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

The 3S122−3D522 interval in atomic hydrogen. I. Two-photon line-shape theory

D. A. Van Baak, B. O. Clark, F. M. Pipkin

Published Feb 1, 1979• 9 citations
Publisher

Abstract

This paper reports a theoretical treatment of the line shape for two-photon transitions. The time-dependent perturbation-theory treatment is equally appropriate for a fast atomic beam interacting with a microwave field in a waveguide, and for laser excitation of a thermal beam. Two important features of the physical systems are successfully incorporated into the theory. First, the amplitude of the external field to which the atoms are exposed varies in time; the envelope function affects the resonance linewidth and power shift. Second, the theory includes the natural decay of the atomic states; the decay amplitude produces a novel "lifetime shift," which displaces the two-photon resonance from its expected location, even in the limit of weak external fields. This paper gives detailed predictions for shifts and other distortions caused by nonidealities of the experimental apparatus used for the measurement of the $3^{2}S_{\frac{1}{2}}\ensuremath{-}3^{2}D_{\frac{5}{2}}$ transition in atomic hydrogen.

DOI
10.1103/physreva.19.787

Related papers

Two-Photon Spectroscopy of Trapped Atomic Hydrogen

Claudio Lenz Cesar, Dale G. Fried, T. C. Killian +6 more

We report observation of the 1S-2S two-photon transition in hydrogen confined in a magnetic trap at submillikelvin temperatures. The excitation spectrum can display a sharp central feature arising from periodic motion of the trapped atoms. The metastable 2S atoms remain trapped, and have a lifetime close to the natural lifetime of 122 ms. These developments open the way to achieving the transition's natural linewidth. We have also demonstrated that the temperature of the gas can be determined from the line shape, providing an important tool for the study of cold trapped hydrogen. The resolution in these experiments appears to be limited by laser stability, currently 3 kHz.

Physical Review Letters•Jul 8, 1996•169 citations

Multiple-time-scale perturbation theory: Radiative decay of coupled atomic states

G. L. Brooks, Leonard M. Scarfone

The spontaneous radiative decay to the ground state of an atomic system initially in the higher of two excited states, coupled in a radiationless fashion by an external field, is investigated by the method of multiple-time-scale perturbation theory. The coupled differential equations of motion for the probability amplitudes are solved to second order, while the usual secular behavior of conventional time-dependent perturbation theory is eliminated in terms of two natural time scales: a fast time scale corresponding to the reciprocal of the level transition frequency and a slower time scale associated with the inverse of the radiation linewidth. Expressions are obtained to this order for the energy shifts and decay characteristics of the excited states and the energy distribution of the final-state photons, quantities previously determined by Fourier analysis and contour integration and by the phenomenological approach of Weisskopf and Wigner. A detailed comparison of these various methods of solution includes conditions under which the present results agree to second order with the previous calculations.

Physical Review A•Dec 1, 1982•4 citations

Line shape and strength of two-photon absorption in an atomic vapor with a resonant or nearly resonant intermediate state

John E. Bjorkholm, P. F. Liao

The line shape and strength of two-photon absorption in an atomic vapor are studied both theoretically and experimentally for the case of absorption of unequal-frequency photons. Special attention is given to the situation in which the intermediate state is resonant or nearly resonant. It is shown that for the resonant case, maximum absorption rates and Doppler-free spectra are simultaneously obtained. Either counterpropagating or copropagating beams can be used. With counterpropagating beams the two-photon linewidths are quite insensitive to power broadening of the intermediate state. With copropagating beams the two-photon spectra can also reveal the intermediate-state structure with a resolution determined mainly by the intermediate-state lifetime (nearly as well as can be done using any spectroscopic technique). The theoretical analysis provides a closed-form solution for the line shape and strength of the two-photon spectrum. In general the line shape is composed of two features. One is Doppler broadened and predominates when the intermediate state is nonresonant. The second feature is Doppler free, and it predominates with a resonant intermediate state. Detailed comparisons of experimental measurements of the line shape and strength of two-photon absorption in Na vapor are made with the theory and found to be in excellent agreement. Signal strengths for the onresonance case are 6 \ifmmode\times\else\texttimes\fi{} ${10}^{9}$ larger than the case of equal-frequency photons with no loss in resolution.

Physical Review A•Aug 1, 1976•149 citations

Comparison of classical and second quantized description of the dynamic Stark shift

Haas, M, Ulrich D. Jentschura, Christoph H. Keitel

We compare the derivation of the dynamic Stark shift of hydrogenic energy levels in a classical framework with an adiabatically damped laser-atom interaction, which is equivalent to the Gell-Mann-Low-Sucher formula, and a treatment based on time-independent perturbation theory, with a second-quantized laser-atom dipole interaction Hamiltonian. Our analysis applies to a laser that excites a two-photon transition in atomic hydrogen or in a hydrogenlike ion with low nuclear charge number. Our comparisons serve to demonstrate why the dynamic Stark shift may be interpreted as a stimulated radiative correction and illustrates connections between the two derivations. The simplest of the derivations is the fully quantized approach. The classical and the second-quantized treatment are shown to be equivalent in the limit of large photon numbers.

