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

Quantum electrodynamics of intense photon beams. New approximation method

Iwo Białynicki‐Birula, Zofia Białynicka-Birula

Published Sep 1, 1976• 81 citations
Publisher

Abstract

We develop a new approximation method for determining resonance properties of atomic systems interacting with intense photon beams. This method, based on an improved iteration procedure, leads to analytic expressions for the atomic density matrix from which positions of the resonances are determined. Our iteration procedure is more rapidly convergent than the continued-fraction method, and already in its second step reproduces the Bloch-Siegert shift of the one-photon resonance within 1 ppm.

DOI
10.1103/physreva.14.1101

Related papers

Bloch-Siegert shift for multiphoton resonances

Peter L. Hagelstein, Irfan U. Chaudhary

Recently there has been theoretical and experimental interest in Bloch-Siegert shifts in an intense photon field. A perturbative treatment becomes difficult in this multiphoton regime. We present a unitary transform and rotated model, which allows us to get accurate results away from the level anticrossings. A simple variational energy estimate leads to a new expression for the dressed two-level system energy which is accurate, and useful over a wide range of the dimensionless coupling constant.

arXiv:0709.1958•Sep 12, 2007•1 citation

Multiphoton transitions: Approximations for the effective Hamiltonian

Leonard Rosenberg

The problem of calculating transition probabilities for an atom interacting with an intense radiation field is set up within the context of an effective Hamiltonian formalism. This has the virtue that resonance effects are properly accounted for at the outset; more generally, it provides a convenient framework for approximations. Through the restriction of the class of intermediate states to be included in the construction of the effective potential, a unitary (nonperturbative) model is obtained. A successive approximation procedure for determining the effective potential, which is based on continued-fraction representations, is described. While very likely intractable for the true problem, this successive approximation procedure can be implemented, for the model effective potential, with the aid of a generalized Rayleigh-Ritz procedure described here. The level-shift matrix is constructed from the effective potential; it determines the transition probabilities, linewidths, and energy-level displacements induced by the field. We derive variational expressions of the Kohn type for each of the elements of the model level-shift matrix.

Physical Review A•Sep 1, 1976•14 citations

Micromaser equations without the rotating-wave approximation: the nonresonant case

F. De Zela, E. Solano, A. M. Gago

The equations for the micromaser are derived without assuming the validity of the rotating- wave approximation (RWA) in the Scully-Lamb model for a single-mode maser off resonance. The treatment is based on Swain's continued fractions approach, by which the eigenvalues and eigenvectors of the Hamiltonian describing the system of atoms plus cavity field can be iteratively determined to any desired order and then used to obtain the micromaser equations. These are valid to second order in the parameter g, the coupling constant of the atom-field interaction. The procedure can be extended, to any desired order in g, by successive iterations. Through numerically evaluating the micromaser spectrum we compare our results with those of the RWA. We predict a relative shift, stemming from the Bloch-Siegert shift, which in case of the spectra corresponding to two-photon correlations should be measurable through atomic selective field ionization.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 5, 1996•0 citations

Perturbation Method for Atoms in Intense Light Beams

Walter C. Henneberger

The problem of interaction of atoms with intense light is reformulated via a time-dependent unitary transformation. An effective electronic binding potential is obtained. The effective perturbation remains bounded as the intensity of the incident light increases.

Physical Review Letters•Sep 16, 1968•720 citations

Quantum Electrodynamics of Intense Photon Beams

Iwo Białynicki‐Birula, Zofia Białynicka-Birula

A new formula for induced transition amplitudes in intense photon beams is derived which relates the photon-number description to the coherent-field description. According to this formula transition amplitudes describing processes in which $m$ photons are added to the intense one-mode beam or subtracted from that beam are equal to the Fourier coefficients of the corresponding amplitude in the external field, expanded with respect to the phase of the classical field. The same formula is used to study the expectation values of dynamical variables in $n$-photon states leading to the conclusion that for large $n$ such states are very much like classical statistical states with a given amplitude and evenly distributed phase.

Physical Review A•Dec 1, 1973•29 citations

Resonance behavior of a two-level quantum system in a two-frequency field

Wilhelmus M. Ruyten

Based on the vanishing-damping continued-fraction method which I developed previously for the analysis of the resonance behavior of a two-level atom in a two-frequency field with equal intensities in the two field modes [W. M. Ruyten, Phys. Rev. A 40, 1447 (1989)], I analyze here the related problem in which the two field intensities are unequal. Several analytical results are derived, namely, expressions for the lowest-order Bloch-Siegert shifts of all resonances, and an expression for the positions of the resonances in the limit of one strong and one weak field. It is shown that, in this limit, the resonances exhibit level crossings of the field-atom system.

Physical Review A•Oct 1, 1992•12 citations
We develop a new approximation method for determining resonance properties of atomic systems interacting with intense photon beams. This method, based on an improved iteration procedure, leads to analytic expressions for the atomic density matrix from which positions of the resonances are determined. Our iteration procedure is more rapidly convergent than the continued-fraction method, and already in its second step reproduces the Bloch-Siegert shift of the one-photon resonance within 1 ppm.
The problem of calculating transition probabilities for an atom interacting with an intense radiation field is set up within the context of an effective Hamiltonian formalism. This has the virtue that resonance effects are properly accounted for at the outset; more generally, it provides a convenient framework for approximations. Through the restriction of the class of intermediate states to be included in the construction of the effective potential, a unitary (nonperturbative) model is obtained. A successive approximation procedure for determining the effective potential, which is based on continued-fraction representations, is described. While very likely intractable for the true problem, this successive approximation procedure can be implemented, for the model effective potential, with the aid of a generalized Rayleigh-Ritz procedure described here. The level-shift matrix is constructed from the effective potential; it determines the transition probabilities, linewidths, and energy-level displacements induced by the field. We derive variational expressions of the Kohn type for each of the elements of the model level-shift matrix.
The equations for the micromaser are derived without assuming the validity of the rotating- wave approximation (RWA) in the Scully-Lamb model for a single-mode maser off resonance. The treatment is based on Swain's continued fractions approach, by which the eigenvalues and eigenvectors of the Hamiltonian describing the system of atoms plus cavity field can be iteratively determined to any desired order and then used to obtain the micromaser equations. These are valid to second order in the parameter g, the coupling constant of the atom-field interaction. The procedure can be extended, to any desired order in g, by successive iterations. Through numerically evaluating the micromaser spectrum we compare our results with those of the RWA. We predict a relative shift, stemming from the Bloch-Siegert shift, which in case of the spectra corresponding to two-photon correlations should be measurable through atomic selective field ionization.
A new formula for induced transition amplitudes in intense photon beams is derived which relates the photon-number description to the coherent-field description. According to this formula transition amplitudes describing processes in which mmm photons are added to the intense one-mode beam or subtracted from that beam are equal to the Fourier coefficients of the corresponding amplitude in the external field, expanded with respect to the phase of the classical field. The same formula is used to study the expectation values of dynamical variables in nnn-photon states leading to the conclusion that for large nnn such states are very much like classical statistical states with a given amplitude and evenly distributed phase.
Based on the vanishing-damping continued-fraction method which I developed previously for the analysis of the resonance behavior of a two-level atom in a two-frequency field with equal intensities in the two field modes [W. M. Ruyten, Phys. Rev. A 40, 1447 (1989)], I analyze here the related problem in which the two field intensities are unequal. Several analytical results are derived, namely, expressions for the lowest-order Bloch-Siegert shifts of all resonances, and an expression for the positions of the resonances in the limit of one strong and one weak field. It is shown that, in this limit, the resonances exhibit level crossings of the field-atom system.