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

Probing a laser field by measuring photon replica transitions

C. Jung

Published Jul 1, 1981• 11 citations
Publisher

Abstract

How much information about a laser field can be reconstructed is considered if multiphoton transitions have been measured but if the laser-flux distribution in the experiment is unknown. It is shown how this reconstruction is done in detail if the relative strengths of the photon replicas of some atomic or molecular transitions are given. The resulting information about the laser field turns out to be the power moments of a weight function which indicates the relative weight with which a particular laser-flux value has contributed to the observed multiphoton transitions. Some analytically soluble examples are presented for the connection between the laser-flux distribution in space and time, the resulting moments of the weight function, and the weight function itself.

DOI
10.1103/physreva.24.360

Related papers

Atoms in strong laser fields

J P Connerade

Multiphoton spectroscopy The subject of multiphoton excitation spectroscopy began in 1931 when Göppert-Mayer [450] wrote a theoretical paper in which she calculated the transition rate for an atom in the presence of two photons rather than just one. At the time, the process seemed rather exotic, and it was reassuring that the calculated rate was so low as to guarantee that it could not readily be observed in the laboratory with conventional sources. This conclusion was reassuring because it implies that a simple perturbative theory (one photon per transition is the weak-field limit) is adequate for most purposes. The subject came to life with the advent of lasers, when it became easy to create intense beams of light. Since the probability of excitation by two photons grows as the square of the photon density, whereas the probability of single-photon excitation grows only linearly with photon density, two-photon transitions gain in relative strength with increasing intensity despite the small value of the rate coefficient. The development of multiphoton spectroscopy has followed that of lasers: as the available power has increased, so has the number of photons involved in individual transitions. More significantly, it has become apparent that the physics of the interaction between radiation and matter is not the same at high laser powers as under weak illumination, i.e. that there is a qualitative change which sets in at strong laser fields. This is normally expressed by saying that perturbative approximations break down.

Cambridge University Press eBooks•May 7, 1998•2 citations

Field-Correlation Effects in Multiphoton Absorption Processes

G. S. Agarwal

The dependence of the multiphoton absorption probability for an atomic system on the statistical properties of the incident light is investigated. It is shown, by means of $n\mathrm{th}$-order time-dependent perturbation theory, that the multiphoton absorption probability depends on the $(n, n)\mathrm{th}$ normally ordered correlation functions of the electromagnetic field. For stationary fields, the transition probability per unit time is constant and is directly related to the reduced cross-spectral correlation function of the electromagnetic field. This expression for the transition probability is then analyzed under various conditions of coherence. Explicit calculations are carried out for thermal light and for laser light, and the transition rates are compared when each has a Lorentzian spectrum. In particular, when the width of the final atomic level is much larger than the bandwidth of the field, the transition rate for thermal light is $n$! times higher than with laser light of the same mean intensity. The other extreme case, i.e., when the width of the final atomic level is much smaller than the bandwidth of the field, is also considered in detail. An equation for the density operator of the field is derived; this equation governs the change in the statistical properties of the photon system in $n$-photon absorption processes. On the basis of this equation, the time-dependent properties of the photon system are then studied and some physical consequences of these equations are discussed. Some numerical solutions relating to the time dependence of the factorial moments in two-photon absorption processes are presented.

Physical Review A•May 1, 1970•216 citations

Quantum theory of multiphoton lasers. II. Systems without detailed balance

K. J. McNeil, Daniel F. Walls

For pt.I see ibid., vol.8, 104 (1974). Investigations into possible multiphoton laser systems are extended to a less restrictive class than considered in the previous paper. The loss mechanism for the light field is now taken to be a single-photon loss. These systems no longer preserve the property of detailed balance. Explicit solutions are given for the stationary photon distribution for the two-photon laser. This exhibits similar photon statistics to the usual one-photon laser, with no significant increase in relative fluctuations at threshold. The results are equally applicable to multiboson lasers involving say the simultaneous stimulated emission of a photon and a phonon.

Journal of Physics A Mathematical and General•Jan 1, 1975•28 citations

Reconstruction of two-dimensional light intensity distribution from the data of photo-count experiments

Vitaliy N. Kurashov, Andrey V. Kurashov

An analytical method to recover the two-dimensional probability density function (PDF) of a random light field from the PDF of photon counts is presented. Some illustration of the inversion procedure are presented with application to the problem of light intensity interferometry.

Proceedings - International Conference on Image Processing•Dec 24, 2002•0 citations

The 1S → 2S two-photon transition rate in atomic hydrogen

Shifang Li, Edward S. Fry

Theoretical calculations for the 1S → 2S two- photon transition rate in atomic hydrogen are reviewed. They are compared with two experiments via the saturation effects that are observed when three-photon ionization is enhanced by two- photon resonance with the metastable 2S state. There is a significant disagreement between theoretical and experimental results. The disagreement is illustrated by determining the transition rate as a function of intensity for experimental laser profiles: (1) using parameters that give rates in agreement with experimental data, and (2) using theoretical values for the parameters. Finally, experiments that would involve direct observation of the 2S metastable state are considered. It is shown that single-longitudinal-mode laser experiments would provide an accurate measurement of the Rabi frequency for this transition and yield a definitive value for the rate. A Monte Carlo simulation method is used to consider practical effects associated with such an experiment, for example, chirp and ASE noise in the laser. Also, simulations of the multiphoton ionization process in multimode and wide band laser fields are presented.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

On the photon statistics of the fluorescence radiation of a laser-driven single atom

Reinhard Reibold

The subject of the investigation are single atoms, for instance isolated in a Paul trap, which are driven by laser fields while their resonance radiation is measured by photon counters. For a rather wide class of experimental setups or theoretical models, a method is developed to determine the statistics of the photons observed. In contrast to other approaches it avoids referring to 'continuous measurements' or similar concepts, but tries to stay as far as possible within the framework of ordinary quantum mechanics. The method is illustrated by application to simple models.

