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

Two-electron-state molecule in strong electric fields

József Somlói, András Lörincz

Published Mar 1, 1991• 8 citations
Publisher

Abstract

The paper deals with the interaction of strong and pulsed radiation fields with a two-electron-state molecule. The light pulses under discussion are shorter than a vibrational period. The molecule is treated within the framework of the Born-Oppenheimer approximation. The nuclear degree of freedom is modeled as displaced harmonic potentials for the ground and the excited electronic states, respectively. Using coherent states as expansion tools for the nuclear motion, analytical expressions are given for the short-pulse region defined by the duration of the light pulse and the displacement of the potentials. The resonance condition is derived for this region. It is shown that within the short-pulse region the two-electron-state molecule mimics the behavior of a two-electron-state atom. Longer pulses are treated with numerical methods. The concept of resonance is discussed for the longer-pulse case. Limitations on population inversion are considered.

DOI
10.1103/physreva.43.2397

Related papers

Aspects of impulsive stimulated scattering in molecular systems

Vı́ctor Romero-Rochı́n, Jeffrey A. Cina

We introduce a theoretical framework to describe the interaction of an electromagnetic radiation field and a molecular system, such as a single molecule or a molecular crystal. By knowing in advance which electronic transitions are in resonance with the frequencies of the incident radiation, we propose a procedure to reduce the full problem to a description in terms of an effective Hamiltonian that fully takes into account the vibrational (nuclear) degrees of freedom, but that explicitly involves only those electronic states that meet the resonance condition. The influence of the rest of the electronic states appears as the polarizability of the system. We keep only those terms that give rise to Raman scattering but the scheme allows for a systematic inclusion of higher-order multiphoton processes. The resulting effective Hamiltonian is used to study the interaction of ultrashort laser pulses with a single molecule and with a molecular crystal. As applications, we study the interaction of a single ultrashort nonresonant pulse, and a train of such pulses, with a single molecule; we show that via Raman scattering the pulse impulsively transfers momentum to the molecule leaving it in a vibrational coherent state. We also study the interaction of two crossed laser pulses with a molecular crystal and show that a diffraction grating of lattice vibrations is impulsively created.

Physical Review A•Jul 1, 1994•10 citations

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

Excitation of Rydberg states of atoms and diatomic molecules by short laser impulses

G. K. Ivanov, Valeria L. Bodneva

Excitation of multilevel Rydberg states (atoms and diatomic molecules) is studied under an intense time-periodic perturbation that is instantaneously turned on and off. For a one-quantum excitation from a lower lying state, general expressions for the Laplace images of the population amplitudes of Rydberg states are obtained with regard to their decay characteristics. It is shown that the problem considered is reduced to the determination of the positions and widths of the energy levels of a quantum system in the field of monochromatic laser radiation of the same frequency and intensity as that in a pulse mode. To determine these quantities, an integral formulation is proposed for the eigenvalue problem for energies that is relatively simply solved with regard to the effect of the ionic core and its complex vibration-rotation structure on diatomic molecules. The specific features of the excitation of Rydberg states and the behavior of Rydberg wave packets are studied depending on the intensity and duration of laser radiation. A quantum phenomenon of rotational orientation of electron-excited diatomic molecules is considered.

Journal of Experimental and Theoretical Physics•Mar 1, 2003•0 citations

Interaction of Rydberg atoms with two contrapropagating ultrashort laser pulses

Andrey V. Lugovskoy, Igor Bray

In this paper we investigate how Rydberg atoms respond to perturbation by two contrapropagating ultrashort laser pulses. We consider the case where the durations of both pulses ${\ensuremath{\tau}}_{1}$ and ${\ensuremath{\tau}}_{2}$ are shorter than the inverse of the initial-state energy ${\ensuremath{\epsilon}}_{i}^{\ensuremath{-}1}$. When acting alone such a pulse passes through the atom without noticeable alteration in the atomic state. The situation is different if two such pulses interfere in the region of atom localization. In this case the atomic response is significantly enhanced. This is due to the nonzero momentum transferred to the electron by the interplay of the electric field of one pulse and the magnetic field of the other. The sudden perturbation approximation is used to evaluate the transition probabilities. They are shown to depend on the atom position with respect to the pulse interference region. This dependence is determined by the relationship between the atomic diameter ${d}_{i}$ and the interference-region size $l=c({\ensuremath{\tau}}_{1}+{\ensuremath{\tau}}_{2})$ ($c$ is the speed of light). If ${d}_{i}\ensuremath{\ll}l$ this dependence is sensitive to the function form of the pulses. For sufficiently strong fields the atoms can be ionized completely. In the opposite case of ${d}_{i}\ensuremath{\gg}l$ the transition probabilities are sensitive to the electron density distribution along the propagation direction. The probabilities of the initial-state destruction and atom ionization drop as $l∕{d}_{i}$ irrespective of the characteristics of the pulses.

