We present a theory of cascade emission from an array of $N$ fixed, ``three-level'' atoms. The total angular momentum of the ground state of each atom is $J=0$ , that of the intermediate state is $J=1$ , and that of the upper state is $J=0$ . The atoms are prepared in a spatially phased superposition of their ground and upper states, collectively sharing a single excitation. We calculate the time-integrated, joint probability distribution for radiation to be emitted in a given direction with a given polarization on each transition and use this joint probability distribution to calculate the time-integrated intensity emitted on each transition. The dipole-dipole interaction between the atoms is taken into account. Analytic expressions are obtained for two atoms and the calculation is then extended formally to an ensemble of $N$ atoms at arbitrary positions. As expected, the radiation emitted on the upper transition is unpolarized and isotropic. However, somewhat surprisingly, we find that for excitation by counterpropagating fields and for nearly equal ground to intermediate and intermediate to upper level transition frequencies, the radiation on the lower transition is also isotropic and unpolarized, provided the atoms are prepared in a fully symmetric state. We also establish conditions for which there can be a phase-matched enhancement of the joint probability density for specific directions of emissions on the upper and lower transitions.We present a theory of cascade emission from an array of $N$ fixed, ``three-level'' atoms. The total angular momentum of the ground state of each atom is $J=0$, that of the intermediate state is $J=1$, and that of the upper state is $J=0$. The atoms are prepared in a spatially phased superposition of their ground and upper states, collectively sharing a single excitation. We calculate the time-integrated, joint probability distribution for radiation to be emitted in a given direction with a given polarization on each transition and use this joint probability distribution to calculate the time-integrated intensity emitted on each transition. The dipole-dipole interaction between the atoms is taken into account. Analytic expressions are obtained for two atoms and the calculation is then extended formally to an ensemble of $N$ atoms at arbitrary positions. As expected, the radiation emitted on the upper transition is unpolarized and isotropic. However, somewhat surprisingly, we find that for excitation by counterpropagating fields and for nearly equal ground to intermediate and intermediate to upper level transition frequencies, the radiation on the lower transition is also isotropic and unpolarized, provided the atoms are prepared in a fully symmetric state. We also establish conditions for which there can be a phase-matched enhancement of the joint probability density for specific directions of emissions on the upper and lower transitions.

Physical Review AMay 16, 20241 citation

Polarization effects in atomic transitions

Valery Alexandrovich Astapenko, L. A. Bureeva, Valerii S. Lisitsa

Uspekhi Fizicheskih NaukJan 1, 200215 citations

Continuum level-shift effects in the theory of multiphoton transitions

Leonard Rosenberg

A successive-approximation procedure for calculating multiphoton-transition amplitudes is presented. The theory, designed for use in the strong-field domain where ordinary perturbative methods are unsuitable, provides an extension of previous work along these lines by inclusion of the effects of free-free transitions, i.e., interactions with the field which take the atomic system from one continuum state to another. This approach is based on the introduction of an effective Hamiltonian which operates only in the subspace of states, degenerate or nearly degenerate, among which real transitions can take place. Contributions from virtual intermediate states are included in the structure of the effective potential. This approach provides the framework for the construction of models, defined by the approximations made for the effective potential, which build in the constraints of unitarity and which properly account for the effects of intermediate-state resonances. The present work is focussed on those new features of the problem which arise from the fact that both the electron and the residual atom to which it was originally bound can interact with the field in asymptotic states. To avoid complications associated with long-ranged Coulomb effects, the residual atom is assumed to be neutral. (The initial state is a negative ion.) An approximation procedure is described for calculating the field-modified asymptotic states appropriate for such a system. By way of an illustrative example a low-frequency approximation is given which leads to considerable simplification of the calculational procedure.A successive-approximation procedure for calculating multiphoton-transition amplitudes is presented. The theory, designed for use in the strong-field domain where ordinary perturbative methods are unsuitable, provides an extension of previous work along these lines by inclusion of the effects of free-free transitions, i.e., interactions with the field which take the atomic system from one continuum state to another. This approach is based on the introduction of an effective Hamiltonian which operates only in the subspace of states, degenerate or nearly degenerate, among which real transitions can take place. Contributions from virtual intermediate states are included in the structure of the effective potential. This approach provides the framework for the construction of models, defined by the approximations made for the effective potential, which build in the constraints of unitarity and which properly account for the effects of intermediate-state resonances. The present work is focussed on those new features of the problem which arise from the fact that both the electron and the residual atom to which it was originally bound can interact with the field in asymptotic states. To avoid complications associated with long-ranged Coulomb effects, the residual atom is assumed to be neutral. (The initial state is a negative ion.) An approximation procedure is described for calculating the field-modified asymptotic states appropriate for such a system. By way of an illustrative example a low-frequency approximation is given which leads to considerable simplification of the calculational procedure.

