We calculate the two-photon $1S\ensuremath{-}2S$ spectrum of an atomic hydrogen Bose-Einstein condensate in the regime where the cold collision frequency shift dominates the line shape. Wentzel-Kramers-Brillouin and static phase approximations are made to find the intensities for transitions from the condensate to motional eigenstates for $2S$ atoms. The excited-state wave functions are found using a mean field potential, which includes the effects of collisions with condensate atoms. Results agree well with experimental data. This formalism can be used to find condensate spectra for a wide range of excitation schemes.We calculate the two-photon $1S\ensuremath{-}2S$ spectrum of an atomic hydrogen Bose-Einstein condensate in the regime where the cold collision frequency shift dominates the line shape. Wentzel-Kramers-Brillouin and static phase approximations are made to find the intensities for transitions from the condensate to motional eigenstates for $2S$ atoms. The excited-state wave functions are found using a mean field potential, which includes the effects of collisions with condensate atoms. Results agree well with experimental data. This formalism can be used to find condensate spectra for a wide range of excitation schemes.

arXiv:physics/9908002Physical Review AFeb 15, 200020 citations

Two-photon absorption of atomic hydrogen from two light beams

J. H. Tung, A. Z. Tang, Greg J. Salamo +1 more

Within the framework of nonrelativistic quantum mechanics, the analysis of the two-photon absorption by atomic hydrogen is generalized to the case of two incident beams with arbitrary direction and polarization (including circular polarization). In the dipole approximation, the second-order matrix elements responsible for two-photon absorption are transformed into a finite sum consisting of the product of a radial part and an angular part. Exact calculation of the angular part predicts that, for the s–s transition only, transparency is obtained regardless of the frequencies of the two beams with perpendicular polarizations. In addition, circularly polarized light is found to be more efficient (up to a factor of 1.5) for the s–d two-photon transition. The radial parts of the matrix elements are accurately evaluated by using the Coulomb Green’s function technique and an implicit technique of Dalgarno and Lewis. Their calculation indicates that “zeros” exist in the two-photon absorption spectrum, thereby predicting that absorption is not possible at certain frequencies. It should be noted that in the calculated spectrum, near or at resonance points, the linewidths of the intermediate levels must be included in order to obtain accurate results.Within the framework of nonrelativistic quantum mechanics, the analysis of the two-photon absorption by atomic hydrogen is generalized to the case of two incident beams with arbitrary direction and polarization (including circular polarization). In the dipole approximation, the second-order matrix elements responsible for two-photon absorption are transformed into a finite sum consisting of the product of a radial part and an angular part. Exact calculation of the angular part predicts that, for the s–s transition only, transparency is obtained regardless of the frequencies of the two beams with perpendicular polarizations. In addition, circularly polarized light is found to be more efficient (up to a factor of 1.5) for the s–d two-photon transition. The radial parts of the matrix elements are accurately evaluated by using the Coulomb Green’s function technique and an implicit technique of Dalgarno and Lewis. Their calculation indicates that “zeros” exist in the two-photon absorption spectrum, thereby predicting that absorption is not possible at certain frequencies. It should be noted that in the calculated spectrum, near or at resonance points, the linewidths of the intermediate levels must be included in order to obtain accurate results.

Journal of the Optical Society of America BJun 1, 198637 citations

Two-photon absorption by atoms perturbed by collisions

Gerard Nienhuis, F. Schuller

Physica B+CJun 1, 19784 citations

On the multiphoton absorption in atomic hydrogen

Yves Gontier, M. Trahin

Physics Letters AOct 1, 197146 citations

Features of the bremsstrahlung accompanying collisions with a hydrogen atom in an excited state

Andrei V. Korol, O. I. Obolensky, А. В. Соловьев

The features of the bremsstrahlung appearing during a collision of a fast charged particle with a hydrogen atom (or hydrogenic ion) in an excited state are investigated. It is shown that the emission spectrum of photons with energies greater than the ionization potential of a given excited state (except the 2 s state) displays narrow lines, which are caused by de-excitation of the atom in an intermediate state. It is demonstrated that the scattering of a charged particle on an excited hydrogen atom produces a feature which is not observed in the case of scattering on a ground-state hydrogen atom. Expressions are obtained for the generalized dynamic polarizability of the hydrogen atom and hydrogenic ions in the 1 s , 2 s , and 3 s states. A method is developed for deriving expressions for the generalized dynamic polarizabilities of other excited states through the use of the Coulomb Green’s function and representation of the electronic wave function in terms of the differentiation of the generating functions of Laguerre polynomials. The bremsstrahlung cross sections for electrons and positrons colliding with hydrogen atoms in the 1 s , 2 s , and 3 s states are calculated.The features of the bremsstrahlung appearing during a collision of a fast charged particle with a hydrogen atom (or hydrogenic ion) in an excited state are investigated. It is shown that the emission spectrum of photons with energies greater than the ionization potential of a given excited state (except the 2 s state) displays narrow lines, which are caused by de-excitation of the atom in an intermediate state. It is demonstrated that the scattering of a charged particle on an excited hydrogen atom produces a feature which is not observed in the case of scattering on a ground-state hydrogen atom. Expressions are obtained for the generalized dynamic polarizability of the hydrogen atom and hydrogenic ions in the 1 s , 2 s , and 3 s states. A method is developed for deriving expressions for the generalized dynamic polarizabilities of other excited states through the use of the Coulomb Green’s function and representation of the electronic wave function in terms of the differentiation of the generating functions of Laguerre polynomials. The bremsstrahlung cross sections for electrons and positrons colliding with hydrogen atoms in the 1 s , 2 s , and 3 s states are calculated.

Technical PhysicsOct 1, 19994 citations

2S

atoms. The excited-state wave functions are found using a mean field potential, which includes the effects of collisions with condensate atoms. Results agree well with experimental data. This formalism can be used to find condensate spectra for a wide range of excitation schemes.