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

Application of radiative renormalization to strong-field resonant nonlinear optical interactions

O. Blum, P. J. Harshman, T. Kenneth Gustafson, Paul L. Kelley

Published Jun 1, 1993• 12 citations
Publisher

Abstract

The Liouville equation for the density matrix can be recast so that the external-field terms which couple density-matrix elements are second order in the field. This approach is shown to have a profound effect on the steady-state analysis of strong-field resonant nonlinear optical problems. First, in the case where parity or appropriate field restrictions apply, there is a reduction of the number of coupled equations which must be solved by at least a factor of 2. Second, this reformulation naturally leads to radiative-renormalization terms which are directly related to saturation, Stark shifts, and Rabi splittings. We can use this simple formalism to obtain solutions to a number of resonant nonlinear problems including cases where there are two or more strong fields. The renormalization described here is equivalent to a Dyson-equation analysis.

DOI
10.1103/physreva.47.5165

Related papers

Applications of nonperturbative nonlinear optics

Paul L. Kelley, David A. Coppeta, P. J. Harshman +2 more

The Liouville equation for the density matrix can be recast so that the external field terms which couple density matrix elements are second order in the field. This approach is shown to have a profound effect on the analysis of strong field resonant nonlinear optical problems. First, in the case where parity or appropriate field restrictions apply, there is a reduction of the number of coupled equations which must be solved by at least a factor of two. Second, this reformulation naturally leads to radiative renormalization terms which are directly related to saturation, Stark shifts and Rabi splittings. The renormalization is equivalent to a Dyson equation analysis. We use this simple formalism to obtain exact solutions to a number of nonlinear optical problems including cases where there are two or more strong, resonant fields. These problems include: 1) two levels, two strong fields, 2) three levels, two strong fields, and 3) four levels, three and four strong fields. Discussed in detail are the two level case and the three and four level cases where weak fields couple the ground state to other states. We use these results to discuss the physics of optically induced transparency, population beats, optical switching in quantum wells, and fully resonant coherent anti-Stokes Raman scattering (CARS).

IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS)•Dec 17, 2002•0 citations

Analysis of strong light-matter interaction using a dressed propagator approach

James G. Fujimoto, Ting K. Yee

A diagrammatic density matrix technique is developed and applied to study nonlinear optical processes involving responses from weak probe fields interacting with a system under strong excitation. These diagrams consist of lowest-order double-Feynman diagrams which represent the density matrix perturbation terms describing the system response to the weak probe fields1,2 combined with dressed propagators which represent the density matrix elements of the system under strong excitation. The dressed propagators are described by a set of linear equations which, in most cases, may be derived in inspection. The methodology is similar to the bare-atom approach.2 The advantages of using this diagrammatic technique are that (1) it allows one to select and express analytically the dominant and appropriate density matrix elements (diagrams and dressed propagators); (2) analytical expressions may be constructed directly from the diagrams and thus lengthy calculations needed to obtain closed-form solutions are greatly reduced; (3) it provides a physical interpretation for the density matrix solutions and nonlinear optical processes; and (4) it may be generalized to more complicated, multilevel systems. We demonstrate the application of this technique to describe gain saturation, Stark splitting, and Raman scattering.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations

Effective interactions in non-linear optics

A V Ivanova, G G Melikyan

A new theoretical approach to the problem of non-linear polarisation of matter is suggested. The density matrix equation for a low-density gas in a strong light field has been solved without using the phenomenological relaxation constants. Use is made of the general Hamiltonian that explicitly involves, besides the interaction of atoms with the external field, also their interactions with each other and with the vacuum electromagnetic field. The equation is solved by the canonical transformation method (a variant of the Bogolyubov-Mitropolski method of averages). It is generalised and used in the more complicated case of interacting multilevel atoms (molecules) in a strong light field. An expression for the cubic susceptibility is obtained, enabling analysis of the resonant saturation in both stationary and non-stationary cases. The proposed method provides correct expressions for the dynamic Stark shifts, amplitudes of multiphoton transitions and of radiational collisions, as well as for effective interatomic interactions caused by photon exchange. The proposed theoretical approach can also be used in studying non-linear optical processes in dense gases, liquids and solids.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 14, 1988•3 citations

Nonlinear Optical Polarization and Relaxation Phenomena in Dilute Gases

A. Ben‐Reuven, Lewis S. Klein

The Kubo-Zwanzig-Fano relaxation method is extended to the problem of a homogeneous dilute system interacting with arbitrarily strong fields composed of several monochromatic modes, neglecting breakdown and spatial correlations. The Von Neumann equation for the density matrix is solved for classical fields, using a procedure in which the harmonics numbers are treated as the classical analog (in Liouville space) of the quantum fields occupation-number representation. This solution is adapted to the case where memory effects during the absorption or emission of a photon can be neglected. Two examples illustrate the method, which is generally applicable in such problems as saturation, double resonance, and frequency mixing involving the nonlinear response of independent molecules.

Physical Review A•Aug 1, 1971•31 citations

Radiative renormalization analysis of optical double resonance

Paul L. Kelley, P. J. Harshman, O. Blum +1 more

One- and two-photon renormalization is applied to three-level optical double resonance. An exact steady-state solution to the optical Bloch equations is given for arbitrarily strong, near-resonant, monochromatic fields connecting any two of the three possible level pairings. The results are discussed under various conditions and limits.

