Spontaneous two-photon transitions in hydrogen and helium

The collective decay effects between the dipole-active three-level subsystems in the nonlinear interaction with dipole-forbidden transitions, like 2 S − 1 S of hydrogen-like radiators, are proposed, taking into consideration the cooperative exchanges between two species of atoms through the vacuum field in the scattering and the two-photon resonance processes. One of them corresponds to the situation when the total energy of the emitted two photons by the three-level radiator in the cascade configuration enters into the two-photon resonance with another type of dipole-forbidden transitions of hydrogen-like (or helium-like) atoms. The similar situation appears in the cooperative scattering between two species of quantum emitters when the difference of the excited energies of the two dipole-active transitions of the three-level radiators is in the resonance with the dipole-forbidden transitions of the Hydrogen-like radiators. These effects are accompanied by the interference between single- and two-quantum collective transitions of the inverted radiators from the ensemble. The two-particle collective decay rate is defined in the description of the atomic correlation functions taking into consideration the phase retardation between them. The kinetic equations which describe the cooperative processes as the function of time and correlation are obtained. The behavior of the system of radiators at short and long time intervals in comparison with the retardation time between them is studied.The collective decay effects between the dipole-active three-level subsystems in the nonlinear interaction with dipole-forbidden transitions, like 2 S − 1 S of hydrogen-like radiators, are proposed, taking into consideration the cooperative exchanges between two species of atoms through the vacuum field in the scattering and the two-photon resonance processes. One of them corresponds to the situation when the total energy of the emitted two photons by the three-level radiator in the cascade configuration enters into the two-photon resonance with another type of dipole-forbidden transitions of hydrogen-like (or helium-like) atoms. The similar situation appears in the cooperative scattering between two species of quantum emitters when the difference of the excited energies of the two dipole-active transitions of the three-level radiators is in the resonance with the dipole-forbidden transitions of the Hydrogen-like radiators. These effects are accompanied by the interference between single- and two-quantum collective transitions of the inverted radiators from the ensemble. The two-particle collective decay rate is defined in the description of the atomic correlation functions taking into consideration the phase retardation between them. The kinetic equations which describe the cooperative processes as the function of time and correlation are obtained. The behavior of the system of radiators at short and long time intervals in comparison with the retardation time between them is studied.

IntechOpen eBooksMay 16, 20190 citations

Two-photon transitions to Rydberg states of hydrogen

Rachna Joshi

Physics Letters ASep 30, 20067 citations

Magnetic-field-enhanced spontaneous two-photon emission of hydrogenic atoms

P. C. Stancil, G. E. Copeland

Two-photon transitions for hydrogen and hydrogenlike ions in arbitrary magnetic fields are investigated using currently available nonrelativistic energy levels and one-photon dipole transition probabilities. For hydrogen, the 2s-1s two-photon spontaneous-decay rate is shown to increase rapidly with the strength of the applied field from its field-free value of 8.2284 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ to a maximum of 1.537\ifmmode\times\else\texttimes\fi{} ${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 1.41\ifmmode\times\else\texttimes\fi{} ${10}^{6}$ T, approaching that of the 2p-1s one-photon rate, and to drop slightly to 1.055\ifmmode\times\else\texttimes\fi{} ${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 4.7\ifmmode\times\else\texttimes\fi{} ${10}^{8}$ T. The transition rate is shown to scale as ${\mathit{Z}}^{4}$ for hydrogenic ions with nuclear charge Z in fields \ensuremath{\ge}3300 ${\mathit{Z}}^{2}$ T. The spectral distribution of the photons for the 2s-1s transition in a large field reveals interesting features including resonances due to migration of the 2 ${\mathit{p}}_{0}$ and 2${\mathit{p}}_{\mathrm{\ensuremath{-}}1}$ energy levels between the 1s and 2s levels and the appearance of minima resulting from destructive interference between the intermediate-state dipole terms. In the field-free case, these spectral features are only present for high-lying-state transitions, i.e., 3s-1s, 4s-1s, etc.Two-photon transitions for hydrogen and hydrogenlike ions in arbitrary magnetic fields are investigated using currently available nonrelativistic energy levels and one-photon dipole transition probabilities. For hydrogen, the 2s-1s two-photon spontaneous-decay rate is shown to increase rapidly with the strength of the applied field from its field-free value of 8.2284 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ to a maximum of 1.537\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 1.41\ifmmode\times\else\texttimes\fi{}${10}^{6}$ T, approaching that of the 2p-1s one-photon rate, and to drop slightly to 1.055\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 4.7\ifmmode\times\else\texttimes\fi{}${10}^{8}$ T. The transition rate is shown to scale as ${\mathit{Z}}^{4}$ for hydrogenic ions with nuclear charge Z in fields \ensuremath{\ge}3300${\mathit{Z}}^{2}$ T. The spectral distribution of the photons for the 2s-1s transition in a large field reveals interesting features including resonances due to migration of the 2${\mathit{p}}_{0}$ and 2${\mathit{p}}_{\mathrm{\ensuremath{-}}1}$ energy levels between the 1s and 2s levels and the appearance of minima resulting from destructive interference between the intermediate-state dipole terms. In the field-free case, these spectral features are only present for high-lying-state transitions, i.e., 3s-1s, 4s-1s, etc.

Physical Review AJul 1, 19938 citations

Two-photon spectroscopy in helium (A)

W. M. Fairbank, L. Hlousek, GEORGE J. COLLINS

Journal of the Optical Society of America AOct 1, 19780 citations

{10}^{8}

${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 1.41\ifmmode\times\else\texttimes\fi{}

{10}^{6}

T, approaching that of the 2p-1s one-photon rate, and to drop slightly to 1.055\ifmmode\times\else\texttimes\fi{}

{10}^{8}

${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 4.7\ifmmode\times\else\texttimes\fi{}

{10}^{8}

T. The transition rate is shown to scale as

{\mathit{Z}}^{4}

for hydrogenic ions with nuclear charge Z in fields \ensuremath{\ge}3300

{\mathit{Z}}^{2}

T. The spectral distribution of the photons for the 2s-1s transition in a large field reveals interesting features including resonances due to migration of the 2

{\mathit{p}}_{0}

and 2${\mathit{p}}_{\mathrm{\ensuremath{-}}1}$ energy levels between the 1s and 2s levels and the appearance of minima resulting from destructive interference between the intermediate-state dipole terms. In the field-free case, these spectral features are only present for high-lying-state transitions, i.e., 3s-1s, 4s-1s, etc.