Physical Review A

Lifetime of excited atomic states

James D. Cresser, A. Z. Tang, Greg J. Salamo, F. T. Chan

Published Mar 1, 1986• 26 citations

Abstract

In this paper we derive an expression for the lifetime of excited atomic states taking account of contributions due to nonresonant two-photon transitions. Explicit integration of the two-photon emission spectrum is not required. The results are applied to the case of the hydrogen atom.

DOI: 10.1103/physreva.33.1677

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Comment on ‘‘Lifetime of excited atomic states’’

Viorica Florescu, I. F. Schneider, Ion Nicolae Mihailescu

We show that the two-photon nonresonant contribution to the lifetime of excited 3s and 3d states of hydrogen, as given by a formula recently derived by Cresser et al. [Phys. Rev. A 33, 1677 (1986)], can be evaluated in an economic way using the analytic expressions of the amplitudes of 3s-1s and 3d-1s two-photon transitions. Our numerical evaluation confirms the numbers given by Cresser et al.

Physical Review AAug 1, 198816 citations

Two-photon decay of hydrogenic atoms

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Nonresonant effects in one- and two-photon transitions

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Role of symmetric and antisymmetric states in spontaneous emission by two initially excited atoms

Kikuo Ujihara

An analysis for investigation of the role of symmetric and antisymmetric states in cooperative spontaneous emission by two initially excited atoms is presented taking into account the finite photon transit time between the atoms. The iterative calculation can go beyond the Markov approximation.

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Spectral profiles of certain atomic lines

Rosemary Beatrice Higgins

Jan 1, 19740 citations

Physical Review A

Lifetime of excited atomic states

James D. Cresser, A. Z. Tang, Greg J. Salamo, F. T. Chan

Published Mar 1, 1986• 26 citations

Publisher

Abstract

DOI: 10.1103/physreva.33.1677

Related papers

Comment on ‘‘Lifetime of excited atomic states’’

Viorica Florescu, I. F. Schneider, Ion Nicolae Mihailescu

Physical Review AAug 1, 198816 citations

Two-photon decay of hydrogenic atoms

J. H. Tung, X. M. Salamo, F. T. Chan

The two-photon decay mode of hydrogenic atoms from an arbitrary state ( ${n}_{1}$ , ${l}_{1}$ , ${m}_{1}$ ) to an arbitrary state ( ${n}_{2}$ , ${l}_{2}$ , ${m}_{2}$ ) is studied within the framework of nonrelativistic quantum mechanics. In the dipole approximation, these decay rates, which involve infinite summation over intermediate states, are derived exactly via a general second-order matrix element obtained by Kelsey and Macek and an implicit technique introduced by Dalgarno and Lewis. The results are expressed in terms of hypergeometric functions. For transitions ${n}_{1}s\ensuremath{\rightarrow}{n}_{2}s$, our results reduce to those of Klarsfeld whose starting point is the Coulomb Green's function. For transitions to the ground state, an alternative expression involving a simple one-dimensional integral is presented. The decay rate of the $2s$ metastable state of atomic hydrogen is calculated as an illustration of the method. The result, $\frac{1}{\ensuremath{\tau}}=8.2284$ ${\mathrm{sec}}^{\ensuremath{-}1}$, agrees with Klarsfeld. For transitions of ${n}_{1}s\ensuremath{\rightarrow}1s$ and ${n}_{1}d\ensuremath{\rightarrow}1s ({n}_{1}\ensuremath{\ge}3)$, the transition rates exhibit interesting and unexpected structures. In particular, "zeros" are found in the two-photon emission spectrum indicating that two-photon emission is not possible at certain frequencies. Physically, these "zeros" are the result of destructive interference between the radiating dipole terms associated with the sum over intermediate states. In addition to the emission spectrum the expected coincidence signal between two detectors monitoring the two photons simultaneously emitted during a two-photon transition is calculated as a function of the angle between the detectors. The angular distribution for the ${n}_{1}d\ensuremath{\rightarrow}1s$ transitions is shown to be significantly different from the ${n}_{1}s\ensuremath{\rightarrow}1s$ transitions. Finally, a possible experiment is suggested to test the results presented in this paper.The two-photon decay mode of hydrogenic atoms from an arbitrary state (${n}_{1}$, ${l}_{1}$, ${m}_{1}$) to an arbitrary state (${n}_{2}$, ${l}_{2}$, ${m}_{2}$) is studied within the framework of nonrelativistic quantum mechanics. In the dipole approximation, these decay rates, which involve infinite summation over intermediate states, are derived exactly via a general second-order matrix element obtained by Kelsey and Macek and an implicit technique introduced by Dalgarno and Lewis. The results are expressed in terms of hypergeometric functions. For transitions ${n}_{1}s\ensuremath{\rightarrow}{n}_{2}s$, our results reduce to those of Klarsfeld whose starting point is the Coulomb Green's function. For transitions to the ground state, an alternative expression involving a simple one-dimensional integral is presented. The decay rate of the $2s$ metastable state of atomic hydrogen is calculated as an illustration of the method. The result, $\frac{1}{\ensuremath{\tau}}=8.2284$ ${\mathrm{sec}}^{\ensuremath{-}1}$, agrees with Klarsfeld. For transitions of ${n}_{1}s\ensuremath{\rightarrow}1s$ and ${n}_{1}d\ensuremath{\rightarrow}1s ({n}_{1}\ensuremath{\ge}3)$, the transition rates exhibit interesting and unexpected structures. In particular, "zeros" are found in the two-photon emission spectrum indicating that two-photon emission is not possible at certain frequencies. Physically, these "zeros" are the result of destructive interference between the radiating dipole terms associated with the sum over intermediate states. In addition to the emission spectrum the expected coincidence signal between two detectors monitoring the two photons simultaneously emitted during a two-photon transition is calculated as a function of the angle between the detectors. The angular distribution for the ${n}_{1}d\ensuremath{\rightarrow}1s$ transitions is shown to be significantly different from the ${n}_{1}s\ensuremath{\rightarrow}1s$ transitions. Finally, a possible experiment is suggested to test the results presented in this paper.

