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

ac Stark splitting in double optical resonance and resonance fluorescence by a nonmonochromatic chaotic field

P. Zoller

Published Sep 1, 1979• 68 citations
Publisher

Abstract

A detailed theoretical analysis of ac Stark splitting in double optical resonance and resonance fluorescence by a nonmonochromatic complex chaotic field is presented. It is shown that a one-photon transition undergoes Stark splitting, which is strongly affected by the intensity fluctuations of the chaotic light. On resonance, the lines in the doublet structure of double optical resonance and the sidebands of the triplet structure in resonance fluorescence are broadened by the intensity fluctuations and tend to copy the Rayleigh distribution of the field amplitude. Off resonance, the asymmetry of the doublet in double optical resonance is reversed and a sideband asymmetry appears in resonance fluorescence for finite bandwidth of the incident light. While on resonance the splitting is always reduced, off resonance the intensity fluctuations may lead to an enhancement of the splitting in comparison to phase-diffusing light.

DOI
10.1103/physreva.20.1019

Related papers

Saturation and Stark Splitting of Resonant Transitions in Strong Chaotic Fields of Arbitrary Bandwidth

A. T. Georges, P. Lambropoulos, P. Zoller

We report the solution of the problem of saturation and ac Stark splitting of a resonant transition in a strong chaotic field of arbitrary bandwidth. We present results for double optical resonance and resonance fluorescence and compare them to those obtained for a phase-diffusion field.

Physical Review Letters•Jun 11, 1979•51 citations

ac Stark splitting in intense stochastic driving fields with Gaussian statistics and non-Lorentzian line shape

P. Zoller, G. Alber, R. Salvador

Lorentzian models for laser line shapes lead to qualitatively incorrect results for off-resonance excitation of atoms. This paper is the first attempt to present a theory of the nonperturbative interaction of an atom with a chaotic field (representing multimode laser radiation having strong amplitude fluctuations) with a line shape falling off faster than a Lorentzian. To this end we suggest a stochastic Markovian model for a non-Lorentzian chaotic field. To solve the multiplicative stochastic differential equations describing the atom-field interaction we propose a "marginal characteristic function approach." This not only reproduces our earlier results in a more elegant way and establishes the relationship between approaches used by other authors in a different context, but also provides the simplest possible basis for our present discussion of ac Stark splitting in double optical resonance. While for a chaotic field with a Lorentzian line shape the asymmetry of the two-peaked off-resonance spectrum is reversed for all values of the detuning compared with the monochromatic case, our present model predicts a reversed peak asymmetry only for detunings smaller than a few laser bandwidths in agreement with experiment. The on-resonance spectrum is dominated by the amplitude fluctuations and is only weakly affected by changes of the spectral line shape of the laser.

Physical Review A•Jul 1, 1981•85 citations

ac Stark splitting in doubly resonant three-photon ionization with nonmonochromatic fields

A. T. Georges, P. Lambropoulos

We present a theory of Stark splitting in doubly resonant three-photon ionization (three-level system) with nonmonochromatic fields. The asymmetry of the peaks of the resonance curve due to Stark splitting is shown to be reversed when the laser bandwidth is larger than the width of the atomic transitions of the resonant states. It is further shown that ionization as well as the probe field have a significant effect on the features of the splitting. Similar effects are found with monochromatic fields in the presence of an additional level near the initial level (four-level system). The results of the analysis are in general qualitative agreement with existing observations.

Physical Review A•Aug 1, 1978•104 citations

Saturation and Stark splitting of an atomic transition in a stochastic field

A. T. Georges, P. Lambropoulos

The authors investigate the saturation and Stark splitting of an atomic transition in (i) a phase-diffusion field and (ii) a chaotic field of arbitrary bandwidth. The theory takes into account the infinite sequence of field-correlation functions. It is shown that a chaotic field is less effective than a phase-diffusion field in saturating a single- or multiphoton transition. This is contrary to the weak-field case, where the intensity fluctuations and the associated photon bunching make the chaotic field more effective in exciting a multiphoton transition. It is also shown that the Stark splitting of an atomic transition, as observed in double resonance, is influenced dramatically by the intensity fluctuations in the chaotic field.

