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

Excited states as resonances in the photon-atom continuum and the natural-line-shape problem

Lixin Xiao, Jurij W. Darewych, Marko Horbatsch

Published Oct 1, 1992• 3 citations
Publisher

Abstract

A variational Hamiltonian method for quantum field theory is applied to the problem of natural line shape. Within scalar quantum electrodynamics, coupled variational equations are derived for the scattering of photons from a scalar (pionic) atom. It is shown that the coupled equations have a continuous spectrum for all energies above the atomic ground state. Excited states of the atom appear as resonances in particular partial-wave cross sections. The line center and shape are derived from the behavior of the photon-atom scattering phase shifts.

DOI
10.1103/physreva.46.4026

Related papers

Quantum electrodynamical theory for the natural shape of the spectral line

В. М. Шабаев

In order to study the natural spectral line shape in the framework of quantum electrodynamics the resonance photon scattering on the relativistic few-electron atom is considered. The general case of the few overlapping levels is studied. In the resonance approximation the calculation formulae for the differential and total scattering cross-sections are obtained. The equations allowing improvement of the resonance approximation are also derived.

Journal of Physics A Mathematical and General•Dec 7, 1991•20 citations

Natural Line Shape

Francis E. Low

The covariant methods of Feynman and Dyson are applied to the problem of line shape. It is shown that the line center depends almost completely on the form of the ${{S}_{\mathrm{Fe}}}^{\ensuremath{'}}$ function, that is the Feynman-type Green's function for the electron interacting with an external field ${{A}_{\ensuremath{\mu}}}^{e}$ and with the quantized radiation field. A finite equation for ${{S}_{\mathrm{Fe}}}^{\ensuremath{'}}$ is derived, from which the line center and shape may be calculated to any desired accuracy. The method is illustrated by two examples: the elastic scattering of photons by a one electron atom in its ground state and the emission of photons by the same type of atom following thermal excitation.

Physical Review•Oct 1, 1952•189 citations

Spectral Theory of an Exactly Solvable Quantum-Optical Oscillator

Sam Johar, Joseph Kraisler

We study a one-dimensional single-excitation model of a scalar photon field coupled to a continuum of two-level atoms with quadratic density. The resulting matrix Hamiltonian has an unbounded spatially varying coupling and is not semibounded. We prove that it is essentially self-adjoint and determine its spectrum explicitly. The continuous spectrum is the half-line $(-\infty,Ω]$, where $Ω$ is the atomic resonance frequency, while the spectrum above $Ω$ consists of a strictly increasing sequence of simple eigenvalues. These eigenvalues are characterized by the interlaced zeros of the Airy function and its derivative and satisfy \begin{align*} ω_n = \left(\frac{3πg n}{4}\right)^{1/2} + \fracΩ{4} + O(n^{-1/2}). \end{align*} The analysis is based on a nonlinear spectral reduction that yields a confining massless relativistic oscillator above $Ω$ and an inverted oscillator below $Ω$.

arXiv:2610.18421•Oct 13, 2026•0 citations

On the gauge of the natural lineshape

Adam Stokes

We use a general formulation of nonrelativistic quantum electrodynamics in which the gauge freedom is carried by the arbitrary transverse component of the the Green’s function for the divergence operator to calculate the natural lineshape of spontaneous emission, thus discerning the full dependence of the result on the choice of gauge. We also use a representation of the Hamiltonian in which the virtual field associated with the atomic ground state is explicitly absent. We con-sider two processes by which the atom is excited; the first is resonant absorption of incident radiation with a sharp line. This treatment is then adapted to derive a resonance fluorescence rate associated with the Lamb line in atomic hydrogen. Sec-ond we consider the atom’s excitation due to irradiation with a laser pulse treated semi-classically. An experiment could be used to reveal which of the calculated line-shape distributions is closest to the measured one. This would provide an answer to a question of fundamental importance; how does one best describe atom-radiation interactions with the canonical formalism? 1

•Jan 1, 2014•5 citations

SPECTROSCOPY OF ATOMS IN A STRONG LASER FIELD: NEW METHOD TO SENSING AC STARK EFFECT, MULTIPHOTON RESONANCES PARAMETERS AND IONIZATION CROSS-SECTIONS

В. В. Буяджи, О. В. Глушков, Valery F. Mansarliysky +2 more

The resonant multiphoton resonances shifts and widths and ionization cross-sections for multielectron atoms in a intense laser radiation field are studied. It is carried out a new consistent approach to atom in a strong realistic laser field, based on the relativistic energy formalism (S-matrix adiabatic formalism), relativistic Dirac equation Green function method and relativistic many-body perturbation theory with the Dirac-Kohn-Sham zeroth approximation. In relativistic theory, the Gell-Mann and Low adiabatic formula for energy shift is connected with electrodynamical scattering matrice, which includes interaction with as a laser field as a photon vacuum field (radiative decay). The optimized basis of the relativistic orbitals is generated with using a minimization procedure for the gauge-non-invariant contribution (the fourth-order of the QED perturbation theory) to the radiation width of atomic state. An approach to treating the multiphoton atomic processes is outlined on example of H, Cs, Kr,Mg etc. Analysis shows that the shift and width of the multi-photon resonance line for the interaction “atom- multimode laser pulse” is greater than the corresponding shift and width for a case of the “atom- single-mode pulse” (the Lorenz pulse model) interaction. From the physical point of view it is naturally provided by action of the photon-correlation effects and influence of the laser pulse multi-modity.

