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

Russian Journal of Physical Chemistry B

Modeling of the population dynamics of the states of a three-level molecule in the field of a monochromatic light wave

V. A. Morozov, Nikolai D. Chuvylkin, E. A. Smolensky

Published Nov 1, 2015• 2 citations
Publisher

Abstract

The formalism and the results of modeling the population dynamics of the states of a three-level model molecule by using the optical Bloch equations are compared with the formalism and results of modeling the population dynamics of the states of the molecule–radiation field system by means of quantum electrodynamics. Examples of significant differences between the results of application of these approaches regarding the behavior of the time dependences of the populations of the states of the molecule, the values of the quantum yield of the photoreaction or the intensity of Rayleigh and resonance Raman scattering are given. These differences are the greater, the higher the rate of the radiative decay of the resonantly excited state with the transition of the molecule to the ground state as compared to the rate of the decay of this state with the transition of the molecule to the third molecule (undecaying) state.

DOI
10.1134/s1990793115060081

Related papers

Mathematical modeling of the dynamics of photoreactions of a five-level molecule

V. A. Morozov, Yu. M. Dubina, Evgenii A. Smolenskii

A mathematical modeling of the time evolution of the populations of the states of a five-level molecule during transformation of resonant monochromatic irradiation and spontaneous emission from the highest-energy state excited by a short pulse of light is performed. The formalism of the optical Bloch equations and quantum theory of radiation are applied a composite system consisting of a molecule and a quantized radiation field. The results of simulation of the evolution of the population of the states of the molecule in the case of spontaneous emission are similar for both of these two approaches, but differ significantly in the case of conversion by the molecule of monochromatic radiation. These differences are the greater, the higher the intensity of resonance Rayleigh scattering or (and) relaxed fluorescence, as a result of which the molecule returns to the initial ground state. An explanation of the nature of these differences is given.

Russian Journal of Physical Chemistry B•Mar 1, 2017•1 citation

Modeling of quantum beats of the state populations of a molecule

V. A. Morozov

Analytical expressions for describing the dynamics of the populations of the states of a five-level model molecule during fluorescence reflecting the quantum beats of the populations of its two excited degenerate states coupled by dynamic interaction are derived. The cases of excitation of the molecule by a short light pulse in a state with an energy higher than the energy of the degenerate states and into one of the degenerate states are considered. The populations of states are determined by solving the Schrödinger equation for the amplitudes of probability of populating the states of the composite system comprised of the molecule and a quantized radiation field. It was found that the resulting expressions satisfy the optical Bloch equations for the considered dynamics of the populations of the molecule’s states. Significant distinctions of the present results on the simulation of quantum beats from the corresponding simulation results reported in some works, performed based on different approaches, are revealed. The reasons for these differences are discussed.

Russian Journal of Physical Chemistry B•May 1, 2017•0 citations

Modeling the Dynamics of Secondary Photoreactions

V. A. Morozov

Abstract A system of equations is obtained for describing the dynamics of the secondary photoreaction of two-level molecules emitting spontaneous fluorescence at initial excitation of one of them. The system is derived using the Schrödinger equation for the compound system of a reagent molecule, a reaction product molecule, and a quantized radiation field. Unlike those commonly used in similar modeling, optical Bloch equations describing the dynamics of a non-selective (collective) population of the ground states of two molecules (i.e., the total number of molecules of a pair in their ground states), the system of equations (and its generalization allowing for the longitudinal and transverse relaxation of excited states of molecules) allows estimates of the relative number of reagent molecules and the product in their ground states, the use of which provides a complete idea of the effectiveness of the reaction.