•Oct 17, 2005•16 citations

Comparison of classical and second quantized description of the dynamic Stark shift

M. Haas, Ulrich D. Jentschura, C. H. Keitel

We compare the derivation of the dynamic Stark shift of hydrogenic energy levels in a classical framework with an adiabatically damped laser-atom interaction, which is equivalent to the Gell-Mann-Low-Sucher formula, and a treatment based on time-independent perturbation theory, with a second-quantized laser-atom dipole interaction Hamiltonian. Our analysis applies to a laser that excites a two-photon transition in atomic hydrogen or in a hydrogenlike ion with low nuclear charge number. Our comparisons serve to demonstrate why the dynamic Stark shift may be interpreted as a stimulated radiative correction and illustrates connections between the two derivations. The simplest of the derivations is the fully quantized approach. The classical and the second-quantized treatment are shown to be equivalent in the limit of large photon numbers.

arXiv:physics/0510160•American Journal of Physics•Dec 21, 2005•35 citations

Two-photon transitions to excited states in atomic hydrogen

A. Quattropani, F. Bassani, Sandra Carillo

Resonant two-photon transition rates from the ground state of atomic hydrogen to ns excited states have been computed as a function of photon frequencies in the length and velocity gauges in order to test the accuracy of the calculation and to discuss the rate of convergence over the intermediate states. The dramatic structure of the transition rates produced by intermediate-state resonances is exhibited. A two-photon transparency is found in correspondence to each resonance.

Physical Review A•Jun 1, 1982•62 citations
This paper reports a theoretical treatment of the line shape for two-photon transitions. The time-dependent perturbation-theory treatment is equally appropriate for a fast atomic beam interacting with a microwave field in a waveguide, and for laser excitation of a thermal beam. Two important features of the physical systems are successfully incorporated into the theory. First, the amplitude of the external field to which the atoms are exposed varies in time; the envelope function affects the resonance linewidth and power shift. Second, the theory includes the natural decay of the atomic states; the decay amplitude produces a novel "lifetime shift," which displaces the two-photon resonance from its expected location, even in the limit of weak external fields. This paper gives detailed predictions for shifts and other distortions caused by nonidealities of the experimental apparatus used for the measurement of the 32S12\ensuremath−32D523^{2}S_{\frac{1}{2}}\ensuremath{-}3^{2}D_{\frac{5}{2}}32S21​​\ensuremath−32D25​​ transition in atomic hydrogen.
We report observation of the 1S-2S two-photon transition in hydrogen confined in a magnetic trap at submillikelvin temperatures. The excitation spectrum can display a sharp central feature arising from periodic motion of the trapped atoms. The metastable 2S atoms remain trapped, and have a lifetime close to the natural lifetime of 122 ms. These developments open the way to achieving the transition's natural linewidth. We have also demonstrated that the temperature of the gas can be determined from the line shape, providing an important tool for the study of cold trapped hydrogen. The resolution in these experiments appears to be limited by laser stability, currently 3 kHz.
The spontaneous radiative decay to the ground state of an atomic system initially in the higher of two excited states, coupled in a radiationless fashion by an external field, is investigated by the method of multiple-time-scale perturbation theory. The coupled differential equations of motion for the probability amplitudes are solved to second order, while the usual secular behavior of conventional time-dependent perturbation theory is eliminated in terms of two natural time scales: a fast time scale corresponding to the reciprocal of the level transition frequency and a slower time scale associated with the inverse of the radiation linewidth. Expressions are obtained to this order for the energy shifts and decay characteristics of the excited states and the energy distribution of the final-state photons, quantities previously determined by Fourier analysis and contour integration and by the phenomenological approach of Weisskopf and Wigner. A detailed comparison of these various methods of solution includes conditions under which the present results agree to second order with the previous calculations.
The line shape and strength of two-photon absorption in an atomic vapor are studied both theoretically and experimentally for the case of absorption of unequal-frequency photons. Special attention is given to the situation in which the intermediate state is resonant or nearly resonant. It is shown that for the resonant case, maximum absorption rates and Doppler-free spectra are simultaneously obtained. Either counterpropagating or copropagating beams can be used. With counterpropagating beams the two-photon linewidths are quite insensitive to power broadening of the intermediate state. With copropagating beams the two-photon spectra can also reveal the intermediate-state structure with a resolution determined mainly by the intermediate-state lifetime (nearly as well as can be done using any spectroscopic technique). The theoretical analysis provides a closed-form solution for the line shape and strength of the two-photon spectrum. In general the line shape is composed of two features. One is Doppler broadened and predominates when the intermediate state is nonresonant. The second feature is Doppler free, and it predominates with a resonant intermediate state. Detailed comparisons of experimental measurements of the line shape and strength of two-photon absorption in Na vapor are made with the theory and found to be in excellent agreement. Signal strengths for the onresonance case are 6 \ifmmode\times\else\texttimes\fi{} 109{10}^{9}109 larger than the case of equal-frequency photons with no loss in resolution.
We compare the derivation of the dynamic Stark shift of hydrogenic energy levels in a classical framework with an adiabatically damped laser-atom interaction, which is equivalent to the Gell-Mann-Low-Sucher formula, and a treatment based on time-independent perturbation theory, with a second-quantized laser-atom dipole interaction Hamiltonian. Our analysis applies to a laser that excites a two-photon transition in atomic hydrogen or in a hydrogenlike ion with low nuclear charge number. Our comparisons serve to demonstrate why the dynamic Stark shift may be interpreted as a stimulated radiative correction and illustrates connections between the two derivations. The simplest of the derivations is the fully quantized approach. The classical and the second-quantized treatment are shown to be equivalent in the limit of large photon numbers.
We compare the derivation of the dynamic Stark shift of hydrogenic energy levels in a classical framework with an adiabatically damped laser-atom interaction, which is equivalent to the Gell-Mann-Low-Sucher formula, and a treatment based on time-independent perturbation theory, with a second-quantized laser-atom dipole interaction Hamiltonian. Our analysis applies to a laser that excites a two-photon transition in atomic hydrogen or in a hydrogenlike ion with low nuclear charge number. Our comparisons serve to demonstrate why the dynamic Stark shift may be interpreted as a stimulated radiative correction and illustrates connections between the two derivations. The simplest of the derivations is the fully quantized approach. The classical and the second-quantized treatment are shown to be equivalent in the limit of large photon numbers.