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

Generalized dressed-atom approach to atom-strong-field interactions—application to the theory of lasers and Bloch-Siegert shifts

P. R. Berman, Jehuda Ziegler

Published May 1, 1977• 33 citations
Publisher

Abstract

A generalized dressed-atom approach (GDAA) is developed to study the interaction of two or more strong fields with atomic and molecular systems. In the GDAA, part of the atom-field interaction is incorporated into the free-atom, free-field Hamiltonian and this expanded Hamiltonian is said to characterize a "dressed atom." The remaining atom-field interaction may then be thought to constitute a probe field interaction for this dressed atom. Provided that the dressed atom constitutes a reasonably good approximation to the true interaction, the GDAA should offer a relatively simple means for semiquantitatively predicting the positions of absorption resonances in quite complex atom-field systems. The GDAA is applied to the theory of a high-intensity, single-mode, standing-wave gas laser, the theory of Bloch-Siegert shifts, and the analysis of Autler-Townes or saturation spectroscopy experiments. The agreement between the GDAA and computer-determined values for laser resonance positions and Bloch-Siegert shifts is found to be surprisingly good over the entire range of applied field strengths. Some methods for using the GDAA to study complex spectroscopic systems are discussed.

DOI
10.1103/physreva.15.2042

Related papers

Comparison between dressed-atom and bare-atom pictures in laser spectroscopy

P. R. Berman, Rainer Salomaa

The theory of the interaction between radiation fields and atoms as applied to laser spectroscopy can be approached using either a bare-atom picture (BAP) or dressed-atom picture (DAP). In the BAP, the basis states are those of the free atoms and free field while, in the DAP, the basis states encompass some part of the atom-field interaction. The theory of saturation spectroscopy in three-level systems is discussed using both approaches. Whereas calculations are usually more easily done using the BAP, one can gain useful insight into the underlying physical processes from the DAP. Moreover, when the radiation field strengths (in frequency units) are larger than the relaxation rates in the problem, the DAP equations simplify considerably and lead to line-shape expressions which may be given a simple interpretation. The DAP is used to obtain resonance conditions for traveling-wave fields interacting with three- and four-level atoms and for a standing-wave saturator and traveling-wave probe interacting with a three-level atom. In addition, the DAP is applied to several problems involving optical coherent transients. A comparison is made between the various advantages of the BAP and DAP and an interesting duality between the two approaches is noted.

Physical Review A•May 1, 1982•89 citations

Autler-Townes effect for an atom in a 100% amplitude-modulated laser field. I. A dressed-atom approach

Michael F. Van Leeuwen, Stephanos Papademetriou, Carlos R. Stroud

A dressed-state rate-equation model is used to describe the Autler-Townes effect that is produced by a resonant 100% amplitude-modulated field driving a two-level resonance. The purpose of using this model is to give an intuitive interpretation of the rather complex absorption spectra that are produced when a weak probe field couples this strongly driven transition to a third atomic state. We obtain analytic expressions for the positions, strengths, and widths of the components of the absorption spectra, which are in excellent agreement with experimentally obtained spectra presented in the accompanying paper [S. Papademetriou, following paper, Phys. Rev. A 53, 997 (1996)]. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Feb 1, 1996•31 citations

Theory of dressed states in quantum optics

Marco Frasca

The dual Dyson series [M. Frasca, Phys. Rev. A $58$ 3439 (1998)] is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In fact, both the Dyson series and its dual, by renormalization-group methods to remove secular terms from the perturbation series, give the opportunity for a full study of the solution of the Schr\"odinger equation in different ranges of the parameters of the given Hamiltonian. In view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom-field interaction, showing that these are just the leading order of the dual Dyson series when the Hamiltonian is expressed in the interaction picture. In order to best exploit the method, a study is accomplished of the well-known Jaynes-Cummings model in the rotating-wave approximation, whose exact solution is known, comparing the perturbative solutions obtained by the Dyson series and its dual with the same approximations obtained by Taylor expanding the exact solution. Finally, a full perturbative study of high-order harmonic generation is given, obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even if the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spectrum it is necessary to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the energy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines.

arXiv:quant-ph/9811037•Physical Review A•Jul 1, 1999•32 citations

Theory of High Intensity Multimode Gas Lasers - Inclusion of Collisional Effects.

P. R. Berman

Several topics in laser theory and the interaction of radiation with matter have been addressed. First, a mathematical theory of a high intensity single mode gas laser has been developed. New computational techniques have been applied which serve to unite several previous approaches to single mode laser theory. A generalized dressed atom approach was formulated to provide a new way of viewing the physical processes occurring when high intensity fields interact with matter. Second, a theoretical study of the manner in which laser sepctroscopy can be used to probe collision effects in atomic and molecular systems has been undertaken. Both two and three level systems were studied; steady state and coherent transient techniques were examined. It is now apparent that laser spectroscopy will be a useful tool for the determination of various excited state differential and total cross sections. (Author)

•May 31, 1977•0 citations

Dressed-atom description of resonance fluorescence and absorption spectra of a multi-level atom in an intense laser beam

Claude N. Cohen-Tannoudji, Serge Reynaud

A dressed-atom approach to resonance fluorescence in intense laser fields is presented. Simple and general results are derived which include the now well known predictions concerning two-level atoms but are not restricted to such simple cases. The positions of the various components of the fluorescence and absorption spectra are given by the allowed Bohr frequencies of the total system: atom+laser mode (dressed atom). The master equation, describing spontaneous emission from the dressed atom is solved in the limit of high intensities. Simple expressions, taking into account the effect of cascades, are derived for the widths of the components.