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Multiphoton Processes in a Hydrogen Atom

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Within the framework of time-dependent perturbation theory, general expressions are derived for the cross section of multiphoton processes induced by radiation acting on a hydrogen atom. Bound-bound transitions involving emission of a single quantum and bound-free transitions are calculated for a wide range of photon energies. In the case of resonance, the transition probability is also discussed. The procedure used to evaluate the sums over intermediate states is described. The numerical computation allows one to compare the results obtained for various competing processes.Within the framework of time-dependent perturbation theory, general expressions are derived for the cross section of multiphoton processes induced by radiation acting on a hydrogen atom. Bound-bound transitions involving emission of a single quantum and bound-free transitions are calculated for a wide range of photon energies. In the case of resonance, the transition probability is also discussed. The procedure used to evaluate the sums over intermediate states is described. The numerical computation allows one to compare the results obtained for various competing processes.

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Nonresonant effects in one- and two-photon transitions

Ulrich D. Jentschura, Peter J. Mohr

We investigate nonresonant contributions to resonant Rayleigh-scattering cross sections of atoms. The problematic nonresonant contributions set a limit to the accuracy to which atomic spectra determine energy levels. We discuss the off-resonance effects in one-photon transitions. We also show that off-resonance contributions for the 1S2S two-photon transition in atomic hydrogen are negligible at current and projected levels of experimental accuracy. The possibility of a differential measurement for the detection of off-resonance effects in one-photon transitions in atomic hydrogen is discussed. PACS Nos.: 31.15-p, 12.20DsWe investigate nonresonant contributions to resonant Rayleigh-scattering cross sections of atoms. The problematic nonresonant contributions set a limit to the accuracy to which atomic spectra determine energy levels. We discuss the off-resonance effects in one-photon transitions. We also show that off-resonance contributions for the 1S2S two-photon transition in atomic hydrogen are negligible at current and projected levels of experimental accuracy. The possibility of a differential measurement for the detection of off-resonance effects in one-photon transitions in atomic hydrogen is discussed. PACS Nos.: 31.15-p, 12.20Ds

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Role of symmetric and antisymmetric states in spontaneous emission by two initially excited atoms

Kikuo Ujihara

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Spectral profiles of certain atomic lines

