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 Polonica A

Linearized Riccati Equation as a Tool for Nonlinear Optics of Weakly Excited Two-Level Systems

R. Parzyński, T. Kopyciuk

Published Jun 1, 2020• 1 citation
Publisher

Abstract

Linearized version of the Riccati-type differential equation for the ratio of population amplitudes in a laserdriven two-level system is used to calculate analytically the induced electric dipole moment.The formula found for the dipole moment is valid for weak excitations by smooth-shape pulses of arbitrary off-resonant frequencies, i.e., those producing neither exact one-photon nor odd multiphoton resonances.For a given pulse shape, the formula allows to express the Fourier components of the induced dipole moment as functions of both laser frequency and intensity and to find the field-dependent refractive index of the system versus laser frequency.

DOI
10.12693/aphyspola.137.1080

Related papers

Strong versus Weak Excitation in Frequency Mixing and Harmonic Generation by Two-Level Systems

R. Parzyński, T. Kopyciuk

In the limits of weak and strong excitation, we solve analytically the Riccati-type differential equation for a two-level system in the field of two different lasers and then use these solutions to find easy to handle formulae for the induced electric-dipole moment of the system.We apply these formulae to describe the effects of strong excitation in both the higher harmonics generation and multiphoton frequency mixing, namely the diminishing of the generation of harmonics of a given laser when an additional laser is turned on and the diminishing of the radiation at mixed frequencies with increasing strength of lasers under the condition of multiphoton excitation.

Acta Physica Polonica A•Nov 1, 2021•0 citations

Extreme Nonlinear Optics in Terms of Riccati-Type Equation

R. Parzyński, Agnieszka Pluciñska

In an approach based on the nonlinear Riccati-type differential equation for the ratio of the level population amplitudes, rather than on the optical Bloch equations, we describe the response of a two-level system to a few--cycle light pulse of intensity from the regime of extreme nonlinear optics, i.e., when the Rabi and transition frequencies are comparable.Emphasis is put on the dependence of the spectra of the scattered light on the carrier--envelope phase, duration and strength of both resonant and off-resonant pulses.

Acta Physica Polonica A•Dec 1, 2005•2 citations

Coherent radiation by two-level quantum systems with permanent dipole moments under multiphoton resonant laser excitation

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

The theory of coherent radiation emission in two-level quantum systems with permanent dipole moments at the multiphoton resonant excitation by moderately strong laser fields is presented. A simple analytic formula for the expectation value of a dipole moment operator is obtained. The spectrum corresponding to harmonic generation and low-frequency radiation on the generalized Rabi frequency is investigated both analytically and numerically. The effect of dynamic Stark shift on a dipole spectrum under direct multiphoton resonant excitation is considered.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 19, 2011•20 citations

Two-level system in a strong laser field: A comparative analysis between the Landau-Lifshitz solution and an exact numerical one

Raanan Bavli, Yuri I. Dakhnovskii

We numerically solve the problem of a two-level system in a near-resonance time-dependent electric field of arbitrary amplitude. The obtained radiation spectrum of the dipole moment is compared both to that of a Landau-Lifshitz (LL) textbook solution [Quantum Mechanics (Pergamon, New York, 1987), p. 145] and to an off-resonance analytical solution [Dakhnovskii and Bavli (unpublished)] obtained recently for both optical and tunneling initial conditions. We show that the LL solution is valid at low field intensities while the off-resonance analytic solution qualitatively describes the intermediate- and high-intensity regimes.

Physical Review A•Aug 1, 1993•9 citations

An Iterative Method for Extreme Optics of Two-Level Systems

R. Parzyński, Michał Sobczak, Agnieszka Pluciñska

We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period.The analytical solutions for subsequent intervals are then stuck together in an iterative procedure to cover the whole scale time of the laser pulse.Very good quality of the iterative method is shown by recovering with it a number of subtle effects met in earlier numerically calculated photon--emission spectra from model molecular ions, double quantum wells, atoms, and semiconductors.The method is used to describe novel, carrier-envelope offset phase effects in the region of extreme nonlinear optics, i.e., when two--level systems are exposed to pulses of only a few cycles in duration and strength ensuring the Rabi frequency to approach the laser light frequence.