Physical Review A•Jun 2, 2006•3 citations

On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules

Alex Brown, William J. Meath

The absolute laser phase dependence of the time-dependent populations of the molecular states, including the steady-state (long time) populations of the states, associated with the interaction of a molecule with a pulsed laser is investigated using illustrative two-level examples. One-photon transitions, including the effects of permanent dipoles, are discussed as a function of the pulse duration, intensity, and (absolute) laser phase, for selected laser frequencies. The effects of laser phase can be large, depending on the values of the pulse duration for a given frequency and intensity. The effects of permanent dipoles, relative to no permanent dipoles, are significant for large laser field strengths ε0. When the laser-molecule coupling parameter b=μ12ε0/E21⩾0.2, where μ12 and E21 are the transition dipole and energy difference between the ground and excited states, respectively, the dynamics of the pulse-molecule interaction are (strongly) phase dependent, independent of pulse duration, whereas the corresponding steady-state populations of the molecular states may or may not be phase-dependent depending on the pulse duration. Analytical rotating wave approximations for pulsed laser-molecule interactions are useful for interpreting the dynamics and the steady-state results as a function of field strength and pulse duration, including the effects of permanent dipole moments. The results reported in this paper are based on molecular parameters associated with an S0→S1 electronic transition in a dipolar molecule. However, they are presented in reduced form and therefore can be scaled to other regions of the electromagnetic spectrum. Short, intense pulses at or beyond the limits of current laser technology will often be required for the types of absolute laser phase effects of this paper to be appreciable for electronic excitations. The discussion, in the UV-VIS, also suffers from the use of a two-level model and from the requirement of field intensities that can be beyond the Keldysh limit. For other spectral regions, these absolute laser phase effects will be much more readily applicable.

The Journal of Chemical Physics•Dec 1, 1998•37 citations

Model of coherent electron dynamics in molecules

Jan Šenk

An ultrashort laser pulse photoionizing the molecule produces a superposition of a few cationic states. The coupling between the electrons and the nuclei has been predicted to cause fast decoherence. In this thesis, a two-dimensional model of coupled electron- nuclear dynamics in molecules is constructed. It is based on a harmonic potential in the nuclear degree of freedom and a double harmonic potential representing two centers that bind the electrons. The electronic potential's dependence on the nuclear configuration facilitates the coupling. Thanks to the simplicity of the model, it is numerically exactly solvable. We use the basis of its eigenstates to calculate the evolution of any initial state. Several quantities are used to measure decoherence and unravel the underlying mecha- nisms. Especially useful is the Wigner quasiprobability distribution. A few fundamental cases of the model are analyzed, and it is used to approximate the coherence dynamics in the normal modes of the H2O+ cation. 1