Sensor Electronics and Microsystem Technologies•Oct 1, 2015•21 citations

Effects of coupled atomic states on the resonance scattering of radiation

Rajat Srivastava, Peter R. Fontana

The excitation and decay probabilities for resonance scattering of radiation from an atom with two coupled excited states in an external static field are calculated as a function of time and frequency. Various oscillatory terms are found in the probabilities. These oscillations depend on the frequency of radiation, the external coupling and the energy difference between the excited states. Two special cases are investigated in detail. In the first case where one of the excited states does not decay a 'hole' appears in the emission line at a frequency equal to the frequency difference between the ground state and the unperturbed non-decaying excited state. In the second case where the two excited states decay with the same rate, one of the two lines in the emission spectrum is suppressed and the other is enhanced.

Journal of Physics B Atomic and Molecular Physics•Jun 1, 1974•3 citations
A variational Hamiltonian method for quantum field theory is applied to the problem of natural line shape. Within scalar quantum electrodynamics, coupled variational equations are derived for the scattering of photons from a scalar (pionic) atom. It is shown that the coupled equations have a continuous spectrum for all energies above the atomic ground state. Excited states of the atom appear as resonances in particular partial-wave cross sections. The line center and shape are derived from the behavior of the photon-atom scattering phase shifts.
The covariant methods of Feynman and Dyson are applied to the problem of line shape. It is shown that the line center depends almost completely on the form of the ${{S}_{\mathrm{Fe}}}^{\ensuremath{'}}$ function, that is the Feynman-type Green's function for the electron interacting with an external field ${{A}_{\ensuremath{\mu}}}^{e}$ and with the quantized radiation field. A finite equation for ${{S}_{\mathrm{Fe}}}^{\ensuremath{'}}$ is derived, from which the line center and shape may be calculated to any desired accuracy. The method is illustrated by two examples: the elastic scattering of photons by a one electron atom in its ground state and the emission of photons by the same type of atom following thermal excitation.
We study a one-dimensional single-excitation model of a scalar photon field coupled to a continuum of two-level atoms with quadratic density. The resulting matrix Hamiltonian has an unbounded spatially varying coupling and is not semibounded. We prove that it is essentially self-adjoint and determine its spectrum explicitly. The continuous spectrum is the half-line (−∞,Ω](-\infty,Ω](−∞,Ω], where ΩΩΩ is the atomic resonance frequency, while the spectrum above ΩΩΩ consists of a strictly increasing sequence of simple eigenvalues. These eigenvalues are characterized by the interlaced zeros of the Airy function and its derivative and satisfy \begin{align*} ω_n = \left(\frac{3πg n}{4}\right)^{1/2} + \fracΩ{4} + O(n^{-1/2}). \end{align*} The analysis is based on a nonlinear spectral reduction that yields a confining massless relativistic oscillator above ΩΩΩ and an inverted oscillator below ΩΩΩ.
We use a general formulation of nonrelativistic quantum electrodynamics in which the gauge freedom is carried by the arbitrary transverse component of the the Green’s function for the divergence operator to calculate the natural lineshape of spontaneous emission, thus discerning the full dependence of the result on the choice of gauge. We also use a representation of the Hamiltonian in which the virtual field associated with the atomic ground state is explicitly absent. We con-sider two processes by which the atom is excited; the first is resonant absorption of incident radiation with a sharp line. This treatment is then adapted to derive a resonance fluorescence rate associated with the Lamb line in atomic hydrogen. Sec-ond we consider the atom’s excitation due to irradiation with a laser pulse treated semi-classically. An experiment could be used to reveal which of the calculated line-shape distributions is closest to the measured one. This would provide an answer to a question of fundamental importance; how does one best describe atom-radiation interactions with the canonical formalism? 1
The resonant multiphoton resonances shifts and widths and ionization cross-sections for multielectron atoms in a intense laser radiation field are studied. It is carried out a new consistent approach to atom in a strong realistic laser field, based on the relativistic energy formalism (S-matrix adiabatic formalism), relativistic Dirac equation Green function method and relativistic many-body perturbation theory with the Dirac-Kohn-Sham zeroth approximation. In relativistic theory, the Gell-Mann and Low adiabatic formula for energy shift is connected with electrodynamical scattering matrice, which includes interaction with as a laser field as a photon vacuum field (radiative decay). The optimized basis of the relativistic orbitals is generated with using a minimization procedure for the gauge-non-invariant contribution (the fourth-order of the QED perturbation theory) to the radiation width of atomic state. An approach to treating the multiphoton atomic processes is outlined on example of H, Cs, Kr,Mg etc. Analysis shows that the shift and width of the multi-photon resonance line for the interaction “atom- multimode laser pulse” is greater than the corresponding shift and width for a case of the “atom- single-mode pulse” (the Lorenz pulse model) interaction. From the physical point of view it is naturally provided by action of the photon-correlation effects and influence of the laser pulse multi-modity.
The excitation and decay probabilities for resonance scattering of radiation from an atom with two coupled excited states in an external static field are calculated as a function of time and frequency. Various oscillatory terms are found in the probabilities. These oscillations depend on the frequency of radiation, the external coupling and the energy difference between the excited states. Two special cases are investigated in detail. In the first case where one of the excited states does not decay a 'hole' appears in the emission line at a frequency equal to the frequency difference between the ground state and the unperturbed non-decaying excited state. In the second case where the two excited states decay with the same rate, one of the two lines in the emission spectrum is suppressed and the other is enhanced.