Russian Journal of Physical Chemistry A•Aug 1, 2021•2 citations

Mathematical modeling of the population dynamics of “dark” states of a three-level system

V. A. Morozov, Yu. M. Dubina

Mathematical modeling of the population dynamics is performed for states of a three-level system (atom) with a V-type configuration transforming a light pulse. It is assumed that the excited eigenstates of the atom are degenerate and coupled by coherent interaction, one of the states being radiating (radiative), while the other state is nonradiating (“dark”). The population dynamics of atomic states is described on the basis of numerical solutions of equations for the matrix elements of the density operator. The dependence of the efficiency of population of the atomic dark state from the values of the parameters of an irradiation pulse and from the ratio of the period of population oscillations of excited atomic states (caused by their coherent interaction) to the lifetime of the atomic radiating state is determined. Typical examples of the time dependence of the population of states of the atom considered are presented for the cases of irradiation by a short (as compared to the lifetime of the radiating state) sinusoidal light pulse and by a long rectangular light pulse with the resonance carrier frequency.

Optics and Spectroscopy•May 1, 2012•0 citations

Modeling the Dynamics of the Excitation of Two-Level Particles with Pulses of Bichromatic Irradiation

V. A. Morozov

Abstract Mathematical modeling of the excitation dynamics of an isolated two-level particle under bichromatic irradiation is carried out on basis of solutions of the Schrödinger equation for the probability amplitudes of the states of the composite system of the particle and an interaction two-mode quantized radiation field, with the photons for each of which in a superposition state at the initial time. An analytical expression describing the change in the time of the population of the excited state of a particle in the adsorption of one of the irradiation photons in the simplest case when the irradiation is a sequence of identical pulses of a sinusoidal form is obtained. The obtained time dependence is compared with the time dependence of the diagonal matrix element of the statistical operator of the particle in the excited state found on the basis of the numerical solution of the system of the optical Bloch equations, with the corresponding irradiation described by the classical theory. Examples of significant differences in the type of these compared time dependences for a number of characteristic cases of irradiation are given.

Russian Journal of Physical Chemistry B•May 1, 2019•0 citations

Time- and frequency-resolved light scattering by isolated molecules. I. Nonperturbative treatment of a single-doorway model

S. L. Wang, E. C. Lim, Willem Siebrand

Light scattering by isolated small and intermediate-size molecules is studied theoretically. A quantum-mechanical model is developed that treats the molecule and the radiation field on equal terms and allows a nonperturbative solution for arbitrary wave forms and field strengths. The molecular states are described in terms of a basis set of zeroth-order states chosen so as to minimize the number of excited molecular states in the laser frequency range that combines radiatively with the initial (ground) state, i.e., that act as doorways for the field. Detailed calculations are restricted to the case of a single doorway. Closed-form expressions are obtained for the frequency-resolved scattering rates and time-resolved scattering spectra, including fluorescence and Rayleigh–Raman components, for a variety of conditions, including δ(t) excitation, excitation by a Lorentzian light pulse, by a coherent train of pulses and stationary excitation. The case of nonlinear scattering by very intense pulses is also investigated. Model calculations are reported for systems of 1–3 molecular levels. It is found that in general phase relations are maintained so that the coherence survives as long as the signal.