Rosemary Beatrice Higgins

Several calculations have been carried out using the transition operator technique. The radiative decay in a two-level quantum system with excited state coupled by an external perturbation has been investigated and an expression obtained for P(t), the probability of finding the atom in its excited state at time t. This is seen to possess a steady value for yt >> 1 and a third term which decays at nearly half the rate of its second. Next radiative decay of an atom with two close-lying excited states is considered and |bq| 2 , the spectral density for spontaneous emission from the uppermost level, calculated. This shows that the proximity of the upper two levels makes the line-shape non-Lorentxian. Heisenberg equations of motion were then derived for the transitions operators of an ℓ-level atom undergoing radiative decay, the possibility of overlapping pairs of levels being ignored. These master equations were then used to obtain the spectral profiles of certain atomic lines, employing the so-far avoided Markoff approximation. First the spectral density of the scattered radiation was found for transitions between levels 5P3/2 and 4S (ground state), and 6S and 5P 3/2, in the potassium atom when driving fields of arbitrary strength coupled levels 6S and 4P3/2, and 4P 3/2 and 4S. Triple-peaked profiles were obtained. Spectral profiles for emission were then derived for transitions between levels 3P and (ground state), and 3P and in the hydrogen atom when a driving field of arbitrary strength coupled levels The former profile was double the latter quadruple-peaked. Lastly master equations were derived for an atom, with two excited levels undergoing radiative decay, when allowance was made for thepossibility of their overlapping. A driving field of arbitrary magnitude coupled the uppermost and ground states. The spectrum for the scattered light resulting from transitions between the uppermost and ground state was found and graphs computed for various field strengths and separations of the excited states.Several calculations have been carried out using the transition operator technique. The radiative decay in a two-level quantum system with excited state coupled by an external perturbation has been investigated and an expression obtained for P(t), the probability of finding the atom in its excited state at time t. This is seen to possess a steady value for yt >> 1 and a third term which decays at nearly half the rate of its second. Next radiative decay of an atom with two close-lying excited states is considered and |bq| 2 , the spectral density for spontaneous emission from the uppermost level, calculated. This shows that the proximity of the upper two levels makes the line-shape non-Lorentxian. Heisenberg equations of motion were then derived for the transitions operators of an ℓ-level atom undergoing radiative decay, the possibility of overlapping pairs of levels being ignored. These master equations were then used to obtain the spectral profiles of certain atomic lines, employing the so-far avoided Markoff approximation. First the spectral density of the scattered radiation was found for transitions between levels 5P3/2 and 4S (ground state), and 6S and 5P 3/2, in the potassium atom when driving fields of arbitrary strength coupled levels 6S and 4P3/2, and 4P 3/2 and 4S. Triple-peaked profiles were obtained. Spectral profiles for emission were then derived for transitions between levels 3P and (ground state), and 3P and in the hydrogen atom when a driving field of arbitrary strength coupled levels The former profile was double the latter quadruple-peaked. Lastly master equations were derived for an atom, with two excited levels undergoing radiative decay, when allowance was made for thepossibility of their overlapping. A driving field of arbitrary magnitude coupled the uppermost and ground states. The spectrum for the scattered light resulting from transitions between the uppermost and ground state was found and graphs computed for various field strengths and separations of the excited states.

Jan 1, 19740 citations

The two-photon decay mode of hydrogenic atoms from an arbitrary state (

{n}_{1}

{l}_{1}

{m}_{1}

) to an arbitrary state (

{n}_{2}

{l}_{2}

{m}_{2}

) is studied within the framework of nonrelativistic quantum mechanics. In the dipole approximation, these decay rates, which involve infinite summation over intermediate states, are derived exactly via a general second-order matrix element obtained by Kelsey and Macek and an implicit technique introduced by Dalgarno and Lewis. The results are expressed in terms of hypergeometric functions. For transitions ${n}_{1}s\ensuremath{\rightarrow}{n}_{2}s$, our results reduce to those of Klarsfeld whose starting point is the Coulomb Green's function. For transitions to the ground state, an alternative expression involving a simple one-dimensional integral is presented. The decay rate of the

2s

metastable state of atomic hydrogen is calculated as an illustration of the method. The result, $\frac{1}{\ensuremath{\tau}}=8.2284$ ${\mathrm{sec}}^{\ensuremath{-}1}$, agrees with Klarsfeld. For transitions of ${n}_{1}s\ensuremath{\rightarrow}1s$ and ${n}_{1}d\ensuremath{\rightarrow}1s ({n}_{1}\ensuremath{\ge}3)$, the transition rates exhibit interesting and unexpected structures. In particular, "zeros" are found in the two-photon emission spectrum indicating that two-photon emission is not possible at certain frequencies. Physically, these "zeros" are the result of destructive interference between the radiating dipole terms associated with the sum over intermediate states. In addition to the emission spectrum the expected coincidence signal between two detectors monitoring the two photons simultaneously emitted during a two-photon transition is calculated as a function of the angle between the detectors. The angular distribution for the ${n}_{1}d\ensuremath{\rightarrow}1s$ transitions is shown to be significantly different from the ${n}_{1}s\ensuremath{\rightarrow}1s$ transitions. Finally, a possible experiment is suggested to test the results presented in this paper.