Physical Review ADec 1, 19786 citations

Advances in the Measurement of Atomic Transition Probabilities

Thomas R. O’Brian

Jan 1, 19910 citations

A new experimental technique for measuring atomic transition probabilities

J. L. Kohl

Physics Letters AJan 1, 196711 citations

Polarization of the fluorescent light of Ne atoms interacting with a laser beam measurement of several relaxation times

Bernard Decomps, M. Dumont

The fluorescent light from two atomic levels is studied assuming that the atoms are subjected to a gas discharge, to a static magnetic field, and, simultaneously, to a laser beam having the transition frequency between the atomic levels. Calculations are developed in the formalism of irreducible tensor operators. One takes into account the existence of isotropic relaxations and cascade effects due to spontaneous emission between the upper and the lower levels. Following Lamb, the laser beam is described classically by its electric field, and its effects are calculated by perturbation theory. It is predicted that the σ component of fluorescent light exhibits the Hanle effect, which allows one to measure the relaxation rates\Gamma(0)and\Gamma(2)of the population and of the alignment of the emitting level, respectively. Experimental agreement with the theoretical analysis has been found for the3s_{2}, 2s_{2}, and2P_{4}levels of Ne. Among the experimental results obtained by this method are the natural widths and the collision cross sections for population (quenching collision) and for alignment. Several transition probabilities are also derived. Furthermore, the theory of coherent imprisonment of the fluorescent line has been found valid even if laser pumping light is used.The fluorescent light from two atomic levels is studied assuming that the atoms are subjected to a gas discharge, to a static magnetic field, and, simultaneously, to a laser beam having the transition frequency between the atomic levels. Calculations are developed in the formalism of irreducible tensor operators. One takes into account the existence of isotropic relaxations and cascade effects due to spontaneous emission between the upper and the lower levels. Following Lamb, the laser beam is described classically by its electric field, and its effects are calculated by perturbation theory. It is predicted that the σ component of fluorescent light exhibits the Hanle effect, which allows one to measure the relaxation rates\Gamma(0)and\Gamma(2)of the population and of the alignment of the emitting level, respectively. Experimental agreement with the theoretical analysis has been found for the3s_{2}, 2s_{2}, and2P_{4}levels of Ne. Among the experimental results obtained by this method are the natural widths and the collision cross sections for population (quenching collision) and for alignment. Several transition probabilities are also derived. Furthermore, the theory of coherent imprisonment of the fluorescent line has been found valid even if laser pumping light is used.

IEEE Journal of Quantum ElectronicsNov 1, 196845 citations

We present a theory of cascade emission from an array of

N

fixed, ``three-level'' atoms. The total angular momentum of the ground state of each atom is

J=0

, that of the intermediate state is

J=1

, and that of the upper state is

J=0

. The atoms are prepared in a spatially phased superposition of their ground and upper states, collectively sharing a single excitation. We calculate the time-integrated, joint probability distribution for radiation to be emitted in a given direction with a given polarization on each transition and use this joint probability distribution to calculate the time-integrated intensity emitted on each transition. The dipole-dipole interaction between the atoms is taken into account. Analytic expressions are obtained for two atoms and the calculation is then extended formally to an ensemble of

N

atoms at arbitrary positions. As expected, the radiation emitted on the upper transition is unpolarized and isotropic. However, somewhat surprisingly, we find that for excitation by counterpropagating fields and for nearly equal ground to intermediate and intermediate to upper level transition frequencies, the radiation on the lower transition is also isotropic and unpolarized, provided the atoms are prepared in a fully symmetric state. We also establish conditions for which there can be a phase-matched enhancement of the joint probability density for specific directions of emissions on the upper and lower transitions.