Physical Review A•Sep 1, 1979•98 citations

AC Stark effect and fluorescence in modulated laser beams. II. Two-photon stepwise excitations

Ragini Saxena, G. S. Agarwal

For pt.I see ibid., vol.12, no.12, p.1939 (1979). The modulated fluorescence in an optical double resonance experiment, i.e. when an atom interacts with two intense monochromatic laser beams each of which is weakly modulated in amplitude at frequency Omega , is studied in detail. The modulation rate corresponding to the steady-state population of the highest atomic level exhibits resonant structures at the modulation frequencies Omega =0, +or- alpha 0 , +or-2 alpha 0 due to the dynamical Stark splitting of the various energy levels; alpha 0 being related to the Rabi frequencies alpha 1 and alpha 2 associated with the two lasers and the two atomic transitions, by alpha 0 2 = mod alpha 1 mod 2 + mod alpha 2 mod 2 . The peak at Omega =+or- alpha 0 is the most intense and exhibits splitting when the applied fields are detuned from exact resonance with the respective atomic frequencies. Resonances are observed in the modulation rate of the intermediate-level population at the modulation frequencies Omega =0, +or-2 alpha 0 . In the presence of detunings of the applied fields, additional resonant structures occur at Omega =+or- alpha 0 which increase in magnitude with higher detunings and split. Explicit expressions for the positions, widths and weights of these resonant components are obtained analytically for intense, resonant fields. Numerical results for general values of the laser field strengths and the detunings are given.

Journal of Physics B Atomic and Molecular Physics•Feb 14, 1980•21 citations

AC Stark effect and fluorescence using modulated laser beams. I. Effect of laser fluctuations and arbitrary relaxation parameters

Ragini Saxena, G. S. Agarwal

The influence of relaxation parameters, as well as temporal fluctuations in the laser field on the modulation rate and phaseshift of the fluorescence from a two-level atom excited by a weakly modulated source is studied in detail. It is shown that, for intense resonant laser fields, the resonance in the modulation rate occurs at the modulation frequency Omega =2 due to the dynamical Stark splitting and has a width equal to 1 / 2 (T 1 -1 +T 2 -1 ). When temporal fluctuations of the exciting laser field are taken into account, the phaseshift of the scattered light is found to be strongly dependent on the bandwidth of the exciting source, as well as the frequency of modulation; hence experimental results on the determination of the lifetime by the phaseshift method have to be interpreted carefully. Numerical results for the modulation rates and phaseshift at different field strengths and various values of T 1 -1 , T 2 -1 , Delta laser bandwidth and Doppler broadening are presented.

