution [11] holds for a virtually degenerate two-level model only (see below) which is unapplicable to the experimental conditions [1-4,7,9]; besides, no relaxation was considered in [10,11].