arXiv:quant-ph/0407141•Acta Physica Polonica A•Dec 1, 2004•2 citations

Harmonic generation from ionization-damped two-level system in the framework of nonlinear Riccati-type equation

A. Plucińska, R. Parzyński

We formulate the problem of harmonic generation by a two-level system with ionization in terms of a nonlinear Riccati-type differential equation. Different simplified forms of this equation are solved analytically and the resulting photon-emission spectra are compared with those obtained by others along different lines. For the complete-form Riccati-type equation, we give an iterative code solving this equation for arbitrary laser pulses. The code is used to study the effect of ionization and turn-on of the laser pulse on the harmonic spectrum.

Journal of Modern Optics•Mar 12, 2007•9 citations
Linearized version of the Riccati-type differential equation for the ratio of population amplitudes in a laserdriven two-level system is used to calculate analytically the induced electric dipole moment.The formula found for the dipole moment is valid for weak excitations by smooth-shape pulses of arbitrary off-resonant frequencies, i.e., those producing neither exact one-photon nor odd multiphoton resonances.For a given pulse shape, the formula allows to express the Fourier components of the induced dipole moment as functions of both laser frequency and intensity and to find the field-dependent refractive index of the system versus laser frequency.
In the limits of weak and strong excitation, we solve analytically the Riccati-type differential equation for a two-level system in the field of two different lasers and then use these solutions to find easy to handle formulae for the induced electric-dipole moment of the system.We apply these formulae to describe the effects of strong excitation in both the higher harmonics generation and multiphoton frequency mixing, namely the diminishing of the generation of harmonics of a given laser when an additional laser is turned on and the diminishing of the radiation at mixed frequencies with increasing strength of lasers under the condition of multiphoton excitation.
In an approach based on the nonlinear Riccati-type differential equation for the ratio of the level population amplitudes, rather than on the optical Bloch equations, we describe the response of a two-level system to a few--cycle light pulse of intensity from the regime of extreme nonlinear optics, i.e., when the Rabi and transition frequencies are comparable.Emphasis is put on the dependence of the spectra of the scattered light on the carrier--envelope phase, duration and strength of both resonant and off-resonant pulses.
The theory of coherent radiation emission in two-level quantum systems with permanent dipole moments at the multiphoton resonant excitation by moderately strong laser fields is presented. A simple analytic formula for the expectation value of a dipole moment operator is obtained. The spectrum corresponding to harmonic generation and low-frequency radiation on the generalized Rabi frequency is investigated both analytically and numerically. The effect of dynamic Stark shift on a dipole spectrum under direct multiphoton resonant excitation is considered.
We numerically solve the problem of a two-level system in a near-resonance time-dependent electric field of arbitrary amplitude. The obtained radiation spectrum of the dipole moment is compared both to that of a Landau-Lifshitz (LL) textbook solution [Quantum Mechanics (Pergamon, New York, 1987), p. 145] and to an off-resonance analytical solution [Dakhnovskii and Bavli (unpublished)] obtained recently for both optical and tunneling initial conditions. We show that the LL solution is valid at low field intensities while the off-resonance analytic solution qualitatively describes the intermediate- and high-intensity regimes.
We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period.The analytical solutions for subsequent intervals are then stuck together in an iterative procedure to cover the whole scale time of the laser pulse.Very good quality of the iterative method is shown by recovering with it a number of subtle effects met in earlier numerically calculated photon--emission spectra from model molecular ions, double quantum wells, atoms, and semiconductors.The method is used to describe novel, carrier-envelope offset phase effects in the region of extreme nonlinear optics, i.e., when two--level systems are exposed to pulses of only a few cycles in duration and strength ensuring the Rabi frequency to approach the laser light frequence.
We formulate the problem of harmonic generation by a two-level system with ionization in terms of a nonlinear Riccati-type differential equation. Different simplified forms of this equation are solved analytically and the resulting photon-emission spectra are compared with those obtained by others along different lines. For the complete-form Riccati-type equation, we give an iterative code solving this equation for arbitrary laser pulses. The code is used to study the effect of ionization and turn-on of the laser pulse on the harmonic spectrum.