Physical Review A

Double- and Triple-Photon Decay of Metastable P03 Atomic States

Robert William Schmieder

Published May 1, 1973• 29 citations

Abstract

The radiative decay of metastable nsnp $^{3}P_{0}$ atomic states is found to occur only by odd-parity multiphoton modes such as $E1M1$ and $3E1$, in the absence of hyperfine structure. A detailed calculation of the $E1M1$ rates for several members of the Be sequence is presented, in the nonrelativistic approximation. Only the general properties of $3E1$ decay are presented. Among other results, the $3E1$ rate is found to be zero if any two photons have the same energy, and its spectrum, unlike the symmetrical two-photon spectra, is found to be irregular and asymmetric, being peaked somewhat below half the transition energy.

DOI: 10.1103/physreva.7.1458

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Spectroscopic and relaxation character of the P03−H43 transition in La F3 : Pr3+ measured by photon echoes

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Physical review. B, Condensed matterJan 1, 198064 citations

Multiphoton excitation and subsequent ionization detection of metastable atoms: measurement of n^3S–n^3D splittings in He

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Physical Review A

Double- and Triple-Photon Decay of Metastable P03 Atomic States

Robert William Schmieder

Published May 1, 1973• 29 citations

Publisher

Abstract

The radiative decay of metastable nsnp

^{3}P_{0}

atomic states is found to occur only by odd-parity multiphoton modes such as

E1M1

and

3E1

, in the absence of hyperfine structure. A detailed calculation of the

E1M1

rates for several members of the Be sequence is presented, in the nonrelativistic approximation. Only the general properties of

3E1

decay are presented. Among other results, the

3E1

rate is found to be zero if any two photons have the same energy, and its spectrum, unlike the symmetrical two-photon spectra, is found to be irregular and asymmetric, being peaked somewhat below half the transition energy.

DOI: 10.1103/physreva.7.1458

Related papers

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.

Physical Review ASep 1, 198472 citations

Hyperfine quenching of the metastable P0,23 states in divalent atoms

S. G. Porsev, Andrei Derevianko

Hyperfine quenching rates of the lowest-energy metastable $^{3}P_{0}$ and $^{3}P_{2}$ states of Mg, Ca, Sr, and Yb atoms are computed. The calculations are carried out using ab initio relativistic many-body methods. The computed lifetimes may be useful for designing novel ultraprecise optical clocks and trapping experiments with the $^{3}P_{2}$ fermionic isotopes. The resulting natural widths of the $^{3}P_{0}\ensuremath{-}^{1}S_{0}$ clock transition are $0.44\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{25}\mathrm{Mg}$ , $2.2\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{43}\mathrm{Ca}$ , $7.6\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{87}\mathrm{Sr}$ , $43.5\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{171}\mathrm{Yb}$ , and $38.5\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{173}\mathrm{Yb}$ . Compared to the bosonic isotopes, the lifetime of the $^{3}P_{2}$ states in fermionic isotopes is noticeably shortened by the hyperfine quenching but still remains long enough for trapping experiments.Hyperfine quenching rates of the lowest-energy metastable $^{3}P_{0}$ and $^{3}P_{2}$ states of Mg, Ca, Sr, and Yb atoms are computed. The calculations are carried out using ab initio relativistic many-body methods. The computed lifetimes may be useful for designing novel ultraprecise optical clocks and trapping experiments with the $^{3}P_{2}$ fermionic isotopes. The resulting natural widths of the $^{3}P_{0}\ensuremath{-}^{1}S_{0}$ clock transition are $0.44\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{25}\mathrm{Mg}$, $2.2\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{43}\mathrm{Ca}$, $7.6\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{87}\mathrm{Sr}$, $43.5\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{171}\mathrm{Yb}$, and $38.5\phantom{\rule{0.3em}{0ex}}\text{mHz}$ for $^{173}\mathrm{Yb}$. Compared to the bosonic isotopes, the lifetime of the $^{3}P_{2}$ states in fermionic isotopes is noticeably shortened by the hyperfine quenching but still remains long enough for trapping experiments.

arXiv:physics/0312006Physical Review AApr 7, 2004117 citations

Two-photon Decay of Singlet Metastable Helium

A. Dalgarno, David Robert Bates

The probability of two-photon decay of helium in the 21S metastable level is calculated to be 46 s−1. The intensity distribution of the two-photon continuum is obtained.

Monthly Notices of the Royal Astronomical SocietyJan 1, 196639 citations

The two-photon decay of metastable atomic hydrogen

D O'Connell, K J Kollath, Alan J. Duncan +1 more

Journal of Physics B Atomic and Molecular PhysicsAug 1, 197534 citations

Spectroscopic and relaxation character of the P03−H43 transition in La F3 : Pr3+ measured by photon echoes

Y.C. Chen, Kophu P. Chiang, Sven R. Hartmann

The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La ${\mathrm{F}}_{3}$ : ${\mathrm{Pr}}^{3+}$ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of ${10}^{5}$ and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the $^{3}P_{0}$ and $^{3}H_{4}$ states. In the $^{3}P_{0}(^{3}H_{4})$ state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the $^{3}H_{4}$ state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of ${10}^{5}$ and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the $^{3}P_{0}$ and $^{3}H_{4}$ states. In the $^{3}P_{0}(^{3}H_{4})$ state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the $^{3}H_{4}$ state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.

Physical review. B, Condensed matterJan 1, 198064 citations

Multiphoton excitation and subsequent ionization detection of metastable atoms: measurement of n^3S–n^3D splittings in He

R. L. Panock, Richard R. Freeman, J. C. White +1 more

Optics LettersApr 1, 19807 citations

The radiative decay of metastable nsnp

^{3}P_{0}

atomic states is found to occur only by odd-parity multiphoton modes such as

E1M1

and

3E1

, in the absence of hyperfine structure. A detailed calculation of the

E1M1

rates for several members of the Be sequence is presented, in the nonrelativistic approximation. Only the general properties of

3E1

decay are presented. Among other results, the

3E1

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.

Hyperfine quenching rates of the lowest-energy metastable

^{3}P_{0}

and

^{3}P_{2}

states of Mg, Ca, Sr, and Yb atoms are computed. The calculations are carried out using ab initio relativistic many-body methods. The computed lifetimes may be useful for designing novel ultraprecise optical clocks and trapping experiments with the

^{3}P_{2}

fermionic isotopes. The resulting natural widths of the $^{3}P_{0}\ensuremath{-}^{1}S_{0}$ clock transition are

0.44\phantom{\rule{0.3em}{0ex}}\text{mHz}

for

^{25}\mathrm{Mg}

2.2\phantom{\rule{0.3em}{0ex}}\text{mHz}

for

^{43}\mathrm{Ca}

7.6\phantom{\rule{0.3em}{0ex}}\text{mHz}

for

^{87}\mathrm{Sr}

43.5\phantom{\rule{0.3em}{0ex}}\text{mHz}

for

^{171}\mathrm{Yb}

, and

38.5\phantom{\rule{0.3em}{0ex}}\text{mHz}

for

^{173}\mathrm{Yb}

. Compared to the bosonic isotopes, the lifetime of the

^{3}P_{2}

states in fermionic isotopes is noticeably shortened by the hyperfine quenching but still remains long enough for trapping experiments.

The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La

{\mathrm{F}}_{3}

{\mathrm{Pr}}^{3+}

(0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of

{10}^{5}

and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the

^{3}P_{0}

and

^{3}H_{4}

states. In the

^{3}P_{0}(^{3}H_{4})

state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the

^{3}H_{4}

state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.