•Jan 1, 2023•0 citations
The paper deals with the interaction of strong and pulsed radiation fields with a two-electron-state molecule. The light pulses under discussion are shorter than a vibrational period. The molecule is treated within the framework of the Born-Oppenheimer approximation. The nuclear degree of freedom is modeled as displaced harmonic potentials for the ground and the excited electronic states, respectively. Using coherent states as expansion tools for the nuclear motion, analytical expressions are given for the short-pulse region defined by the duration of the light pulse and the displacement of the potentials. The resonance condition is derived for this region. It is shown that within the short-pulse region the two-electron-state molecule mimics the behavior of a two-electron-state atom. Longer pulses are treated with numerical methods. The concept of resonance is discussed for the longer-pulse case. Limitations on population inversion are considered.
We introduce a theoretical framework to describe the interaction of an electromagnetic radiation field and a molecular system, such as a single molecule or a molecular crystal. By knowing in advance which electronic transitions are in resonance with the frequencies of the incident radiation, we propose a procedure to reduce the full problem to a description in terms of an effective Hamiltonian that fully takes into account the vibrational (nuclear) degrees of freedom, but that explicitly involves only those electronic states that meet the resonance condition. The influence of the rest of the electronic states appears as the polarizability of the system. We keep only those terms that give rise to Raman scattering but the scheme allows for a systematic inclusion of higher-order multiphoton processes. The resulting effective Hamiltonian is used to study the interaction of ultrashort laser pulses with a single molecule and with a molecular crystal. As applications, we study the interaction of a single ultrashort nonresonant pulse, and a train of such pulses, with a single molecule; we show that via Raman scattering the pulse impulsively transfers momentum to the molecule leaving it in a vibrational coherent state. We also study the interaction of two crossed laser pulses with a molecular crystal and show that a diffraction grating of lattice vibrations is impulsively created.
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.
Excitation of multilevel Rydberg states (atoms and diatomic molecules) is studied under an intense time-periodic perturbation that is instantaneously turned on and off. For a one-quantum excitation from a lower lying state, general expressions for the Laplace images of the population amplitudes of Rydberg states are obtained with regard to their decay characteristics. It is shown that the problem considered is reduced to the determination of the positions and widths of the energy levels of a quantum system in the field of monochromatic laser radiation of the same frequency and intensity as that in a pulse mode. To determine these quantities, an integral formulation is proposed for the eigenvalue problem for energies that is relatively simply solved with regard to the effect of the ionic core and its complex vibration-rotation structure on diatomic molecules. The specific features of the excitation of Rydberg states and the behavior of Rydberg wave packets are studied depending on the intensity and duration of laser radiation. A quantum phenomenon of rotational orientation of electron-excited diatomic molecules is considered.
In this paper we investigate how Rydberg atoms respond to perturbation by two contrapropagating ultrashort laser pulses. We consider the case where the durations of both pulses ${\ensuremath{\tau}}_{1}$ and ${\ensuremath{\tau}}_{2}$ are shorter than the inverse of the initial-state energy ${\ensuremath{\epsilon}}_{i}^{\ensuremath{-}1}$. When acting alone such a pulse passes through the atom without noticeable alteration in the atomic state. The situation is different if two such pulses interfere in the region of atom localization. In this case the atomic response is significantly enhanced. This is due to the nonzero momentum transferred to the electron by the interplay of the electric field of one pulse and the magnetic field of the other. The sudden perturbation approximation is used to evaluate the transition probabilities. They are shown to depend on the atom position with respect to the pulse interference region. This dependence is determined by the relationship between the atomic diameter di{d}_{i}di​ and the interference-region size $l=c({\ensuremath{\tau}}_{1}+{\ensuremath{\tau}}_{2})$ (ccc is the speed of light). If ${d}_{i}\ensuremath{\ll}l$ this dependence is sensitive to the function form of the pulses. For sufficiently strong fields the atoms can be ionized completely. In the opposite case of ${d}_{i}\ensuremath{\gg}l$ the transition probabilities are sensitive to the electron density distribution along the propagation direction. The probabilities of the initial-state destruction and atom ionization drop as l∕dil∕{d}_{i}l∕di​ irrespective of the characteristics of the pulses.
The absolute laser phase dependence of the time-dependent populations of the molecular states, including the steady-state (long time) populations of the states, associated with the interaction of a molecule with a pulsed laser is investigated using illustrative two-level examples. One-photon transitions, including the effects of permanent dipoles, are discussed as a function of the pulse duration, intensity, and (absolute) laser phase, for selected laser frequencies. The effects of laser phase can be large, depending on the values of the pulse duration for a given frequency and intensity. The effects of permanent dipoles, relative to no permanent dipoles, are significant for large laser field strengths ε0. When the laser-molecule coupling parameter b=μ12ε0/E21⩾0.2, where μ12 and E21 are the transition dipole and energy difference between the ground and excited states, respectively, the dynamics of the pulse-molecule interaction are (strongly) phase dependent, independent of pulse duration, whereas the corresponding steady-state populations of the molecular states may or may not be phase-dependent depending on the pulse duration. Analytical rotating wave approximations for pulsed laser-molecule interactions are useful for interpreting the dynamics and the steady-state results as a function of field strength and pulse duration, including the effects of permanent dipole moments. The results reported in this paper are based on molecular parameters associated with an S0→S1 electronic transition in a dipolar molecule. However, they are presented in reduced form and therefore can be scaled to other regions of the electromagnetic spectrum. Short, intense pulses at or beyond the limits of current laser technology will often be required for the types of absolute laser phase effects of this paper to be appreciable for electronic excitations. The discussion, in the UV-VIS, also suffers from the use of a two-level model and from the requirement of field intensities that can be beyond the Keldysh limit. For other spectral regions, these absolute laser phase effects will be much more readily applicable.
An ultrashort laser pulse photoionizing the molecule produces a superposition of a few cationic states. The coupling between the electrons and the nuclei has been predicted to cause fast decoherence. In this thesis, a two-dimensional model of coupled electron- nuclear dynamics in molecules is constructed. It is based on a harmonic potential in the nuclear degree of freedom and a double harmonic potential representing two centers that bind the electrons. The electronic potential's dependence on the nuclear configuration facilitates the coupling. Thanks to the simplicity of the model, it is numerically exactly solvable. We use the basis of its eigenstates to calculate the evolution of any initial state. Several quantities are used to measure decoherence and unravel the underlying mecha- nisms. Especially useful is the Wigner quasiprobability distribution. A few fundamental cases of the model are analyzed, and it is used to approximate the coherence dynamics in the normal modes of the H2O+ cation. 1