Journal of Physics A Mathematical and General•Jan 7, 1993•5 citations
How much information about a laser field can be reconstructed is considered if multiphoton transitions have been measured but if the laser-flux distribution in the experiment is unknown. It is shown how this reconstruction is done in detail if the relative strengths of the photon replicas of some atomic or molecular transitions are given. The resulting information about the laser field turns out to be the power moments of a weight function which indicates the relative weight with which a particular laser-flux value has contributed to the observed multiphoton transitions. Some analytically soluble examples are presented for the connection between the laser-flux distribution in space and time, the resulting moments of the weight function, and the weight function itself.
Multiphoton spectroscopy The subject of multiphoton excitation spectroscopy began in 1931 when Göppert-Mayer [450] wrote a theoretical paper in which she calculated the transition rate for an atom in the presence of two photons rather than just one. At the time, the process seemed rather exotic, and it was reassuring that the calculated rate was so low as to guarantee that it could not readily be observed in the laboratory with conventional sources. This conclusion was reassuring because it implies that a simple perturbative theory (one photon per transition is the weak-field limit) is adequate for most purposes. The subject came to life with the advent of lasers, when it became easy to create intense beams of light. Since the probability of excitation by two photons grows as the square of the photon density, whereas the probability of single-photon excitation grows only linearly with photon density, two-photon transitions gain in relative strength with increasing intensity despite the small value of the rate coefficient. The development of multiphoton spectroscopy has followed that of lasers: as the available power has increased, so has the number of photons involved in individual transitions. More significantly, it has become apparent that the physics of the interaction between radiation and matter is not the same at high laser powers as under weak illumination, i.e. that there is a qualitative change which sets in at strong laser fields. This is normally expressed by saying that perturbative approximations break down.
The dependence of the multiphoton absorption probability for an atomic system on the statistical properties of the incident light is investigated. It is shown, by means of nthn\mathrm{th}nth-order time-dependent perturbation theory, that the multiphoton absorption probability depends on the (n,n)th(n, n)\mathrm{th}(n,n)th normally ordered correlation functions of the electromagnetic field. For stationary fields, the transition probability per unit time is constant and is directly related to the reduced cross-spectral correlation function of the electromagnetic field. This expression for the transition probability is then analyzed under various conditions of coherence. Explicit calculations are carried out for thermal light and for laser light, and the transition rates are compared when each has a Lorentzian spectrum. In particular, when the width of the final atomic level is much larger than the bandwidth of the field, the transition rate for thermal light is nnn! times higher than with laser light of the same mean intensity. The other extreme case, i.e., when the width of the final atomic level is much smaller than the bandwidth of the field, is also considered in detail. An equation for the density operator of the field is derived; this equation governs the change in the statistical properties of the photon system in nnn-photon absorption processes. On the basis of this equation, the time-dependent properties of the photon system are then studied and some physical consequences of these equations are discussed. Some numerical solutions relating to the time dependence of the factorial moments in two-photon absorption processes are presented.
For pt.I see ibid., vol.8, 104 (1974). Investigations into possible multiphoton laser systems are extended to a less restrictive class than considered in the previous paper. The loss mechanism for the light field is now taken to be a single-photon loss. These systems no longer preserve the property of detailed balance. Explicit solutions are given for the stationary photon distribution for the two-photon laser. This exhibits similar photon statistics to the usual one-photon laser, with no significant increase in relative fluctuations at threshold. The results are equally applicable to multiboson lasers involving say the simultaneous stimulated emission of a photon and a phonon.
Theoretical calculations for the 1S → 2S two- photon transition rate in atomic hydrogen are reviewed. They are compared with two experiments via the saturation effects that are observed when three-photon ionization is enhanced by two- photon resonance with the metastable 2S state. There is a significant disagreement between theoretical and experimental results. The disagreement is illustrated by determining the transition rate as a function of intensity for experimental laser profiles: (1) using parameters that give rates in agreement with experimental data, and (2) using theoretical values for the parameters. Finally, experiments that would involve direct observation of the 2S metastable state are considered. It is shown that single-longitudinal-mode laser experiments would provide an accurate measurement of the Rabi frequency for this transition and yield a definitive value for the rate. A Monte Carlo simulation method is used to consider practical effects associated with such an experiment, for example, chirp and ASE noise in the laser. Also, simulations of the multiphoton ionization process in multimode and wide band laser fields are presented.
The subject of the investigation are single atoms, for instance isolated in a Paul trap, which are driven by laser fields while their resonance radiation is measured by photon counters. For a rather wide class of experimental setups or theoretical models, a method is developed to determine the statistics of the photons observed. In contrast to other approaches it avoids referring to 'continuous measurements' or similar concepts, but tries to stay as far as possible within the framework of ordinary quantum mechanics. The method is illustrated by application to simple models.