Journal of Physics B Atomic and Molecular Physics•Jun 28, 1979•16 citations
A detailed theoretical analysis of ac Stark splitting in double optical resonance and resonance fluorescence by a nonmonochromatic complex chaotic field is presented. It is shown that a one-photon transition undergoes Stark splitting, which is strongly affected by the intensity fluctuations of the chaotic light. On resonance, the lines in the doublet structure of double optical resonance and the sidebands of the triplet structure in resonance fluorescence are broadened by the intensity fluctuations and tend to copy the Rayleigh distribution of the field amplitude. Off resonance, the asymmetry of the doublet in double optical resonance is reversed and a sideband asymmetry appears in resonance fluorescence for finite bandwidth of the incident light. While on resonance the splitting is always reduced, off resonance the intensity fluctuations may lead to an enhancement of the splitting in comparison to phase-diffusing light.
Lorentzian models for laser line shapes lead to qualitatively incorrect results for off-resonance excitation of atoms. This paper is the first attempt to present a theory of the nonperturbative interaction of an atom with a chaotic field (representing multimode laser radiation having strong amplitude fluctuations) with a line shape falling off faster than a Lorentzian. To this end we suggest a stochastic Markovian model for a non-Lorentzian chaotic field. To solve the multiplicative stochastic differential equations describing the atom-field interaction we propose a "marginal characteristic function approach." This not only reproduces our earlier results in a more elegant way and establishes the relationship between approaches used by other authors in a different context, but also provides the simplest possible basis for our present discussion of ac Stark splitting in double optical resonance. While for a chaotic field with a Lorentzian line shape the asymmetry of the two-peaked off-resonance spectrum is reversed for all values of the detuning compared with the monochromatic case, our present model predicts a reversed peak asymmetry only for detunings smaller than a few laser bandwidths in agreement with experiment. The on-resonance spectrum is dominated by the amplitude fluctuations and is only weakly affected by changes of the spectral line shape of the laser.
We present a theory of Stark splitting in doubly resonant three-photon ionization (three-level system) with nonmonochromatic fields. The asymmetry of the peaks of the resonance curve due to Stark splitting is shown to be reversed when the laser bandwidth is larger than the width of the atomic transitions of the resonant states. It is further shown that ionization as well as the probe field have a significant effect on the features of the splitting. Similar effects are found with monochromatic fields in the presence of an additional level near the initial level (four-level system). The results of the analysis are in general qualitative agreement with existing observations.
The authors investigate the saturation and Stark splitting of an atomic transition in (i) a phase-diffusion field and (ii) a chaotic field of arbitrary bandwidth. The theory takes into account the infinite sequence of field-correlation functions. It is shown that a chaotic field is less effective than a phase-diffusion field in saturating a single- or multiphoton transition. This is contrary to the weak-field case, where the intensity fluctuations and the associated photon bunching make the chaotic field more effective in exciting a multiphoton transition. It is also shown that the Stark splitting of an atomic transition, as observed in double resonance, is influenced dramatically by the intensity fluctuations in the chaotic field.
For pt.I see ibid., vol.12, no.12, p.1939 (1979). The modulated fluorescence in an optical double resonance experiment, i.e. when an atom interacts with two intense monochromatic laser beams each of which is weakly modulated in amplitude at frequency Omega , is studied in detail. The modulation rate corresponding to the steady-state population of the highest atomic level exhibits resonant structures at the modulation frequencies Omega =0, +or- alpha 0 , +or-2 alpha 0 due to the dynamical Stark splitting of the various energy levels; alpha 0 being related to the Rabi frequencies alpha 1 and alpha 2 associated with the two lasers and the two atomic transitions, by alpha 0 2 = mod alpha 1 mod 2 + mod alpha 2 mod 2 . The peak at Omega =+or- alpha 0 is the most intense and exhibits splitting when the applied fields are detuned from exact resonance with the respective atomic frequencies. Resonances are observed in the modulation rate of the intermediate-level population at the modulation frequencies Omega =0, +or-2 alpha 0 . In the presence of detunings of the applied fields, additional resonant structures occur at Omega =+or- alpha 0 which increase in magnitude with higher detunings and split. Explicit expressions for the positions, widths and weights of these resonant components are obtained analytically for intense, resonant fields. Numerical results for general values of the laser field strengths and the detunings are given.
The influence of relaxation parameters, as well as temporal fluctuations in the laser field on the modulation rate and phaseshift of the fluorescence from a two-level atom excited by a weakly modulated source is studied in detail. It is shown that, for intense resonant laser fields, the resonance in the modulation rate occurs at the modulation frequency Omega =2 due to the dynamical Stark splitting and has a width equal to 1 / 2 (T 1 -1 +T 2 -1 ). When temporal fluctuations of the exciting laser field are taken into account, the phaseshift of the scattered light is found to be strongly dependent on the bandwidth of the exciting source, as well as the frequency of modulation; hence experimental results on the determination of the lifetime by the phaseshift method have to be interpreted carefully. Numerical results for the modulation rates and phaseshift at different field strengths and various values of T 1 -1 , T 2 -1 , Delta laser bandwidth and Doppler broadening are presented.