Journal of the Optical Society of America B•Nov 1, 1994•16 citations

Strong-field theory of nonlinear polarization spectroscopy Fundamentals and the two-level system

Wichard J. D. Beenken, Volkhard May

To formulate a description of nonlinear polarization spectroscopy that is valid over a wide range of pump intensities, we present an approach that considers any order of the external fields. The Liouville von Neumann equation governing the dynamics of a multilevel molecular system is made tractable by expansion of the particular density matrix into powers of the carrier waves of the external fields. For a two-level system a solution of the resulting set of equations to first order of the probe field but to all orders of pump field is demonstrated. A remarkable change in the homogeneously broadened line shape is obtained at high pump intensities, caused by the optical Stark effect among others. Improvements over results derived by other authors are discussed.

Journal of the Optical Society of America B•Nov 1, 1997•15 citations
The Liouville equation for the density matrix can be recast so that the external-field terms which couple density-matrix elements are second order in the field. This approach is shown to have a profound effect on the steady-state analysis of strong-field resonant nonlinear optical problems. First, in the case where parity or appropriate field restrictions apply, there is a reduction of the number of coupled equations which must be solved by at least a factor of 2. Second, this reformulation naturally leads to radiative-renormalization terms which are directly related to saturation, Stark shifts, and Rabi splittings. We can use this simple formalism to obtain solutions to a number of resonant nonlinear problems including cases where there are two or more strong fields. The renormalization described here is equivalent to a Dyson-equation analysis.
The Liouville equation for the density matrix can be recast so that the external field terms which couple density matrix elements are second order in the field. This approach is shown to have a profound effect on the analysis of strong field resonant nonlinear optical problems. First, in the case where parity or appropriate field restrictions apply, there is a reduction of the number of coupled equations which must be solved by at least a factor of two. Second, this reformulation naturally leads to radiative renormalization terms which are directly related to saturation, Stark shifts and Rabi splittings. The renormalization is equivalent to a Dyson equation analysis. We use this simple formalism to obtain exact solutions to a number of nonlinear optical problems including cases where there are two or more strong, resonant fields. These problems include: 1) two levels, two strong fields, 2) three levels, two strong fields, and 3) four levels, three and four strong fields. Discussed in detail are the two level case and the three and four level cases where weak fields couple the ground state to other states. We use these results to discuss the physics of optically induced transparency, population beats, optical switching in quantum wells, and fully resonant coherent anti-Stokes Raman scattering (CARS).
A diagrammatic density matrix technique is developed and applied to study nonlinear optical processes involving responses from weak probe fields interacting with a system under strong excitation. These diagrams consist of lowest-order double-Feynman diagrams which represent the density matrix perturbation terms describing the system response to the weak probe fields1,2 combined with dressed propagators which represent the density matrix elements of the system under strong excitation. The dressed propagators are described by a set of linear equations which, in most cases, may be derived in inspection. The methodology is similar to the bare-atom approach.2 The advantages of using this diagrammatic technique are that (1) it allows one to select and express analytically the dominant and appropriate density matrix elements (diagrams and dressed propagators); (2) analytical expressions may be constructed directly from the diagrams and thus lengthy calculations needed to obtain closed-form solutions are greatly reduced; (3) it provides a physical interpretation for the density matrix solutions and nonlinear optical processes; and (4) it may be generalized to more complicated, multilevel systems. We demonstrate the application of this technique to describe gain saturation, Stark splitting, and Raman scattering.
A new theoretical approach to the problem of non-linear polarisation of matter is suggested. The density matrix equation for a low-density gas in a strong light field has been solved without using the phenomenological relaxation constants. Use is made of the general Hamiltonian that explicitly involves, besides the interaction of atoms with the external field, also their interactions with each other and with the vacuum electromagnetic field. The equation is solved by the canonical transformation method (a variant of the Bogolyubov-Mitropolski method of averages). It is generalised and used in the more complicated case of interacting multilevel atoms (molecules) in a strong light field. An expression for the cubic susceptibility is obtained, enabling analysis of the resonant saturation in both stationary and non-stationary cases. The proposed method provides correct expressions for the dynamic Stark shifts, amplitudes of multiphoton transitions and of radiational collisions, as well as for effective interatomic interactions caused by photon exchange. The proposed theoretical approach can also be used in studying non-linear optical processes in dense gases, liquids and solids.
The Kubo-Zwanzig-Fano relaxation method is extended to the problem of a homogeneous dilute system interacting with arbitrarily strong fields composed of several monochromatic modes, neglecting breakdown and spatial correlations. The Von Neumann equation for the density matrix is solved for classical fields, using a procedure in which the harmonics numbers are treated as the classical analog (in Liouville space) of the quantum fields occupation-number representation. This solution is adapted to the case where memory effects during the absorption or emission of a photon can be neglected. Two examples illustrate the method, which is generally applicable in such problems as saturation, double resonance, and frequency mixing involving the nonlinear response of independent molecules.
To formulate a description of nonlinear polarization spectroscopy that is valid over a wide range of pump intensities, we present an approach that considers any order of the external fields. The Liouville von Neumann equation governing the dynamics of a multilevel molecular system is made tractable by expansion of the particular density matrix into powers of the carrier waves of the external fields. For a two-level system a solution of the resulting set of equations to first order of the probe field but to all orders of pump field is demonstrated. A remarkable change in the homogeneously broadened line shape is obtained at high pump intensities, caused by the optical Stark effect among others. Improvements over results derived by other authors are discussed.