The Journal of Chemical Physics•Jun 15, 1986•5 citations
The formalism and the results of modeling the population dynamics of the states of a three-level model molecule by using the optical Bloch equations are compared with the formalism and results of modeling the population dynamics of the states of the molecule–radiation field system by means of quantum electrodynamics. Examples of significant differences between the results of application of these approaches regarding the behavior of the time dependences of the populations of the states of the molecule, the values of the quantum yield of the photoreaction or the intensity of Rayleigh and resonance Raman scattering are given. These differences are the greater, the higher the rate of the radiative decay of the resonantly excited state with the transition of the molecule to the ground state as compared to the rate of the decay of this state with the transition of the molecule to the third molecule (undecaying) state.
A mathematical modeling of the time evolution of the populations of the states of a five-level molecule during transformation of resonant monochromatic irradiation and spontaneous emission from the highest-energy state excited by a short pulse of light is performed. The formalism of the optical Bloch equations and quantum theory of radiation are applied a composite system consisting of a molecule and a quantized radiation field. The results of simulation of the evolution of the population of the states of the molecule in the case of spontaneous emission are similar for both of these two approaches, but differ significantly in the case of conversion by the molecule of monochromatic radiation. These differences are the greater, the higher the intensity of resonance Rayleigh scattering or (and) relaxed fluorescence, as a result of which the molecule returns to the initial ground state. An explanation of the nature of these differences is given.
Analytical expressions for describing the dynamics of the populations of the states of a five-level model molecule during fluorescence reflecting the quantum beats of the populations of its two excited degenerate states coupled by dynamic interaction are derived. The cases of excitation of the molecule by a short light pulse in a state with an energy higher than the energy of the degenerate states and into one of the degenerate states are considered. The populations of states are determined by solving the Schrödinger equation for the amplitudes of probability of populating the states of the composite system comprised of the molecule and a quantized radiation field. It was found that the resulting expressions satisfy the optical Bloch equations for the considered dynamics of the populations of the molecule’s states. Significant distinctions of the present results on the simulation of quantum beats from the corresponding simulation results reported in some works, performed based on different approaches, are revealed. The reasons for these differences are discussed.
Abstract A system of equations is obtained for describing the dynamics of the secondary photoreaction of two-level molecules emitting spontaneous fluorescence at initial excitation of one of them. The system is derived using the Schrödinger equation for the compound system of a reagent molecule, a reaction product molecule, and a quantized radiation field. Unlike those commonly used in similar modeling, optical Bloch equations describing the dynamics of a non-selective (collective) population of the ground states of two molecules (i.e., the total number of molecules of a pair in their ground states), the system of equations (and its generalization allowing for the longitudinal and transverse relaxation of excited states of molecules) allows estimates of the relative number of reagent molecules and the product in their ground states, the use of which provides a complete idea of the effectiveness of the reaction.
Mathematical modeling of the population dynamics is performed for states of a three-level system (atom) with a V-type configuration transforming a light pulse. It is assumed that the excited eigenstates of the atom are degenerate and coupled by coherent interaction, one of the states being radiating (radiative), while the other state is nonradiating (“dark”). The population dynamics of atomic states is described on the basis of numerical solutions of equations for the matrix elements of the density operator. The dependence of the efficiency of population of the atomic dark state from the values of the parameters of an irradiation pulse and from the ratio of the period of population oscillations of excited atomic states (caused by their coherent interaction) to the lifetime of the atomic radiating state is determined. Typical examples of the time dependence of the population of states of the atom considered are presented for the cases of irradiation by a short (as compared to the lifetime of the radiating state) sinusoidal light pulse and by a long rectangular light pulse with the resonance carrier frequency.
Abstract Mathematical modeling of the excitation dynamics of an isolated two-level particle under bichromatic irradiation is carried out on basis of solutions of the Schrödinger equation for the probability amplitudes of the states of the composite system of the particle and an interaction two-mode quantized radiation field, with the photons for each of which in a superposition state at the initial time. An analytical expression describing the change in the time of the population of the excited state of a particle in the adsorption of one of the irradiation photons in the simplest case when the irradiation is a sequence of identical pulses of a sinusoidal form is obtained. The obtained time dependence is compared with the time dependence of the diagonal matrix element of the statistical operator of the particle in the excited state found on the basis of the numerical solution of the system of the optical Bloch equations, with the corresponding irradiation described by the classical theory. Examples of significant differences in the type of these compared time dependences for a number of characteristic cases of irradiation are given.
Light scattering by isolated small and intermediate-size molecules is studied theoretically. A quantum-mechanical model is developed that treats the molecule and the radiation field on equal terms and allows a nonperturbative solution for arbitrary wave forms and field strengths. The molecular states are described in terms of a basis set of zeroth-order states chosen so as to minimize the number of excited molecular states in the laser frequency range that combines radiatively with the initial (ground) state, i.e., that act as doorways for the field. Detailed calculations are restricted to the case of a single doorway. Closed-form expressions are obtained for the frequency-resolved scattering rates and time-resolved scattering spectra, including fluorescence and Rayleigh–Raman components, for a variety of conditions, including δ(t) excitation, excitation by a Lorentzian light pulse, by a coherent train of pulses and stationary excitation. The case of nonlinear scattering by very intense pulses is also investigated. Model calculations are reported for systems of 1–3 molecular levels. It is found that in general phase relations are maintained so that the coherence survives as long as the signal.