Journal of Physics B Atomic and Molecular Physics•Feb 21, 1977•655 citations

Optical spectrum of strongly coupled dressed atomic states

William Graham Greenwood, Peter R. Fontana

A strong radio-frequency field couples two excited atomic states which also interact with the virtual radiation field. The radio-frequency field dresses the atomic states and the virtual radiation field causes them to decay spontaneously. The spectrum of the emitted radiation is calculated by Fourier transforming the differential equations for the amplitudes. The solutions are given in terms of recurrence relationships which can be evaluated to any desired accuracy. The optical radiation field acts as a probe on the dressed atomic states. The spectrum shows all the radio-frequency induced resonances. The frequencies of the states and the Bloch-Siegert shifts of the multi-photon resonances can be deduced from this spectrum.

Journal of Physics B Atomic and Molecular Physics•Sep 4, 1982•1 citation
A generalized dressed-atom approach (GDAA) is developed to study the interaction of two or more strong fields with atomic and molecular systems. In the GDAA, part of the atom-field interaction is incorporated into the free-atom, free-field Hamiltonian and this expanded Hamiltonian is said to characterize a "dressed atom." The remaining atom-field interaction may then be thought to constitute a probe field interaction for this dressed atom. Provided that the dressed atom constitutes a reasonably good approximation to the true interaction, the GDAA should offer a relatively simple means for semiquantitatively predicting the positions of absorption resonances in quite complex atom-field systems. The GDAA is applied to the theory of a high-intensity, single-mode, standing-wave gas laser, the theory of Bloch-Siegert shifts, and the analysis of Autler-Townes or saturation spectroscopy experiments. The agreement between the GDAA and computer-determined values for laser resonance positions and Bloch-Siegert shifts is found to be surprisingly good over the entire range of applied field strengths. Some methods for using the GDAA to study complex spectroscopic systems are discussed.
The theory of the interaction between radiation fields and atoms as applied to laser spectroscopy can be approached using either a bare-atom picture (BAP) or dressed-atom picture (DAP). In the BAP, the basis states are those of the free atoms and free field while, in the DAP, the basis states encompass some part of the atom-field interaction. The theory of saturation spectroscopy in three-level systems is discussed using both approaches. Whereas calculations are usually more easily done using the BAP, one can gain useful insight into the underlying physical processes from the DAP. Moreover, when the radiation field strengths (in frequency units) are larger than the relaxation rates in the problem, the DAP equations simplify considerably and lead to line-shape expressions which may be given a simple interpretation. The DAP is used to obtain resonance conditions for traveling-wave fields interacting with three- and four-level atoms and for a standing-wave saturator and traveling-wave probe interacting with a three-level atom. In addition, the DAP is applied to several problems involving optical coherent transients. A comparison is made between the various advantages of the BAP and DAP and an interesting duality between the two approaches is noted.
A dressed-state rate-equation model is used to describe the Autler-Townes effect that is produced by a resonant 100% amplitude-modulated field driving a two-level resonance. The purpose of using this model is to give an intuitive interpretation of the rather complex absorption spectra that are produced when a weak probe field couples this strongly driven transition to a third atomic state. We obtain analytic expressions for the positions, strengths, and widths of the components of the absorption spectra, which are in excellent agreement with experimentally obtained spectra presented in the accompanying paper [S. Papademetriou, following paper, Phys. Rev. A 53, 997 (1996)]. \textcopyright{} 1996 The American Physical Society.
The dual Dyson series [M. Frasca, Phys. Rev. A 585858 3439 (1998)] is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In fact, both the Dyson series and its dual, by renormalization-group methods to remove secular terms from the perturbation series, give the opportunity for a full study of the solution of the Schr\"odinger equation in different ranges of the parameters of the given Hamiltonian. In view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom-field interaction, showing that these are just the leading order of the dual Dyson series when the Hamiltonian is expressed in the interaction picture. In order to best exploit the method, a study is accomplished of the well-known Jaynes-Cummings model in the rotating-wave approximation, whose exact solution is known, comparing the perturbative solutions obtained by the Dyson series and its dual with the same approximations obtained by Taylor expanding the exact solution. Finally, a full perturbative study of high-order harmonic generation is given, obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even if the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spectrum it is necessary to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the energy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines.
Several topics in laser theory and the interaction of radiation with matter have been addressed. First, a mathematical theory of a high intensity single mode gas laser has been developed. New computational techniques have been applied which serve to unite several previous approaches to single mode laser theory. A generalized dressed atom approach was formulated to provide a new way of viewing the physical processes occurring when high intensity fields interact with matter. Second, a theoretical study of the manner in which laser sepctroscopy can be used to probe collision effects in atomic and molecular systems has been undertaken. Both two and three level systems were studied; steady state and coherent transient techniques were examined. It is now apparent that laser spectroscopy will be a useful tool for the determination of various excited state differential and total cross sections. (Author)
A dressed-atom approach to resonance fluorescence in intense laser fields is presented. Simple and general results are derived which include the now well known predictions concerning two-level atoms but are not restricted to such simple cases. The positions of the various components of the fluorescence and absorption spectra are given by the allowed Bohr frequencies of the total system: atom+laser mode (dressed atom). The master equation, describing spontaneous emission from the dressed atom is solved in the limit of high intensities. Simple expressions, taking into account the effect of cascades, are derived for the widths of the components.
A strong radio-frequency field couples two excited atomic states which also interact with the virtual radiation field. The radio-frequency field dresses the atomic states and the virtual radiation field causes them to decay spontaneously. The spectrum of the emitted radiation is calculated by Fourier transforming the differential equations for the amplitudes. The solutions are given in terms of recurrence relationships which can be evaluated to any desired accuracy. The optical radiation field acts as a probe on the dressed atomic states. The spectrum shows all the radio-frequency induced resonances. The frequencies of the states and the Bloch-Siegert shifts of the multi-photon resonances can be deduced from this spectrum.